Patent Publication Number: US-2023134841-A1

Title: Triaxial Magnetic Field Correction Coil, Physics Package, Physics Package for Optical Lattice Clock, Physics Package for Atomic Clock, Physics Package for Atom Interferometer, Physics Package for Quantum Information Processing Device, and Physics Package System

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is the United States national phase of International Application No. PCT/JP2021/013473 filed Mar. 30, 2021, and claims priority to Japanese Patent Application No. 2020-065311 filed Mar. 31, 2020, the disclosures of which are hereby incorporated by reference in their entirety. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a triaxial magnetic field correction coil, a physics package, a physics package for an optical lattice clock, a physics package for an atomic clock, a physics package for an atom interferometer, a physics package for a quantum information processing device, and a physics package system. 
     Description of Related Art 
     Optical lattice clocks are atomic clocks proposed by KATORI Hidetoshi, who is one of the inventors of the present application. An optical lattice clock confines an atom population in an optical lattice formed by laser light, and measures the resonant frequency in a visible light range. Accordingly, optical lattice clocks can achieve 18-digit accuracy measurement, which surpasses the accuracies of current cesium clocks. Optical lattice clocks have been eagerly researched and developed not only by the group including the inventors but also by various groups inside and outside of this country, and have been developed as next-generation atomic clocks. 
     The latest technology of optical lattice clocks is described in the following Patent Documents 1 to 3, for example. Patent Document 1 describes that a one-dimensional moving optical lattice is formed in an optical waveguide having a hollow pathway. Patent Document 2 describes an aspect of setting an effective magic frequency. Patent Document 3 describes a radiation shield that reduces adverse effects of blackbody radiation emitted from surrounding walls. 
     The optical lattice clock measures time with high accuracy. Accordingly, the optical lattice clock can detect an elevation difference of 1 cm on the Earth based on the general relativistic effect due to the gravity, as a deviation in temporal progress. Accordingly, if the optical lattice clock is made transportable and usable in a field outside of a laboratory, it would be applicable to new geodetic technologies, such as underground resource exploration, and detection of underground cavities and magma chambers. Optical lattice clocks are mass-produced, and installed at many locations, and temporal variation in gravitational potential is continuously monitored, which allows applications that include detection of diastrophism, and spatial mapping of the gravitational field. Thus, optical lattice clocks are expected to contribute to society as a new fundamental technology beyond the bounds of highly accurate time measurement. 
     The following Non Patent Documents 1 to 5 describe attempts to make optical lattice clocks transportable. For example, Non Patent Document 4 describes a physics package of an optical lattice clock stored in a frame having a length of 99 cm, a width of 60 cm, and a height of 45 cm. In the physics package, an atomic oven, a Zeeman slower, and a vacuum chamber are arranged sequentially in the length direction. Outside of the vacuum chamber there are arranged a pair of square magnetic field correction coils measuring about 30 to 40 cm on a side, for each of three axes, in the length direction, the width direction, and the height direction. For the sake of clock transition spectroscopy of atoms in a zero magnetic field, the magnetic field correction coils are used to compensate the magnetic field distribution in an area around the atoms during spectrometry. 
     CITATION LIST 
     Patent Literature 
     
         
         Patent Document 1: JP 6206973 B 
         Patent Literature 2: JP 2018-510494 A 
         Patent Document 3: JP 2019-129166 A 
       
    
     Non Patent Literature 
     
         
         Non Patent Document 1: Stefan Vogt et al. “A transportable optical lattice clock” Journal of Physics: Conference Series 723 012020, 2016 
         Non Patent Document 2: S. B. Koller et al. “Transportable Optical Lattice Clock with 7×10-17 Uncertainty” Physical review letters 118 073601, 2017 
         Non Patent Document 3: William Bowden et al. “A Pyramid MOT with Integrated Optical Cavities as a Cold Atom Platform for an Optical Lattice Clock” Scientific Reports 9 11704, 2019 
         Non Patent Document 4: S. Origlia et al. “Towards an Optical Clock for Space: Compact, High-Performance Optical Lattice Clock based on Bosonic Atoms” Physical Review A 98, 053443, 2018 
         Non Patent Document 5: N. Poli et al. “Prospect for a Compact Strontium Optical Lattice Clock” Proceedings of SPIE 6673, 2007 
       
    
     The optical lattice clocks described in the aforementioned Non Patent Documents 1 to 5 have room for further improvement in miniaturization and transportability, to facilitate transportation, installation, and the like of the optical lattice clocks, and to improve utilization. 
     In particular, the conventionally used magnetic field correction coils are a factor that prevent miniaturization of the physics packages of optical lattice clocks. Miniaturization or transportability is widely required not only for optical lattice clocks but also for devices used for highly accurate quantum measurement. 
     SUMMARY OF THE INVENTION 
     An object of the present invention is to realize a triaxial magnetic field correction coil usable in a physics package that achieves both miniaturization or transportability, and maintenance or improvement of magnetic field correction accuracy. 
     A triaxial magnetic field correction coil according to the present invention is provided in a vacuum chamber that encloses a clock transition space in which atoms are arranged, the triaxial magnetic field correction coil being configured to have a shape capable of correcting any of a constant term, a first order spatial derivative term, a second order spatial derivative term, and a three or higher order spatial derivative term, or any combination of the terms. 
     A physics package according to the present invention includes: the triaxial magnetic field correction coil; and the vacuum chamber. 
     According to an aspect of the present invention, the vacuum chamber includes an inner wall formed to have a point-symmetric shape centered in the clock transition space in a first axis among the three axes, and the triaxial magnetic field correction coil includes a group of coils that is formed to have a point-symmetric shape centered in the clock transition space in a direction of the first axis, and is arranged on the inner wall or adjacent to the inner wall. 
     According to an aspect of the present invention, the triaxial magnetic field correction coil includes two or more groups of coils that have different coil sizes, coil shapes, or distances in the first axis. 
     An aspect of the present invention further includes a holder that has a sparse structure and is detachably attached around the inner wall of the vacuum chamber, wherein the group of coils is attached to the holder. 
     According to an aspect of the present invention, the vacuum chamber is formed to have a point-symmetric shape centered in the clock transition space in a second axis that is an axis other than the first axis among the three axes, and the triaxial magnetic field correction coil includes a group of coils that is formed to have a point-symmetric shape centered in the clock transition space in a direction of the second axis, and is arranged on the inner wall or adjacent to the inner wall. 
     According to an aspect of the present invention, the vacuum chamber is formed to have a point-symmetric shape centered in the clock transition space in a third axis that is an axis other than the first axis and the second axis among the three axes, and the triaxial magnetic field correction coil includes a group of coils that is formed to have a point-symmetric shape centered in the clock transition space in a direction of the third axis, and is arranged on the inner wall or adjacent to the inner wall. 
     According to an aspect of the present invention, the vacuum chamber is formed to have a substantially cylindrical shape allowing the clock transition space to be disposed on a central axis of the cylinder. 
     According to an aspect of the present invention, the vacuum chamber is formed to have a substantially spherical shape allowing the clock transition space to be disposed at a center of the sphere. 
     According to an aspect of the present invention, at least a pair of walls of the vacuum chamber that face with each other have substantially square shapes, and the clock transition space is formed to have a substantially rectangular shape arranged on an axis connecting centers of the pair of squares. 
     According to an aspect of the present invention, at least part of the group of coils is formed on a flexible printed board, and is attached to the inner wall formed to have the point-symmetric shape or to a holder formed to have a point-symmetric shape around the inner wall. 
     According to an aspect of the present invention, the physics package further includes: a pair of MOT coils that are provided in the vacuum chamber, form a gradient magnetic field, and capture the atoms in a capture space of the MOT device; a bias coil that is provided in the vacuum chamber, and is for generating a bias magnetic field at a position where the atoms are captured; and movement means for moving the atoms captured in the capture space to the clock transition space by a moving optical lattice, and at least part of the triaxial magnetic field correction coil is supported by a supporter that supports the MOT coils. 
     According to an aspect of the present invention, an optical resonator that includes an optical mirror that forms an optical lattice is provided around the clock transition space in the vacuum chamber, and at least part of the triaxial magnetic field correction coil is provided in the optical resonator. 
     According to an aspect of the present invention, at least part of the triaxial magnetic field correction coil is provided around an inner wall of the vacuum chamber. 
     A physics package system of the present invention includes: the triaxial magnetic field correction coil; and a control device that controls current that flows to the triaxial magnetic field correction coil. 
     The physics package according to the present invention may be used as a physics package for an optical lattice clock, a physics package for an atomic clock, a physics package for an atom interferometer, and a physics package for a quantum information processing device for atoms or ionized atoms. 
     An aspect of the present invention further includes at least one atomic laser cooling technology device among a Zeeman slower, a magneto-optical trap, and an optical lattice trap that guide the atoms into the clock transition space. 
     The present invention can facilitate miniaturization or achievement of transportability of a physics package including a clock transition space in a vacuum chamber, and maintain or improve the accuracy of magnetic field correction. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG.  1    schematically shows an overall configuration of an optical lattice clock according to an embodiment. 
         FIG.  2    shows a schematic configuration of a physics package of the optical lattice clock. 
         FIG.  3    schematically shows the appearance of the physics package. 
         FIG.  4    is a partially perspective view of the inside of the physics package in  FIG.  3   . 
         FIG.  5    shows an overall shape of a triaxial magnetic field correction coil. 
         FIG.  6    shows a shape of a first coil group of an X-axis magnetic field correction coil. 
         FIG.  7    shows a shape of a second coil group of the X-axis magnetic field correction coil. 
         FIG.  8    shows a shape of a first coil group of a Y-axis magnetic field correction coil. 
         FIG.  9    shows a shape of a second coil group of the Y-axis magnetic field correction coil. 
         FIG.  10    shows a shape of a first coil group of a Z-axis magnetic field correction coil. 
         FIG.  11    shows a shape of a second coil group of the Z-axis magnetic field correction coil. 
         FIG.  12    shows a shape of a holder of the triaxial magnetic field correction coil. 
         FIG.  13    shows an example of a correction coil using a flexible printed board. 
         FIG.  14    shows an example of a cylindrical correction coil using a flexible printed board. 
         FIG.  15    shows an example of currents flowing in the correction coil. 
         FIG.  16    shows flows of currents equivalent to those in the correction coil in  FIG.  15   . 
         FIG.  17    shows another example of currents flowing in the correction coil. 
         FIG.  18    shows flows of currents equivalent to those in the correction coil in  FIG.  17   . 
         FIG.  19    shows another example of a correction coil using a flexible printed board. 
         FIG.  20    shows a physics package that includes a spherical vacuum chamber. 
         FIG.  21    shows another installation example of a triaxial magnetic field correction coil. 
         FIG.  22    illustrates a mode of supporting the triaxial magnetic field correction coil in  FIG.  21   . 
         FIG.  23 A  schematically shows a mode of correcting magnetic fields. 
         FIG.  23 B  schematically shows a mode of correcting magnetic fields. 
         FIG.  24    is a flowchart of calibration of the triaxial magnetic field correction coil. 
         FIG.  25    is a flowchart showing procedures of correcting the triaxial magnetic field correction coil. 
         FIG.  26    schematically shows another mode of correcting magnetic fields. 
         FIG.  27    shows compensation of a stray magnetic field in a refrigerator. 
         FIG.  28    is a sectional view showing structures of a Zeeman slower and a MOT device. 
         FIG.  29    is a sectional view illustrating a void of a coil. 
         FIG.  30    shows a magnetic field distribution corresponding to the configuration in  FIG.  28   . 
         FIG.  31 A  is a sectional view showing structures of a Zeeman slower and a MOT device. 
         FIG.  31 B  is a sectional view showing structures of the Zeeman slower and the MOT device. 
         FIG.  32    shows a magnetic field distribution corresponding to the configuration in  FIGS.  31 A and  31 B . 
         FIG.  33 A  shows a structure of a modified mode in  FIGS.  31 A and  31 B . 
         FIG.  33 B  shows a structure of a modified mode in  FIGS.  31 A and  31 B . 
         FIG.  34    is a sectional view of a Zeeman coil having a constant coil outer diameter. 
         FIG.  35 A  is a sectional view showing encapsulation of a coil for a Zeeman slower. 
         FIG.  35 B  is a sectional view showing encapsulation of the coil for the Zeeman slower. 
     
    
    
     DESCRIPTION OF THE INVENTION 
     (1) Schematic Configuration of Physics Package 
       FIG.  1    schematically shows an overall configuration of an optical lattice clock  10 . The optical lattice clock included a physics package  12 , an optical system device  14 , a control device  16 , and a PC (Personal Computer)  18 , which are combined with each other. 
     As described in detail next, the physics package  12  is a device that captures an atom population, confines them in an optical lattice, and causes clock transitions. The optical system device  14  is a device that includes optical devices, such as a laser emission device, a laser receiver device, and a laser spectrometer. The optical system device  14  not only emits a laser and transmits the laser to the physics package  12 , but also performs processes of receiving light emitted by clock transitions of the atom population in the physics package  12 , converting it into an electric signal, and dividing the signal into frequency bands. The control device  16  is a device that controls the physics package  12  and the optical system device  14 . The control device  16  is a computer dedicated to the optical lattice clock  10 , and operates by software controlling computer hardware including processors and memories. For example, the control device  16  performs not only operation control of the physics package  12  and operation control of the optical system device  14 , but also analysis processes, such as frequency analysis of clock transition obtained by measurement. The physics package  12 , the optical system device  14 , and the control device  16  mutually, closely cooperate with each other and form the optical lattice clock  10 . 
     The PC  18  is a general-purpose computer, and operates by software controlling computer hardware including processors and memories. An application program for controlling the optical lattice clock  10  is installed in the PC  18 . The PC  18  is connected to the control device  16 , and not only controls the control device  16 , but also entirely controls the optical lattice clock  10 , which includes the physics package  12  and the optical system device  14 . The PC  18  serves as a UI (User Interface) of the optical lattice clock  10 . A user can activate the optical lattice clock  10 , and perform time measurement and verification of results, through the PC  18 . In this embodiment, description is given mainly on the physics package  12 . Note that the physics package  12  and the included components required to control this package are sometimes collectively called a physics package system. The components required for control are included in the control device  16  or the PC  18  in some cases, and are included in the physics package  12  itself. 
       FIG.  2    schematically shows the physics package  12  of the optical lattice clock according to the embodiment.  FIG.  3    schematically shows an example of the appearance of the physics package  12 .  FIG.  4    is a partially perspective view of the internal structure of the physics package  12  shown in  FIG.  3   .  FIGS.  2  to  4    (and the diagrams thereafter) show an XYZ orthogonal rectilinear coordinate system having an origin in a target space (clock transition space  52 ) where atoms mentioned later can reside during clock transition spectroscopy. 
     The physics package  12  includes a vacuum chamber  20 , an atomic oven  40 , a coil  44  for a Zeeman slower, an optical resonator  46 , a coil  48  for a MOT (Magneto-Optical Trap) device, a cryostat reservoir  54 , a thermal link member  56 , a refrigerator  58 , a vacuum pump main body  60 , and a vacuum pump cartridge  62 . 
     The vacuum chamber  20  is a case that maintains the main part of the physics package  12  at vacuum, and is formed to have a substantially cylindrical shape. In particular, the vacuum chamber  20  includes a main body  22  formed to have a large substantially cylindrical shape, and a protruding portion  30  formed to have a small substantially cylindrical shape that protrudes from the main body  22 . The main body  22  is a portion that internally stores the optical resonator  46  to be described later and the like. The main body  22  includes a cylindrical wall  24  that serves as a side surface of the cylinder, and a front circular wall  26  and a rear circular wall  28  which serve as circular surfaces of the cylinder. The front circular wall  26  is a wall provided with the protruding portion  30 . The rear circular wall  28  is a wall opposite to the protruding portion  30 , and has a shape with a larger diameter than that of the cylindrical wall  24 . 
     The protruding portion  30  includes a cylindrical wall  32  serving as a side surface of the cylinder, and a front circular wall  34 . The front circular wall  34  is a circular surface remote from the main body  22 . A portion of the protruding portion  30  adjacent to the main body  22  had an almost open shape, is connected to the main body  22 , and has no wall part. 
     The vacuum chamber  20  is arranged so that the central axis (called a Z-axis) of the cylinder of the main body  22  is substantially horizontal. The central axis (this axis serves as a beam axis) of the cylinder of the protruding portion  30  extends in parallel with the Z-axis above the Z-axis in the vertically upward direction. 
     The vacuum chamber  20  is assumed to be formed to be, for example, about 35 cm or less in the Z-axis direction, and about 20 cm or less in the X-axis direction and the Y-axis direction. Further miniaturization is also assumed so as to be about 30 cm or less, about 25 cm or less, or about 20 cm or less in the Z-axis direction. Also in the X-axis direction and the Y direction, it is assumed to be about 15 cm or less, or about 10 cm or less. The distance between the beam axis and the Z-axis is configured to be, for example, about 10 to 20 mm. 
     In the embodiment, four legs  38  are provided around the four corners at the lower part of the main body  22  of the vacuum chamber  20 , and support the vacuum chamber  20 . The vacuum chamber  20  is made sufficiently robust from metal, such as SUS (stainless steel), so as to withstand difference in air pressure when the inside becomes vacuum. The vacuum chamber  20  is formed so that the rear circular wall  28  and the front circular wall  34  are detachable. These walls are detached at maintenance check. 
     The atomic oven  40  is a device provided around the distal end of the protruding portion  30 . The atomic oven  40  causes a heater to heat an arranged solid metal, emits, through a pore, atoms ejected from the metal owing to thermal agitation, and forms an atom beam  42 . The beam axis on which the atom beam  42  passes is configured in parallel with the Z-axis, and is configured to intersect with the X-axis at a position slightly apart from the origin. The intersecting position corresponds to a capture space  50  that is a minute space where atoms to be described later are captured. The atomic oven  40  is basically provided in the vacuum chamber  20 . However, its heat radiator extends to the outside of the vacuum chamber  20  for cooling. The atomic oven  40  heats the metal to about 750K, for example. As the metal, for example, any of strontium, mercury, cadmium, ytterbium, and the like may be selected. However, there is no limitation thereto. 
     The coil  44  for the Zeeman slower is arranged on the downstream side of the beam axis of the atomic oven  40 , from the protruding portion  30  to the main body  22  of the vacuum chamber  20 . The coil  44  for the Zeeman slower is a device made by integrally including a Zeeman slower that decelerates the atoms of the atom beam  42 , and a MOT device that captures the decelerated atoms. Both the Zeeman slower and the MOT device are devices based on an atomic laser cooling technology. The coil  44  for the Zeeman slower shown in  FIG.  2    is provided with a Zeeman coil used for the Zeeman slower, and one of a pair of MOT coils used for the MOT device, as a series of coils. Although clear classification cannot be made, the large portion from the upstream to the downstream corresponds to the Zeeman coil that generates a magnetic field contributing to the Zeeman slowing method, and the furthest downstream side corresponds to the MOT coil that generates a gradient magnetic field contributing to the MOT method. 
     In the illustrated example, the Zeeman coil is of a decreasing type that has a larger number of turns on the upstream side and a smaller number of turns on the downstream side. The coil  44  for the Zeeman slower is axisymmetrically arranged around the beam axis so that the atom beam  42  passes through the inside of the Zeeman coil and the MOT coil. In the Zeeman coil, a magnetic field caused to have a spatial gradient is formed, and emission of a Zeeman slower optical beam  82  decelerates atoms. 
     The optical resonator  46  is a cylindrical component arranged around the Z-axis, and enables formation of an optical lattice therein. Multiple optical components are installed in the optical resonator  46 . One pair of optical mirrors on the X-axis, and another pair of optical mirrors in parallel therewith are provided, and optical lattice light is multiply reflected between the total four mirrors, thus generating a bow-tie-shaped optical lattice resonator. The atom population captured in the capture space  50  is confined in the optical lattice. When the relative frequencies of two optical lattice light beams (clockwise and counterclockwise) caused to enter the optical resonator  46  are shifted, this resonator forms a moving optical lattice that causes the standing wave of the optical lattice to move. The moving optical lattice moves the atom population to the clock transition space  52 . In the embodiment, an optical lattice including the moving optical lattice is configured to be formed on the X-axis. Note that there may be adopted a two-dimensional or three-dimensional optical lattice with a lattice arranged not only on the X-axis but also on one or both of the Y-axis and the Z-axis. Thus, the optical resonator  46  can be called an optical lattice formation portion forming an optical lattice. The optical resonator  46  is also a device based on atomic laser cooling technology. 
     The coil  48  for the MOT device generates a gradient magnetic field for the capture space  50 . The MOT device emits MOT light beams respectively along three, or the X, Y, and Z axes, in a space where the gradient magnetic field is formed. Accordingly, the MOT device captures atoms in the capture space  50 . The capture space  50  is configured on the X-axis. The coil  44  for the Zeeman slower shown in  FIG.  2    is provided with a Zeeman coil used for the Zeeman slower, and one of the pair of MOT coils used for the MOT device, as a series of coils. In this diagram, the gradient magnetic field that contributes to the MOT method is generated integrally by the coil  48  for the MOT device and part of the coil  44  for the Zeeman slower. 
     The cryostat reservoir  54  is formed so as to enclose the clock transition space  52 , and kept the inner space at a low temperature. Accordingly, in an inner space, blackbody radiation decreases. The thermal link member  56  serving also as a support structure is attached to the cryostat reservoir  54 . The thermal link member  56  transfers heat from the cryostat reservoir  54  to the refrigerator  58 . The refrigerator  58  keeps the cryostat reservoir  54  at a low temperature via the thermal link member  56 . The refrigerator  58  includes a Peltier element, and cools the cryostat reservoir  54  to about 190K, for example. 
     The vacuum pump main body  60  and the vacuum pump cartridge  62  are devices for vacuumizing the vacuum chamber  20 . The vacuum pump main body  60  and the vacuum pump cartridge  62  are devices for subsequently vacuumizing the vacuum chamber  20 . The vacuum pump main body  60  is provided outside of the vacuum chamber  20 . The vacuum pump cartridge  62  is provided in the vacuum chamber  20 . At the start of activation, the vacuum pump cartridge  62  is heated by a heater provided at the vacuum pump main body  60  and is activated. Accordingly, the vacuum pump cartridge  62  is activated, and absorbs atoms, thus achieving a vacuum. 
     The vacuum pump cartridge  62  is installed in the main body  22  so as to be in parallel with the coil  44  for the Zeeman slower. The coil  44  for the Zeeman slower is arranged along the beam axis decentered in the X-axis direction from the central axis of the cylinder of the main body  22 . Accordingly, there is a relatively large space on the opposite side away from the direction in which the coil  44  for the Zeeman slower is eccentrically arranged. The vacuum pump cartridge  62  is installed in this space. 
     The physics package  12  includes, as components of the optical system: vacuum-resistant optical windows  64  and  66  for optical lattice light; a vacuum-resistant optical window  68  for MOT light; vacuum-resistant optical windows  70  and  72  for Zeeman slower light and MOT light; and optical mirrors  74  and  76 . 
     The vacuum-resistant optical windows  64  and  66  for optical lattice are vacuum-resistant optical windows provided on opposite cylindrical walls  24  of the main body  22  of the vacuum chamber  20  so as to face each other. The vacuum-resistant optical window  64  and  66  for optical lattice light are provided so as to allow optical lattice light to enter and be emitted therethrough. 
     The vacuum-resistant optical window  68  for MOT light is provided so as to allow entry and emission therethrough of MOT light beams on two axes, among MOT light beams on the three axes used for the MOT device. 
     The vacuum-resistant optical windows  70  and  72  for Zeeman slower light and MOT light are provided so as to allow Zeeman slower light and MOT light on one axis to enter and be emitted therethrough. 
     The optical mirrors  74  and  76  are provided so as to change the directions of the Zeeman slower light and the MOT light on the one axis. 
     The physics package includes, as components for cooling: a cooler  90  for an atomic oven; a cooler  92  for a Zeeman slower; and a cooler  94  for a MOT device. 
     The cooler  90  for the atomic oven is a water-cooling device that cools the atomic oven  40 . The cooler  90  for the atomic oven is provided outside of the vacuum chamber  20 , and cools a radiator of the atomic oven  40 , the radiator extending outside of the vacuum chamber  20 . The cooler  90  for the atomic oven includes a water-cooling tube that is a tube made of metal and is for cooling, and causes cooling water to flow, which is a liquid coolant, in the tube, thus cooling the vacuum chamber  20 . 
     The cooler  92  for the Zeeman slower is a device that is provided on the wall part of the vacuum chamber  20 , and cools the coil  44  for the Zeeman slower. The cooler  92  for the Zeeman slower includes a tube made of a metal, and flows cooling water in the tube, thus removing Joule heat generated at the coil  44  for the Zeeman slower. 
     The cooler  94  for the MOT device is a heat radiator provided on the circular wall part of the vacuum chamber  20 . At the coil  48  for the MOT device, Joule heat is generated, although the Joule heat is smaller in amount (e.g., about 1/10) than that of the cooler  92  for the Zeeman slower. Accordingly, the metal of the cooler  94  for the MOT device extends to the outside of the vacuum chamber  20  from the coil  48  for the MOT device, and radiates heat to the atmosphere. 
     The physics package  12  further includes, as components for correcting a magnetic field: a triaxial magnetic field correction coil  96 ; a vacuum-resistant electric connector  98 ; an individual magnetic field compensation coil  102  for a refrigerator; and an individual magnetic field compensation coil  104  for the atomic oven. 
     The triaxial magnetic field correction coil  96  is a coil for uniformly nullifying the magnetic field in the clock transition space  52 . The triaxial magnetic field correction coil  96  is formed to have a three-dimensional shape so as to correct the magnetic field in the three, or X, Y, and Z, axes. In the example shown in  FIG.  4   , the triaxial magnetic field correction coil  96  is formed to have a substantially cylindrical shape as a whole. Each of coils constituting the triaxial magnetic field correction coil  96  is formed to have a point-symmetric shape centered in the clock transition space  52  in each axis direction. 
     The vacuum-resistant electric connector  98  is a connector for supplying electric power to the inside of the vacuum chamber  20 , and is provided on the circular wall part of the vacuum chamber  20 . From the vacuum-resistant electric connector  98 , power is supplied to the coil  44  for the Zeeman slower, the coil  48  for the MOT device, and the triaxial magnetic field correction coil  96 . 
     The individual magnetic field compensation coil  102  for the refrigerator is a coil for compensating the stray magnetic field from the refrigerator  58  that cools the cryostat reservoir  54 . The Peltier element included in the refrigerator  58  is a large current device where relatively large current flows, and generates a large magnetic field. Around the Peltier element, the magnetic field is shielded by a high permeability material. However, shielding is not completely achieved, and part of the magnetic field leaks. Accordingly, the individual magnetic field compensation coil  102  for the refrigerator is configured so as to compensate the stray magnetic field in the clock transition space  52 . 
     The individual magnetic field compensation coil  104  for the atomic oven is a coil for compensating the stray magnetic field from the heater of the atomic oven  40 . The heater of the atomic oven  40  is also a large current device, and the stray magnetic field cannot be ignored in some cases even with shielding by a high permeability material. For example, even in a case where a heater circuit is made of noninductive winding, an induced component remains in actuality, in wiring via a wiring terminal and an insulating layer. For example, even if the atomic oven is covered with a high permeability material to facilitate magnetic shielding, a part cannot be covered in actuality, such as an opening of the atom beam. Accordingly, the individual magnetic field compensation coil  104  for the atomic oven is configured so as to compensate the stray magnetic field in the clock transition space  52 . 
     (2) Operation of Physics Package 
     The basic operation of the physics package  12  is described. In the physics package  12 , the vacuum pump cartridge  62  included in the vacuum chamber  20  absorbs atoms, thus vacuumizing the inside of the vacuum chamber  20 . Accordingly, for example, the inside of the vacuum chamber  20  is in a vacuum state of about 10 −8  Pa, which eliminates the effect of air components, such as nitrogen and oxygen. Depending on the type of the vacuum pump to be used, a preprocess is preliminarily executed. For example, for a non-evaporable getter pump (NEG pump) and an ion pump, rough pumping is required to be performed from the atmosphere to a certain degree of vacuum before their operation. In this case, a rough pumping port is provided for the vacuum chamber, and rough pumping is sufficiently performed through the port using a turbomolecular pump, for example. For example, in a case of using an NEG pump as the vacuum pump main body  60 , a step of activation of heating to a high temperature in a vacuum is required to be preliminarily executed. 
     In the atomic oven  40 , the metal is heated by the heater to a high temperature, and atomic vapor w is generated. The atomic vapor emitted from the metal in this process sequentially passes through the pore, is converged, translates, and forms an atom beam  42 . The atomic oven  40  is installed so as to form the atom beam  42  on the beam axis in parallel with the Z-axis. Note that in the atomic oven  40 , an atomic oven main body is heated by a heater. However, the atomic oven main body and a joint that supports this main body are thermally insulated via a thermal insulator. Furthermore, a joint connected to the physics package is cooled by the cooler  90  for the atomic oven, thus preventing the physics package  12  from being affected by a high temperature, or reducing the adverse effect of the high temperature. 
     The coil  44  for the Zeeman slower is installed so as to be axisymmetrical with respect to the beam axis. The inside of the coil  44  for the Zeeman slower is irradiated with the Zeeman slower optical beam  82  and the MOT optical beam  84  on one axis. The Zeeman slower optical beam  82  enters from the vacuum-resistant optical window  70  for Zeeman slower light and MOT light, and is reflected by the optical mirror  74  installed downstream of the beam away from the coil  48  for the MOT. Accordingly, the Zeeman slower optical beam  82  is overlaid on the atom beam  42 , and travels upstream of the beam axis in parallel to the beam axis. In this process, owing to the effect of the Zeeman splitting proportional to the intensity of the magnetic field and the effect of the Doppler shift, the atoms in the atom beam  42  absorb the Zeeman slower light, are given momentum in the deceleration direction, and are decelerated. The Zeeman slower light is reflected upstream of the coil  44  for the Zeeman slower by the optical mirror  76  disposed aside of the beam axis, and is emitted through the vacuum-resistant optical window  72  for Zeeman slower light and MOT light. Note that the coil  44  for the Zeeman slower generates Joule heat. However, cooling is performed by the cooler  92  for the Zeeman slower. Accordingly, the temperature is prevented from being high. 
     The sufficiently decelerated atom beam  42  reaches the MOT device that includes the MOT coil on the furthest downstream side of the coil  44  for the Zeeman slower, and the coil  48  for the MOT device. In the MOT device, a magnetic field having a linear spatial gradient is formed centered in the capture space  50 . The MOT device is irradiated with MOT light in the three-axis directions, on the positive and negative sides. 
     The MOT optical beam  84  in the Z-axis direction is emitted in the negative direction of the Z-axis, and is then reflected outside of the vacuum-resistant optical window  72  for Zeeman slower light and MOT light, thus being emitted also in the positive direction of the Z-axis. MOT optical beams  86   a  and  86   b  on the remaining two axes are emitted into the MOT device through the vacuum-resistant optical window  68  for MOT light and by an optical mirror, not shown. As shown in  FIG.  4   , these two axes are in two directions perpendicular to the Z-axis and inclined respectively from the X-axis and the Y-axis by 45 degrees; emission is performed in these two directions. The configuration allowing the two MOT optical beams  86   a  and  86   b  to be perpendicular to the Z-axis is capable of narrowing the distance between the coil  44  for the Zeeman slower and the coil  48  for the MOT device, thus contributing to miniaturization of the vacuum chamber  20 . In a case where the directions of emission of the MOT optical beams are configured to be inclined respectively from the Z-axis and the Y-axis by 45 degrees, the distance in the beam axis is required to be large so as to prevent the MOT optical beams from interfering with the Zeeman slower and the cryostat reservoir. In this case, the device size is larger than in the case where the two axes of the MOT light beams are perpendicular to the Z-axis. 
     In the MOT device, the atom beam receives a restoring force centered in the capture space  50  by the magnetic field gradient and is decelerated. Accordingly, the atom population is captured in the capture space  50 . Note that the position of the capture space  50  can be finely adjusted by adjusting the offset values for the magnetic field to be generated by the triaxial magnetic field correction coil  96 . The Joule heat generated at the coil  48  for the MOT device is discharged outside of the vacuum chamber  20  by the cooler  94  for the MOT device. 
     An optical lattice light beam  80  enters in the X-axis direction through the vacuum-resistant optical window  64  for optical lattice light toward the vacuum-resistant optical window  66  for optical lattice light. On the X-axis, the optical resonator  46  including two optical mirrors is installed, and causes reflection. Accordingly, on the X-axis there is formed an optical lattice potential with a series of standing waves in the X-axis direction in the optical resonator  46 . The atom population is captured by the optical lattice potential. 
     The optical lattice can be moved along the X-axis by slightly changing the wavelength. By movement means through the moving optical lattice, the atom population is moved to the clock transition space  52 . As a result, the clock transition space  52  is apart from the beam axis of the atom beam  42 . Accordingly, the effects of blackbody radiation emitted from the atomic oven  40  at a high temperature can be removed. The clock transition space  52  is enclosed by the cryostat reservoir  54 , and is shielded from blackbody radiation emitted from ambient materials at ordinary temperatures. In general, blackbody radiation is proportional to the fourth power of the absolute temperature of a material. Accordingly, reduction in temperature by the cryostat reservoir  54  exerts a large advantageous effect of removing the impact of the blackbody radiation. 
     In the clock transition space  52 , atoms are irradiated with laser light whose optical frequency is under control, highly accurate spectroscopy of clock transitions (i.e., resonance transitions of atoms serving as the reference of the clock) is performed, and the frequency that is specific to the atom and invariant is measured. Thus, an accurate atomic clock is achieved. Improvement of the accuracy of the atomic clock requires removal of perturbation around the atoms, and the frequency is accurately read. It is particularly important to remove the frequency shift caused by the Doppler effect due to the thermal agitation of the atoms. In the optical lattice clock, the atom movement is frozen by confining the atoms in a space sufficiently smaller than the wavelength of the clock laser by the optical lattice created by interference of the laser light. Meanwhile, in the optical lattice, the frequencies of atoms are shifted by laser light that forms the optical lattice. For the optical lattice light beam  80 , a specific wavelength or frequency called “magic wavelength” or “magic frequency” is selected, which removes the effects of the optical lattice to the resonant frequency. 
     Furthermore, the clock transitions are also affected by a magnetic field. Atoms in the magnetic field cause Zeeman splitting dependent on the intensity of the magnetic field. Accordingly, the clock transitions cannot accurately measured. In the clock transition space  52 , the magnetic field is corrected so as to equalize and nullify the magnetic field. First, a stray magnetic field caused by the Peltier element of the refrigerator  58  is dynamically compensated by the individual magnetic field compensation coil  102  for the refrigerator that generates a compensation magnetic field dependent on the intensity of the stray magnetic field. Likewise, it is configured so that the stray magnetic field caused by the heater of the atomic oven  40  can be dynamically compensated by the individual magnetic field compensation coil  104  for the atomic oven. Note that for the coil  44  for the Zeeman slower and the coil  48  for the MOT device, the current signal is turned off at timing of measurement of the frequency of clock transition, and energization is not performed, thus preventing effects of the magnetic field. The magnetic field of the clock transition space  52  is further corrected by the triaxial magnetic field correction coil  96 . The triaxial magnetic field correction coil  96  includes multiple coils in each axis, and can remove not only uniform components of the magnetic field but also spatially varying components. 
     Thus, in the state where the disturbances are removed, the atom population is urged to be subjected to clock transition by laser light. Light emitted as a result of the clock transition is received by the optical system device, subjected to a spectroscopic process and the like by the control device, and the frequency is obtained. Hereinafter, embodiments of the physics package  12  are described in detail. 
     (3) Shape and Installation Mode of Magnetic Field Correction Coil 
     By reference to  FIGS.  5  to  11   , the triaxial magnetic field correction coil  96  in the physics package  12  is described. Here, the triaxial magnetic field correction coil  96  is assumed to be formed to have a predetermined shape by winding a covered conductor wire that includes a conducive wire made of copper or the like and having been subjected to an insulating process with a polyimide resin. 
       FIG.  5    is a perspective view showing all the coils of the triaxial magnetic field correction coil  96 .  FIGS.  6  to  11    are perspective views showing individual coils that constitute the triaxial magnetic field correction coil. The triaxial magnetic field correction coil  96  is attached around an inner wall of the main body  22  of the vacuum chamber  20 . Accordingly, the triaxial magnetic field correction coil  96  is formed to have a substantially cylindrical shape centered in the clock transition space  52 . The triaxial magnetic field correction coil  96  includes a first coil group and a second coil group in each of the directions of the X-axis, Y-axis, and Z-axis. 
       FIG.  6    shows a first coil group  120  in the X-axis direction (a direction in which an optical lattice in one axis is formed, and the moving optical lattice moves). The first coil group  120  includes two coils  122  and  124  installed apart from each other by a distance c in the X-axis direction centered in the clock transition space  52 . The coils  122  and  124  are each formed to have a rectangular shape with the length of the side in the Y-axis direction being a, and the length of the side in the Z-axis direction being b. The coils  122  and  124  are formed to have a point-symmetric shape with respect to the clock transition space  52 . 
     The first coil group  120  causes the coils  122  and  124  to constitute a square-shaped Helmholtz-type coil so as to substantially uniformly generate the magnetic field at a central part in the X-axis direction. The square-shaped Helmholtz-type coil includes the coils  122  and  124  formed to have a square shape with a=b, with c/2a= about 0.5445. When currents having the same magnitude flow in the same direction, the coils  122  and  124  serve as a Helmholtz-type coil pair that forms a magnetic field having high uniformity in the X-axis direction. However, in the embodiment, currents having different magnitudes and directions are allowed to flow through the coils  122  and  124 . Note that the coils  122  and  124  can sufficiently improve the uniformly of the magnetic field even in a case of a≠b. In a case of a&gt;b, the deviation of the magnetic field distribution in the Y-axis direction tends to be smaller than that of the magnetic field distribution in the Z-axis direction. In a case of a&lt;b, the deviation of the magnetic field distribution in the Z-axis direction tends to be smaller than that of the magnetic field distribution in the Y-axis direction. In the case of a≠b, and where c is optimized is called a rectangular Helmholtz-type coil. The first coil group  120  may be configured as a rectangular Helmholtz-type coil. 
     The first coil group  120  is used to adjust the value of the magnetic field component in the X-axis direction, and its first order spatial derivative term in the X-axis direction. First, 1) when currents having the same magnitude flow in the same direction through the coils  122  and  124 , a uniform magnetic field having little gradient in the X-axis direction is formed in the clock transition space  52 . On the other hand, 2) when currents having the same magnitude flow in the opposite directions through the coils  122  and  124 , a uniform magnetic field having a substantially uniform gradient in the X-axis direction is formed in the clock transition space  52 . When the magnitudes and directions of currents flowing through the coils  122  and  124  are appropriately changed, a magnetic field of a linear sum of 1) and 2) is formed. Accordingly, the first coil group  120  can correct the constant term component of the magnetic field component Bx in the X-axis direction in the clock transition space  52 , and its first order spatial derivative term in the X-axis direction. 
       FIG.  7    shows a second coil group  130  in the X-axis direction. The second coil group  130  includes two coils  132  and  134  installed apart from each other in the X-axis direction centered in the clock transition space  52 . The coils  132  and  134  are each formed to have shapes obtained by deforming rectangular coils to have a curvature so that the coils can be laid on the same cylindrical p surface having a radius e and are configured so that the central angle is f, and the height in the Z-axis direction is g. The cylindrical surface is formed to have a radius substantially identical to that of a cylindrical surface onto which the first coil group  120  in  FIG.  6    is fixed. Accordingly, the relationship e 2 ≅(a/2) 2 +(c/2) 2  holds. The coils  132  and  134  are formed to have a point-symmetric shape with respect to the clock transition space  52 . 
     The second coil group  130  is a non-Helmholtz-type coil that has a shape different from that of the Helmholtz coil. The coils  132  and  134  of the second coil group are electrically connected to each other. Currents with the same magnitude flow through the coils in the same direction. That is, currents flow in the direction of an arrow  136  or currents flow in the direction of an arrow  138  through both the coils  132  and  134 . Since the second coil group  130  is a non-Helmholtz-type coil, a non-uniform component is also generated in addition to a uniform component according to a Helmholtz coil in the clock transition space  52  at the center. Note that the magnitudes and the directions of currents are the same. Accordingly, the non-uniform component is mainly a second order spatial derivative term component. That is, the second coil group  130  can correct the constant term component of the magnetic field component Bx in the X-axis direction in the clock transition space  52 , and its second order spatial derivative term in the X-axis direction. 
     What controls the magnetic field component Bx in the X-axis direction in the triaxial magnetic field correction coil  96  is basically the first coil group  120  and the second coil group  130  in the X-axis direction. Accordingly, these are collectively called an X-axis magnetic field correction coil. To perform correction, first, the value of the second order spatial derivative term in the X-axis direction is nullified by the second coil group  130 . Subsequently, adjustment of nullifying the value of the first order spatial derivative term in the X-axis direction and nullifying the constant term in the X-axis direction by the first coil group  120  is performed. 
       FIG.  8    shows a first coil group  140  in the Y-axis direction. The first coil group  140  is formed by deforming rectangular coils so as to have a curvature, and is laid on a cylindrical surface having a radius h centered in the clock transition space  52 . The first coil group includes a composite coil  142  made up of a coil  143  and a coil  144 , and a composite coil  145  made up of a coil  146  and a coil  147 , the composite coils being installed apart from each other in the Y-axis direction. The coils  143 ,  144 ,  146 , and  147  are configured so that the central angle is i and the height in the Z-axis direction is j. The coils  143  and  144  are formed so that their edges can overlap with or be adjacent to each other. Likewise, the coils  146  and  147  are formed so that their edges can overlap with or be adjacent to each other. The composite coil  142  and the composite coil  145  are point-symmetrically formed centered in the clock transition space  52 . The coil  143  and the coil  146 , and the coil  144  and the coil  147  are point-symmetrically formed centered in the clock transition space  52 . 
     First, 3) a case is discussed where currents with the same magnitude flow in the same direction through the coils  143  and  144 . In this case, currents at the overlapping or adjacent configuration cancel each other, and the entire composite coil  142  serves as a single large coil. Likewise, in a case where currents with the same magnitude flow in the same direction through the coils  146  and  147 , the composite coil  145  serves as a single large coil. The first coil group  140  is configured so that the composite coil  142  and the composite coil  145  serve as a pair of Helmholtz-type coils. The Helmholtz-type coil on the cylindrical surface shown in  FIG.  8    (i.e., a Helmholtz-type coil obtained by bending two rectangular coils and arranging on the same cylindrical surface) has a central angle of about 120 degrees. No particular limitation is imposed on the length in the Z-axis direction. It is however known that the greater the length in the Z-axis direction is in comparison with the radius of the cylinder, the higher the magnetic field uniformly of the central part. The first coil group  140  can equalize the component of the magnetic field in the Y-axis direction around the center by adjusting the direction and magnitude of the current allowed to flow. 
     Next, 4) the current is slightly changed from the current when the Helmholtz coil is formed. Specifically, only currents through the coil  143  and the coil  147  are slightly increased in the same direction. In this case, the component of the magnetic field in the Y-axis direction has the value of the first order spatial derivative term in the X-axis direction. Note that in a strict sense, the magnetic field formed by the coil  143  and the coil  147  has a component in the X-axis direction. When the first coil group  140  is adjusted, the X-axis magnetic field correction coil is also required to be adjusted. 
       FIG.  9    shows a second coil group  150  in the Y-axis direction. The second coil group  150  shown in  FIG.  9    is made up of a pair of coils  152  and  154  that face each other in the Y-axis direction. Each of the coils  152  and  154  is a non-Helmholtz-type coil formed to have a shape obtained by causing a circular coil having a radius k to have a curvature, and laying the coil on the surface of a cylinder with a radius  1  centered in the clock transition space  52 . The non-Helmholtz-type coil also forms the second order spatial derivative term component of the magnetic field. Accordingly, the second coil group  150  is used to control the X-axis-direction second order spatial derivative term of the magnetic field component By in the Y-axis direction. 
     The first coil group  140  in the Y-axis direction shown in  FIG.  8    and the second coil group  150  in the Y-axis direction shown in  FIG.  9    basically form a Y-axis magnetic field correction coil that corrects the magnetic field component By in the Y-axis direction. The Y-axis magnetic field correction coil can correct the constant term of the magnetic field component By in the Y-axis direction, the first order spatial derivative term in the X-axis direction, and the second order spatial derivative term in the X-axis direction. 
       FIG.  10    shows a first coil group  160  in the Z-axis direction. The first coil group  160  includes circular composite coils  162  and  165  that have a radius m and are arranged to face each other and separated by a distance n. The composite coils  162  and  165  are point-symmetric with respect to the center. The composite coil  162  includes semicircular coils  163  and  164  whose chords overlap with or are adjacent to each other. The semicircular coil  163  is arranged on the positive side of the X-axis, and the semicircular coil  164  is arranged on the negative side of the X-axis. Likewise, the composite coil  165  is formed by combining a semicircular coil  166  on the positive side of the X-axis and a semicircular coil  167  on the negative side of the X-axis. 
     The composite coils  162  and  165  are configured to have sizes and the like so as to serve as a Helmholtz-type coil. The circular Helmholtz coil has a relationship of m=n. The composite coils  162  and  165  are configured so that when currents having the same magnitude flow in the same direction, the uniformity of the magnetic field in the Z direction around the center is substantially equivalent to that of a Helmholtz coil. Note that the directions and magnitudes of the currents through the coils  163  and  164 , which constitute the composite coil  162 , can be changed freely. Accordingly, similar to the first coil group  140  in the Y direction shown in  FIG.  8   , the first coil group  160  can correct the constant term and the X-axis-direction first order spatial derivative term of the magnetic field component Bz in the Z direction. 
       FIG.  11    shows a second coil group  170  in the Z-axis direction. The second coil group  170  includes circular coils  172  and  174  that have a radius p and are apart by a distance q in the Z-axis direction facing each other. The second coil group  170  is a non-Helmholtz-type coil. The non-Helmholtz-type coil has a non-uniform component. Accordingly, the X-axis-direction second order spatial derivative term of the magnetic field component Bz in the Z-axis direction can be corrected. 
     The first coil group  160  in the Z-axis direction shown in  FIG.  10    and the second coil group  170  in the Z-axis direction shown in  FIG.  11    basically form a Z-axis magnetic field correction coil that corrects the magnetic field component Bz in the Z-axis direction. The Z-axis magnetic field correction coil can correct the constant term of the magnetic field component Bz in the Z-axis direction, the first order spatial derivative term in the X-axis direction, and the second order spatial derivative term in the X-axis direction. 
     The triaxial magnetic field correction coil  96  shown in  FIG.  5    is formed by controlling the X-axis magnetic field correction coil, the Y-axis magnetic field correction coil, and the Z-axis magnetic field correction coil in a combined manner. The triaxial magnetic field correction coil  96  can correct the constant term, the X-axis-direction first order spatial derivative term, and the X-axis-direction second order spatial derivative term of the magnetic field component Bx in the X-axis direction. The constant term, the X-axis-direction first order spatial derivative term, and the X-axis-direction second order spatial derivative term of the magnetic field component By in the Y-axis direction can be corrected. The constant term, the X-axis-direction first order spatial derivative term, and the X-axis-direction second order spatial derivative term of the magnetic field component Bz in the Z-axis direction can be corrected. 
     The triaxial magnetic field correction coil  96  performs correction of uniformly nullifying the value of the magnetic field of the clock transition space  52 . In the case of a one-dimensional optical lattice, the clock transition space  52  is configured to have dimensions such as 10 mm in the X-axis direction (the direction of the lattice), and about 1 to 2 mm in the Y-axis and Z-axis directions, for example. In this space, for example, the error of the magnetic field is controlled so as to be within 3 μG, within 1 μG, or within 0.3 μG. The Helmholtz-type coils and the non-Helmholtz-type coils included in the triaxial magnetic field correction coil  96  are configured to have accuracies so as to be capable of forming the magnetic field. 
     As shown in  FIG.  4   , the triaxial magnetic field correction coil  96  is formed to have a point-symmetric shape centered in the clock transition space  52 , and is capable of accurately correcting the magnetic field in the clock transition space  52 . However, in a macroscopic view, the capture space  50  resides around the center of the triaxial magnetic field correction coil. Accordingly, use for correcting the magnetic field of the capture space  50  due to the MOT device is also available. That is, the current is controlled to correct the magnetic field of the capture space  50  in a time period in which the MOT device is activated and captures atoms from the atom beam  42 . After the capture is finished, power transmission to the coil  44  for the Zeeman slower and the coil  48  for the MOT device is stopped, and the magnetic field of the clock transition space  52  is corrected. Thus, the position of the capture space  50  is highly accurately adjusted, and the atom population can be efficiently confined in the optical lattice. 
       FIG.  12    shows a cylindrical holder  180  to which the triaxial magnetic field correction coil  96  is attached. The holder  180  includes circular ring-shaped frames  182  and  184 , and eight linear frames  186  that connect the frames  182  and  184 . The triaxial magnetic field correction coil  96  is attached to the inner wall and the outer wall of the holder  180 . The holder  180  is then fixed to the rear circular wall  28  of the main body  22  of the vacuum chamber  20 . By attaching the triaxial magnetic field correction coil  96  to the holder  180 , the efficiency of assembly and maintenance checkup operations of the physics package  12  is improved. 
     The holder  180  is made of a low-permeability material such as a resin, aluminum, or the like, in order not to affect the magnetic field created by the triaxial magnetic field correction coil  96 . The holder  180  is installed in the main body  22  so as to be coaxial with the central axis of the cylinder of the main body  22 . The holder  180  is formed to have a size close to the inner diameter of the main body  22 . Accordingly, the triaxial magnetic field correction coil  96  and the holder  180  hardly occupy the space in the main body  22 . Note that the coils  122  and  124 , which are the first coil group  120  in the X-axis direction, are attached linearly across the inside of the main body  22 . 
     The holder  180  is formed to have a sparse structure using the frames. The sparse structure is a structure having many interspaces on each surface. The sparse structure of the holder  180  reduces the weight, and facilitates prevention of interference with laser light that enters and is emitted from the vacuum chamber  20 . 
     The triaxial magnetic field correction coil  96  may be, for example, entirely attached to the inner wall of the holder  180  or entirely attached to the outer wall of the holder  180 , instead of being attached to the inner wall and the outer wall of the holder  180 . In this case, for example, fixation can be easily achieved using a circular ring-shaped fastener that presses the triaxial magnetic field correction coil  96  against the outer wall, or a circular ring-shaped fastener that presses the coil against the inner wall. The triaxial magnetic field correction coil  96  can be fixed to the inner wall of the main body  22  without using the holder  180 . 
     It is assumed that the triaxial magnetic field correction coil  96  described above is formed by winding a covered conductor wire one or multiple times. However, the triaxial magnetic field correction coil  96  can be partially or entirely made of a flexible printed board. 
       FIG.  13    shows a flexible printed board developed on a plane. A correction coil  190  is formed on the flexible printed board. The correction coil  190  includes current paths  192  that are made of a printed electric conductor, such as copper, and contribute to forming the magnetic field, and an insulator  194  made of a sheet-shaped flexible resin or the like, and can be flexibly bent. Each current path  192  is connected to a wiring path  196  provided intensively on one end. The wiring path  196  is made of a print made of an electric conductor. The wiring path arranges a pair where currents reciprocate, so as to be adjacent to each other, and canceled magnetic fields to be formed therearound. The wiring path  196  is connected to a terminal connector  198 . 
       FIG.  14    shows the cylindrically bent correction coil  190  along the main body  22  of the vacuum chamber  20 . The correction coil  190  includes a boundary part  199  where the two edges are connected to or arranged adjacent to each other. Note that in  FIG.  14   , the wiring path  196  and the terminal connector  198  are omitted. 
     Similar to the triaxial magnetic field correction coil  96  where the covered conductor wire is wound, the triaxial magnetic field correction coil configured with the flexible printed board is assumed to be attached to the inner wall of the cylindrical main body  22  or to the cylindrical holder  180 . Note that the triaxial magnetic field correction coil  96  includes a current path disengaged from the cylindrical surface, besides the current path arranged on the cylindrical surface. Specifically, a side having a length a of the first coil group  120  in the X-axis direction shown in  FIG.  6   , and a linear part of the first coil group  160  in the Z-axis direction shown in  FIG.  10    are disengaged from the cylindrical surface. Hereinafter, an example is described where among the current paths constituting the triaxial magnetic field correction coil  96 , current paths arranged on the cylindrical surface are formed on a flexible printed board. 
       FIGS.  15  and  16    show an example of forming a coil at the circular part of the first coil group  160  in the Z-axis direction shown in  FIG.  10    using a flexible printed board. As shown in  FIG.  15   , counterclockwise currents flowe through current paths  202  indicated by black lines, but no current flows to current paths  200  indicated by gray lines. At this time, in consideration that the currents that are adjacent to each other and flow in the opposite directions canceled each other, this is equivalent to a case where currents flow through virtual current paths  203  shown in  FIG.  16   . 
       FIGS.  17  and  18    show an example of forming the outermost coil of the first coil group  140  in the Y-axis direction shown in  FIG.  8    using a flexible printed board. As shown in  FIG.  17   , counterclockwise currents flow through current paths  206  indicated by black lines, but no current flows to current paths  204  indicated by gray lines. At this time, in consideration that the currents that are adjacent to each other and flow in the opposite directions cancel each other, this is equivalent to a case where currents flow through virtual current paths  208  shown in  FIG.  18   . 
     As described above, on a flexible printed board, there can be formed various current paths that include a current path going back around the outer periphery of the cylindrical surface about the central axis of the cylinder, and a current path going back on the cylindrical surface not about the central axis of the cylinder. 
     In the developed diagram as shown in  FIG.  13   , on the flexible printed board, a pattern made up of rectangular current paths can be printed. Similarly. for a correction coil  210  shown in  FIG.  19   , a composite pattern that includes rectangular current paths  211  and circular current paths  214  can be printed. In the physics package  12 , a laser light path, a vacuum-resistant optical window, and the like are provided around the wall surface of the vacuum chamber  20 . Accordingly, it is effective to provide the circular current paths  214  and prevent interference. On the flexible printed board, the coils as shown in  FIGS.  16  and  18    may be formed. Multiple flexible printed boards may be used in an overlaid manner. Thus, a part or the entirety of the triaxial magnetic field correction coil may be formed using multiple boards. 
     On the flexible printed board, in some cases a minute amount of gas may be emitted from a resin of the insulator  194 . Accordingly, for the insulator  194 , a material with a small amount of gas emission, such as polyimide resin, is selected. It is conceivable that a production step performs a baking process at an appropriate temperature, in addition to a deaeration process, a defoaming process, a cleaning process, and the like. 
     The triaxial magnetic field correction coil formed of a flexible printed board may be installed in the vacuum chamber  20  in various forms. For example, it is conceivable that the triaxial magnetic field correction coil is installed around the inner wall of the main body  22  in a state of being cylindrically bent, and the triaxial magnetic field correction coil is fixed to the main body  22  with a fastener that presses the coil against the main body  22 . Alternatively, installation may be performed by attaching to the holder  180 . Instead of the holder  180  having the sparse structure, a holder that has a dense structure with not many pores may be adopted so as to support the flexible printed board on a plane. 
     On the other hand, a current path disengaged from the cylindrical surface may be separately formed using a covered conductor wire. Alternatively, by changing the structure of the holder, a current path disengaged from the cylindrical surface may also be created by adopting the flexible printed board. 
     In comparison with the triaxial magnetic field correction coil  96  with the covered conductor wire being wound, the triaxial magnetic field correction coil using the flexible printed board has advantages that facilitate attachment to the vacuum chamber  20 , as well as improved production reproducibility and improved production yield. 
     Note that the coil shape of the triaxial magnetic field correction coil may be variously configured in another form. For example, for each of the three axes, a large-sized circular coil is arranged at the middle of two circular coils, thus enabling formation of a Maxwell type triaxial magnetic field correction coil. For the Maxwell type triaxial magnetic field correction coil, the components of the constant term, the first order spatial derivative term, and the second order spatial derivative term of the magnetic field can be corrected. 
     Furthermore, for each of the three axes, small circular coils that have a predetermined size and are provided at predetermined intervals are arranged outside of a pair of large circular coils that have a predetermined size and are provided at predetermined intervals, thus enabling formation of a tetra type axial magnetic field correction coil. The components of the constant term, the first order spatial derivative term, the second order spatial derivative term, and the third order spatial derivative term of the triaxial magnetic field correction coil can be corrected. 
     The axial magnetic field correction coil described above has a spherical shape or a slightly distorted spherical shape as a whole. Accordingly, in particular, attachment to the inner wall of the substantially spherical vacuum chamber or therearound enables effective utilization of the inner space of the vacuum chamber. 
       FIG.  20    is a diagram corresponding to  FIG.  4   , and schematically shows the appearance and the inside of a physics package  218 . Components identical or corresponding to those in  FIG.  4    are assigned the same or corresponding symbols. A vacuum chamber  220  of the physics package  218  is made up of a substantially spherical main body  222 , and a protruding portion  30 . 
     In the main body  222 , a triaxial magnetic field correction coil  224  made up of circular coils is provided centered in the clock transition space  52 . To simplify the diagram,  FIG.  20    only shows a pair of Helmholtz-type coils in each axis direction. In actuality, one or more non-Helmholtz-type coils are assumed to be further provided on each axis. The outer edge of the triaxial magnetic field correction coil  224  can be configured to form a substantially spherical surface. Accordingly, by installing the triaxial magnetic field correction coil  224  in the substantially spherical main body  222  around the inner wall, interference with the other components installed in the inner space of the main body  222  can be prevented, and design flexibility is improved. 
     Likewise, the triaxial magnetic field correction coil may be constructed using square coils. Similar to the circular coils, there may be adopted a Helmholtz type triaxial magnetic field correction coil including each pair of square coils, a Maxwell type triaxial magnetic field correction coil including three square coils, a tetra type triaxial magnetic field correction coil including two pair of square coils, and the like. These triaxial magnetic field correction coils have a cubic shape or a slightly distorted cubic shape as a whole. Accordingly, attachment to the inner wall or the inner wall surface of the substantially-cubic-shaped or substantially-cuboid-shaped vacuum chamber enables effective utilization of the inner space of the vacuum chamber. 
     The triaxial magnetic field correction coil may be attached to a position closer to the clock transition space  52  than to the inner wall of the main body  22 .  FIG.  21    schematically shows the inside of the optical resonator  46  shown in  FIG.  1    and therearound. Note that in  FIG.  21   , instead of the triaxial magnetic field correction coil  96  in  FIG.  1   , a cubic-shaped triaxial magnetic field correction coil  230  is provided at a space between the coil  44  for the Zeeman slower and the coil  48  for the MOT device. The cubic-shaped triaxial magnetic field correction coil  230  is arranged centered in the clock transition space  52  in the cryostat reservoir  54 . The cubic-shaped triaxial magnetic field correction coil  230  is formed of two pairs of coil groups made up of square coils in each of the three-axis directions. One pair of the two pairs of coil groups is a Helmholtz-type coil, and the other pair is a non-Helmholtz-type coil. In a case where the magnitudes and directions of currents are not specifically limited, the cubic-shaped triaxial magnetic field correction coil  230  is capable of compensating the magnetic field component up to the third order spatial derivative term. Alternatively, in a case where currents having the same magnitude flow in the same direction, similar to the case of the non-Helmholtz-type coils of the triaxial magnetic field correction coils  96  shown in  FIGS.  5  to  11   , the magnetic field component up to the second order spatial derivative term can be simply compensated. 
     In comparison with the triaxial magnetic field correction coils  96  shown in  FIGS.  5  to  11   , the triaxial magnetic field correction coil  230  is significantly small sized, and is close to the clock transition space  52 . Accordingly, the magnetic field formed in the clock transition space  52  varies in a relatively small spatial scale. However, the triaxial magnetic field correction coil  230 , through the Helmholtz-type coil, can compensate the constant term and the first order spatial derivative term over a relatively large range. At least the magnetic field component of the second order spatial derivative term can be compensated through the non-Helmholtz-type coil. Consequently, the magnetic field of the clock transition space  52  is uniformly nullified with sufficiently high accuracy. Since the triaxial magnetic field correction coil  230  resides at a position close to the clock transition space  52 , the current caused to flow to form the magnetic field can be significantly small, thereby achieving excellent power saving capability. 
       FIG.  22    is a side view from a direction A in  FIG.  21   . As shown in  FIG.  22   , the capture space  50  is irradiated with two MOT optical beams  86   a  and  86   b  that are perpendicular to the Z-axis and inclined by 45 degrees from the X-axis and the Y-axis. Also in the direction perpendicular to the sheet, a MOT optical beam  84  is emitted. To adjust the gradient magnetic field formed in and around the capture space  50 , a bias coil  234  is arranged centered in the capture space  50 . The bias coil  234  includes: a pair of Helmholtz type circular coils  234   a  that face each other along the beam axis; a pair of Helmholtz type square coils  234   b  that face each other along the X-axis; and a pair of Helmholtz type square coils  234   c  that face each other along the Y-axis. The bias coil  234  corrects the gradient magnetic field to a desired distribution by adjusting the constant term component or the first order spatial derivative term component through the coils in each axis. 
     In the X-axis passing through the capture space  50 , the optical lattice light beam  80  is emitted. The cryostat reservoir  54  including the clock transition space  52  is provided on the optical lattice light beam  80 . The triaxial magnetic field correction coil  230  is provided centered in the clock transition space  52  around the cryostat reservoir  54 . The triaxial magnetic field correction coil  230  includes: a coil group  230   b  whose plane has a normal in parallel with the Z-axis; and two coil groups  230   a  and  230   c  whose planes have a normal perpendicular to the Z-axis and were inclined from the X-axis and the Y-axis by 45 degrees. That is, the triaxial magnetic field correction coil  230  is arranged in a state where a cubic shape along the X-axis, the Y-axis, and the Z-axis is rotated about the Z-axis by 45 degrees. 
     The triaxial magnetic field correction coil  230  is supported by flanges  44   a  and  48   a  that are support members supporting the MOT device. Accordingly, the triaxial magnetic field correction coil  230  must be arranged close to the capture space  50  at the center of the MOT device. Meanwhile, the triaxial magnetic field correction coil  230  must be arranged so as to prevent interference with the MOT optical beams  86   a  and  86   b  passing through the capture space  50 . Accordingly, the triaxial magnetic field correction coil  230  is arranged to have a shape along the Z-axis and the MOT optical beams  86   a  and  86   b.    
     The triaxial magnetic field correction coil  230  includes a Helmholtz-type coil and a non-Helmholtz-type coil in each axis direction. Equalization of the magnetic field in a large space that includes correction of the higher order spatial derivative terms can be achieved. Accordingly, also in the X-axis direction that is the direction of the optical lattice light beam  80 , the magnetic field can be corrected with high accuracy. 
     Note that the triaxial magnetic field correction coil  230  does not enclose the capture space  50 . Accordingly, the magnetic field in the capture space  50  cannot be corrected. Accordingly, as described above, the bias coil  234  that corrects the gradient magnetic field is provided in the capture space  50 . 
       FIGS.  20  and  21    exemplify the triaxial magnetic field correction coil  230  made of square coils. However, for example, coils having other shapes, such as circular coils instead of the square coils, may be adopted. For example, the cylindrical-shaped triaxial magnetic field correction coil  96  shown in  FIGS.  5  to  11    may be adopted. 
     The triaxial magnetic field correction coil may be provided to each of a position close to the clock transition space  52  and a position around the inner wall of the main body  22 . For example, it is conceivable that a Helmholtz-type coil may be provided around the inner wall of the main body  22 , and a non-Helmholtz-type coil may be provided at a position close to the clock transition space  52 . By providing the non-Helmholtz-type coil at the position close to the clock transition space  52 , a magnetic field having a large curvature can be easily corrected. 
     (4) Adjustment of Magnetic Field Correction Coil 
     Adjustment of the magnetic field by the triaxial magnetic field correction coil is described. To correct the magnetic field, the magnetic field distribution is periodically observed around the clock transition space  52 , and when a non-uniform magnetic field distribution is identified, the currents through the triaxial magnetic field correction coil  96  are operated so as to cancel the magnetic field distribution. The magnetic field distribution is observed by moving the atom population confined in the optical lattice by means of the moving optical lattice. These operations embody a situation where the individual atoms included in the atom group are always in a zero magnetic field. 
       FIGS.  23 A and  23 B  schematically show a process of adjusting the triaxial magnetic field correction coil.  FIG.  23 A  shows a state of moving an atom population  240  confined in the moving optical lattice along the X-axis.  FIG.  23 B  shows the relationship between the fluorescence transition and the clock transition. 
     As shown in  FIG.  23 A , the atom population  240  is confined in the lattices sequential in the X-axis direction with a certain spatial extent. In the diagram, representative positions on the X-coordinate where the atom population  240  moves are represented as a position X 1 , a position X 2 , a position X 3 , a position X 4 , and a position X 5 . These are positions set in a correction space  242  set for correcting the magnetic field. The correction space  242  is set over a wide range including the clock transition space  52  that performed actual measurement. The embodiment adopts the one-dimensional lattice with the optical lattice extending in the X-axis direction, and the atom population  240  ranges in a manner extending in the X-axis direction. It is particularly intended to highly accurately nullify the magnetic field in the X-axis direction. The correction space  242  is set over an extent in the X-axis direction. Note that in a case where the optical lattice is formed two-dimensionally, it is desirable to set a correction space obtained by extending the clock transition space  52  in the two-dimensional direction. In a case where the optical lattice is formed three-dimensionally, it is desirable to set a correction space obtained by extending the clock transition space  52  in a three-dimensional direction. 
     At each position in the moved correction space  242 , the atom population  240  is irradiated with laser light for exciting clock transition, and the clock transition is excited. The frequency of the laser light is swept, and the frequency of clock transition is measured at each position. The electron shelving method is used to observe the excitation rate of clock transition. The electron shelving method excites clock transition and subsequently moves the atoms to a fluorescent observation space  243 . As shown in  FIG.  23 B , by emitting light of fluorescence transition, the atoms emit fluorescent light  244 , depending on the excitation rate. The fluorescent light is observed by an optical receiver  246 . The clock transition is subjected to Zeeman splitting depending on the magnitude of the magnetic field at each position. Accordingly, the magnetic field distribution at each position is obtained from information on the Zeeman splitting. In a lower part of  FIG.  23 A , the thus obtained frequency distribution is shown. According to this method, the magnetic field can be measured even at a location where no fluorescent light can be observed (in a cryo head etc.). Instead of the electron shelving method, a non-destructive measurement method using a measurement of phase shifts of atoms may be applicable to the measurement of the excitation rate of clock transition. 
       FIGS.  24  and  25    are flowcharts illustrating procedures of correcting the magnetic field by the triaxial magnetic field correction coil. First, according to the procedures shown in  FIG.  24   , calibration is performed. In calibration, currents in all the coils constituting the triaxial magnetic field correction coil are stopped (set to 0 A), and the distribution of the magnetic field in the three-axis directions are measured (S 10 ). As for the magnetic field measurement, for example, the magnetic fields in the three-axis directions are measured using a magnetic sensor, such as a small-sized coil or a Hall element. The measured magnetic field represents the value of the background in a state where the triaxial magnetic field correction coil is not used. Next, currents having the same magnitude ( 1  A in  FIG.  24   ) are caused to flow through all the coils (n coils), and the magnetic field distributions in the three-axis directions are measured using the magnetic field sensor or the like (S 12  to S 18 ). By subtracting the background magnetic field from the obtained magnetic field distribution, a basic magnetic field formed by the current of 1 A in each coil can be obtained. 
     The calibration may measure the magnetic field of the correction space  242 . However, the correction space  242  is in the cryostat reservoir  54 . Accordingly, it is not always easy to install a magnetic sensor. Accordingly, the magnetic field may be measured adjacent to the correction space  242 , and the magnetic field may be estimated based on a result of an electromagnetic field simulation combined therewith. The magnetic field may be measured in the atmosphere instead of a vacuum. Accordingly, the basic magnetic field distribution formed by each coil of the triaxial magnetic field correction coil with a current of 1 A may be grasped. In principle, it is sufficient to perform the calibration once at a stage of creating the physics package  12 . 
     Next, according to the procedures shown in  FIG.  25   , the magnetic field is corrected. First, as described above, the atom population  240  is moved by the moving optical lattice, and the frequency of clock transition is measured at each position in the correction space  242  (S 20 ). The effect of Zeeman splitting is estimated, thus obtaining the magnetic field distribution in the correction space  242  (S 22 ). The magnetic field distribution is obtained as the absolute value of the magnetic field. 
     Subsequently, the current corresponding to the magnetic field to be corrected by each coil is determined using an optimization method, such as the least squares method (S 24 ). That is, the superimposition coefficient such that the magnetic field formed in the correction space  242  is uniformly zero when the basic magnetic fields formed by the respective superimposed coils is obtained. Note that as described above, in the case of using both the Helmholtz-type coil and the non-Helmholtz-type coil, first, the optimal superimposition coefficients for the higher order spatial derivative terms generated by the non-Helmholtz-type coil are obtained through the least squares method or the like. Next, the optimal superimposition for the constant term and the first order spatial derivative term generated by the Helmholtz-type coil is obtained by the least squares method or the like. Accordingly, calculation is simplified, and the calculation accuracy is improved. The obtained superimposition coefficients indicate the direction and magnitude of the current caused to flow to each coil. The obtained currents are caused to flow to the triaxial magnetic field correction coil, thereby enabling correction of the magnetic fields of the three axes (S 26 ). 
     The correction indicated in  FIG.  25    is not necessarily frequently performed under a normal condition where the magnetic field vary little. For example, in a case where clock transition is repetitively measured in the clock transition space  52 , it is sufficient to perform the correction shown in  FIG.  25    every predetermined number of times. It is conceivable that in the case where the clock transition is measured in the clock transition space  52 , the magnitude of Zeeman splitting is always verified, and when the magnitude becomes a predetermined value or more, the correction shown in  FIG.  25    is performed. 
     In a case where the magnetic field of the triaxial magnetic field correction coil is corrected for the range of the correction space  242 , it is expected to stably uniformly nullify the magnetic field of the clock transition space  52 , in comparison with the case for the range of the clock transition space  52 . For example, it is conceivable that this is because fine-scale disturbances, such as a slight fluctuation of the magnetic field, the error of magnetic field measurement, and the error of the basic magnetic field of each coil, affect the case where only a narrow space, such as the clock transition space  52 , is adopted as a target. In actuality, in an experiment, the correction space  242  was adopted as a target and corrected, and a result of improved accuracy was obtained. 
     In the example shown in  FIGS.  23 A and  25   , using the moving optical lattice, the atom population  240  is moved to each place in the correction space  242 . On the other hand,  FIG.  26    schematically shows an example of measuring the magnetic field distribution in the correction space  242  at one time. 
     In  FIG.  26   , the atom population  250  is confined in the optical lattice over the entire area of the correction space  242 . The fluorescent light beams  252   a ,  252   b ,  252   c ,  252   d , and  252   e  of the atom population  250  are received at one time with spatial position information being left, by a CCD camera  254 , and the frequencies are obtained. Accordingly, the magnetic field distribution of the correction space  242  is immediately obtained. 
     (5) Individual Magnetic Field Compensation Coil 
     As described in the aforementioned (1), for the Peltier element (refrigerator  58 ), which is a large current device, the individual magnetic field compensation coil  102  for the refrigerator is provided, and compensates the magnetic field in the clock transition space  52 . For the heater of the atomic oven  40 , the individual magnetic field compensation coil  104  for the atomic oven is provided, and compensates the magnetic field in the clock transition space  52 . In a case of compensating the entire large stray magnetic field from the large current device by the triaxial magnetic field correction coil, it is necessary to increase the order of the triaxial magnetic field correction coil, and to increase the current. Accordingly, it is effective to provide individual magnetic field compensation coils to compensate the magnetic field. Here, the individual magnetic field compensation coil  102  for the refrigerator is exemplified and described in detail. 
       FIG.  27    schematically shows an example of configurations of the cryostat reservoir  54 , the thermal link member  56 , the refrigerator  58 , and the individual magnetic field compensation coil  102  for the refrigerator. The cryostat reservoir  54  is a hollow component that encloses the clock transition space  52 . Although not shown, an opening for allowing optical lattice light to pass therethrough internally is provided along the X-axis on the wall part of the cryostat reservoir  54 . The cryostat reservoir  54  is made of oxygen-free copper having high thermal conductivity or the like. 
     The thermal link member  56  is attached to the cryostat reservoir  54 . The thermal link member  56  is a member that serves as a support structure that supports the cryostat reservoir  54  and also as a path that removes heat from the cryostat reservoir  54 . The thermal link member  56  is also made of oxygen-free copper having high thermal conductivity or the like. 
     The refrigerator  58  includes a Peltier element  58   a , a radiator plate  58   b , a heat-insulating member  58   c , and permalloy magnetic field shields  58   d  and  58   e . The Peltier element  58   a  is connected to the thermal link member  56 , and removes heat from the thermal link member  56  with current flowing therethrough. The radiator plate  58   b  is a member made of oxygen-free copper having high thermal conductivity or the like. The radiator plate  58   b  is provided on the outer wall of the vacuum chamber  20 , and radiates heat transmitted from the Peltier element  58   a  to the outside of the vacuum chamber  20 . 
     The heat-insulating member  58   c  secures the heat insulation between the permalloy magnetic field shield  58   d  and the thermal link member  56 . The heat-insulating member  58   c  is made of a member, such as of silica having low thermal conductivity, and is spherically formed in order to reduce the number of contacts between the permalloy magnetic field shield  58   d  and the thermal link member  56 . The permalloy magnetic field shield  58   e  is a magnetic field shield, and is made of permalloy, which has high thermal conductivity and high permeability. The permalloy magnetic field shield  58   e  is provided between the Peltier element  58   a  and the radiator plate  58   b , and transmits heat from the Peltier element  58   a  to the radiator plate  58   b.    
     A temperature sensor  260  that includes a thermocouple, a thermistor, or the like is provided in the cryostat reservoir  54 , and inputs a measured temperature T 1  into a control device  262 . A temperature sensor  264  is provided at or around the radiator plate  58   b , and inputs a measured temperature T 2  into the control device  262 . 
     The control device  262  controlled current so as to keep the temperature T 1  of the cryostat reservoir  54  to a certain low temperature (e.g., 190K). The control is performed, for example, according to PID (Proportional Integral Differential) control in consideration also of the temperature T 2  on the radiator plate  58   b  side. The determined current is caused to flow to the Peltier element  58   a  through a current path  266 . 
     The Peltier element  58   a  is a thermoelectric element that moves heat depending on the flowing current. By causing the current to flow, the Peltier element  58   a  removes heat from the thermal link member  56  (and from the low cryostat reservoir  54  connected to the thermal link member  56 ) on the low temperature side, and releases the heat to the permalloy magnetic field shield  58   e  (and to the radiator plate  58   b  connected to the permalloy magnetic field shield  58   e ) on the high temperature side. 
     Through the Peltier element  58   a , a large current having, for example, about several amperes is caused to flow. Accordingly, a large magnetic field is generated. The majority of the Peltier element  58   a  is covered with the permalloy magnetic field shield  58   d  and the permalloy magnetic field shield  58   e  which are of high permeability material. Accordingly, most of the generated magnetic field flows in these members, and is not leaked to the outside. However, in view of thermal conduction, a magnetic field is not allowed to be provided between the thermal link member  56  and the Peltier element  58   a . Accordingly, a stray magnetic field  270  is generated. The stray magnetic field  270  disturbs the magnetic field in the clock transition space  52  in the cryostat reservoir  54 . 
     In the embodiment, the individual magnetic field compensation coil  102  for the refrigerator is provided around the thermal link member  56  serving as an opening portion where the magnetic field cannot be shielded. The individual magnetic field compensation coil  102  for the refrigerator generates a compensation magnetic field  272  when a current flows. 
     The current is caused to flow to the individual magnetic field compensation coil  102  for the refrigerator by a current path  268  branched off the current path  266 . That is, the Peltier element  58   a  and the individual magnetic field compensation coil  102  for the refrigerator have a relationship of being connected to the same current path in parallel. The electrical resistance of the Peltier element  58   a  and the electrical resistance of the individual magnetic field compensation coil  102  for the refrigerator may be assumed to have constant values in a temperature environment where measurement is performed, although the values vary slightly. Consequently, the current that flows from the control device  262  to the current path  266  is distributed to the Peltier element  58   a  and the individual magnetic field compensation coil  102  for the refrigerator at constant ratios. 
     When the current flowing through the Peltier element  58   a  increases, the current flowing through the individual magnetic field compensation coil  102  for the refrigerator increases proportionally. Accordingly, when the stray magnetic field  270  from the Peltier element  58   a  increases, the compensation magnetic field  272  generated by the individual magnetic field compensation coil  102  for the refrigerator increases in the same manner. The individual magnetic field compensation coil  102  for the refrigerator is formed so as to compensate the stray magnetic field  270  in the clock transition space  52  in the cryostat reservoir  54  (so as to generate a magnetic field having the same magnitude in the opposite direction) when a current having a certain magnitude flows through the current path  266 . Accordingly, even when the current varies, the magnetic field can be compensated. Note that the currents flow also through the current paths  266  and  268 . However, the reciprocating currents flow close to each other through the current paths  266  and  268 . Accordingly, the generated magnetic field is small, which raises no problem. 
     The arrangement of the current paths  266  and  268  may be regarded as compensation current control means for dynamically changing the current flowing through the individual magnetic field compensation coil  102  for the refrigerator depending on the stray magnetic field  270 . The compensation current control means may be constructed in another manner. For example, a mode where the control device  262  causes the current required by the computation to flow through the individual magnetic field compensation coil  102  for the refrigerator can be exemplified. 
     In the example shown in  FIG.  27   , it is assumed that the individual magnetic field compensation coil  102  for the refrigerator is formed of one coil wound around the thermal link member  56 . According to this configuration, the individual magnetic field compensation coil  102  for the refrigerator is provided adjacent to the wall of the vacuum chamber  20 , which can prevent the configuration around the cryostat reservoir  54  from being complicated. However, no specific limitation is imposed on the installation location of the individual magnetic field compensation coil  102  for the refrigerator. For example, it may be installed adjacent to the cryostat reservoir  54 . In a case where the individual magnetic field compensation coil  102  for the refrigerator is installed adjacent to the cryostat reservoir  54 , the individual magnetic field compensation coil  102  for the refrigerator can be reduced in size, and power consumption can be reduced. 
     The individual magnetic field compensation coil  102  for the refrigerator is not necessarily formed of one coil, and may be formed of multiple coils. In a case where the distribution of the stray magnetic field in the clock transition space  52  is complicated, there is a possibility that use of multiple coils can relatively simply achieve compensation. 
     The current device, the individual magnetic field compensation coil, and the compensation current control means constitute the magnetic field compensation module. The magnetic field compensation module can achieve accurate magnetic field compensation. Accordingly, this module is applicable to various devices including the optical lattice clock  10 . 
     (6) Zeeman Slower 
       FIG.  28    shows sectional views of the coil  44  for the Zeeman slower, and the coil  48  for the MOT device. In the illustrated coil  44  for the Zeeman slower, a coil  282  is wound around an elongated cylindrical-shaped bobbin  280  arranged coaxially with the beam axis. A hollow portion of the bobbin around the center is a space through which the atom beam  42  travels along the beam axis. 
     In view of functionality, the greatest part of the coil  282  constitutes a decreasing type Zeeman coil portion  284  where the number of turns decreases slightly from the upstream side to the downstream side of the beam axis. The furthest downstream side of the coil  282  in the beam axis and therearound form a MOT coil portion  286  having a large number of turns. The covered conductor wires of the Zeeman coil portion  284  and the MOT coil portion  286  are continuously connected to each other, the magnetic field formed by the Zeeman coil portion  284  extends adjacent to the MOT coil portion  286 , and the magnetic field formed by the MOT coil portion  286  extends downstream of the Zeeman coil portion  284 . Consequently, it should be noted that the boundary between the Zeeman coil portion  284  and the MOT coil portion  286  cannot be clearly defined. 
     On the beam-axis upstream side of the bobbin  280  there is provided a disk-shaped upstream flange  288  having a larger radius than the maximum diameter portion of the Zeeman coil portion  284 . The upstream flange  288  is attached to the cylindrical wall  32  of the protruding portion  30  of the vacuum chamber  20 . A mirror supporter, not shown, is attached to a front part of the upstream flange  288 . The optical mirror  76  is attached to the distal end of the mirror supporter. 
     On the beam-axis downstream side of the bobbin  280 , two circular ring-shaped downstream flanges  290  and  292  formed to have a diameter substantially identical to that of the MOT coil portion  286  are provided. The downstream flange  290  is formed to have a circular ring shape that is relatively thick along the beam axis direction, and is provided around the boundary between the Zeeman coil portion  284  and the MOT coil portion  286 . The downstream flange  292  is formed to have a circular ring shape that is relatively thin along the beam axis direction, and is provided downstream of the MOT coil portion  286 . The upper parts of the downstream flanges  290  and  292  are attached to an upper support member  312 , and the lower parts of the flanges are attached to a lower support member  314 . The upper support member  312  and the lower support member  314  are attached to the rear circular wall  28  of the main body  22  of the vacuum chamber  20 . 
     The coil  48  for the MOT device is arranged downstream of the coil  44  for the Zeeman slower by a predetermined distance. In the coil  48  for the MOT device, a MOT coil  302  is wound around a short cylindrical-shaped bobbin  300  provided coaxially with the beam axis. On the beam-axis upstream side of the bobbin  300 , a thin circular ring-shaped flange  304  having a diameter substantially identical to that of the MOT coil  302  is provided. On the beam-axis downstream side of the bobbin  300 , a relatively thick circular ring-shaped flange  306  having a diameter substantially identical to that of the MOT coil  302  is provided. The upper parts of the flanges  304  and  306  are attached and fixed to the upper support member  312 . 
     In the coil  44  for the Zeeman slower, the bobbin  280 , the upstream flange  288 , and the downstream flanges  290  and  292  are made of copper or the like, which has high thermal conductivity and low permeability. The bobbin  280 , the upstream flange  288 , and the downstream flanges  290  and  292  are combined to each other by welding to have high strength and to be in close contact. 
     In the coil  44  for the Zeeman slower, more coil is wound around on the beam-axis upstream side. The upstream side has a larger weight than the downstream side. By combining the upstream flange  288  with the cylindrical wall  32  of the protruding portion  30  of the vacuum chamber  20 , the coil  44  for the Zeeman slower is stably arranged in the vacuum chamber  20 . 
     In the coil  44  for the Zeeman slower, heat is generated by the current flowing through the coil  282 . The vacuum chamber  20  is in a vacuum. Unlike the atmosphere, thermal conduction via a gas does not occur. Accordingly, in the coil  44  for the Zeeman slower, a small cooling effect due to blackbody radiation occurs. However, the heat of the coil  282  is mainly required to be removed by thermal conduction via a solid. The bobbin  280  is in contact with the coil  282 , and heat is effectively transferred from the coil  282 . The upstream flange  288  and the downstream flanges  290  and  292  have a large area in contact with the coil  282 , and remove heat from the coil  282 . As shown in  FIG.  2   , the upstream flange  288  is connected to the cooler  92  for the Zeeman slower at the cylindrical wall  32  of the protruding portion  30 . In the cooler  92  for the Zeeman slower, cooling water is circulated in a water-cooling tube made of copper or the like, thereby cooling the upstream flange  288 . Thus, excessive increase in temperature of the coil  44  for the Zeeman slower is prevented. 
     The bobbin  300  and the flanges  304  and  306  of the coil  48  for the MOT device also have high thermal conductivities, and are made of copper or the like having low permeability. The bobbin  300 , and the flanges  304  and  306  are combined with each other by welding to have high strength and to be in close contact. The MOT coil  302  of the coil  48  for the MOT device is of smaller size and lighter weight than the coil  282  of the coil  44  for the Zeeman slower. The entire coil  48  for the MOT device also has a light weight. Accordingly, the coil  48  for the MOT device is stably attached to the rear circular wall  28  via the upper support member  312  to which the flanges  304  and  306  are fixed. 
     The current caused to flow is smaller and the amount of heat generation is smaller in the MOT coil  302  of the coil  48  for the MOT device than in the coil  282  of the coil  44  for the Zeeman slower. The peripheries of the MOT coil  302  in three directions of the coil  48  for the MOT device are enclosed by the bobbin  300  and the flanges  304  and  306 . Accordingly, the heat generated by the MOT coil  302  is transmitted to the cooler  94  for the MOT device via the upper support member  312 . It is assumed that a cooling scheme is adopted for the cooler  94  for the MOT device. However, in a case where the heat quantity to be removed is small, an air cooling scheme may be adopted. 
     In the example in  FIG.  28   , the number of turns of the coil  282  decreases roughly monotonically. However, in detail, irregularities are formed in the beam axis direction. One reason for providing the irregularities is to obtain a desired magnetic field intensity at a specific position on the beam axis. For example, in the capture space  50  that captures atoms, the magnetic field is required to be zero. Another reason may be to adopt a configuration of causing no magnetic field at positions where no magnetic field is required, in view of power saving. It is sufficient that the coil  44  for the Zeeman slower generates a magnetic field necessary to decelerate atoms or confine atoms. A reason for providing irregularities may be a request for mechanical support or thermal radiation. The weight of the coil increases with the number of turns. Accordingly, it becomes difficult to support. Furthermore, the heat discharge from the coil increases. Accordingly, it is conceivable to increase the number of turns of the coil of a portion advantageous for support, or a portion having a high heat radiation efficiently. In the example shown in  FIG.  28   , the coil  282  of the coil  44  for the Zeeman slower is formed to have a relatively convex shape where the number of turns is large at a portion in contact with the upstream flange  288 , and have a relatively concave shape where the number of turns is relatively small on the downstream side. Accordingly, the barycenter of the coil  44  for the Zeeman slower moves toward the upstream flange  288 , and fixation by the upstream flange  288  is stable. The contact area between the coil  282  and the upstream flange  288  is large, and thermal conduction is effectively achieved from the coil  282  to the upstream flange  288 . 
     Here, by reference to  FIG.  29   , a void in the coil is described.  FIG.  29    shows sectional views of upper parts of two Zeeman coils  320  and  330 . In the Zeeman coil  320 , the number of turns monotonically decreases in the beam axis direction including a portion  322 . On the other hand, in the Zeeman coil  330 , the number of turns is locally small at a portion  332  called a void. However, in the Zeeman coil  330 , the number of turns is locally large before and after the portion  332  in the beam axis direction. Accordingly, the distribution of the magnetic field created by the entire Zeeman coil  330  is substantially equal to the distribution of the magnetic field created by the Zeeman coil  320 . 
     The way of forming the coil shape at and around the void can be theoretically obtained. The magnetic field distribution generated by a unit component follows the Biot-Savart law. Conversion from the magnetic field distribution to the current distribution can be dealt with as the deconvolution method, or the inverse problem in a general perspective. The method of obtaining a solution of a minimum current path through the inverse problem is described, for example, in Mansfield P, Grannell PK. “NMR diffraction in solids.” J Phys C: Solid State Phys 6: L422-L427, 1973. However, it is obvious that there are some multiple roots only if there is no restriction to the minimum current. In  FIG.  29   , provided that the solution of the minimum current path satisfying a desired magnetic field distribution is the Zeeman coil  320 , the Zeeman coil  330  with the increased current density around the void could also form a desired magnetic field distribution. 
     As for the coil  282  shown in  FIG.  28   , the downstream flange  290  is provided at the middle of the coil  282 . This means that the downstream flange  290  is provided at the large void. Before and after the downstream flange  290  in the beam direction, the numbers of turns is configured to be greater than in a case without the downstream flange  290 , thus removing or reducing the adverse effects of the downstream flange  290 . 
       FIG.  30    shows the magnetic field distribution at the coil  44  for the Zeeman slower and the coil  48  for the MOT device. The x axis represents the position on the beam axis. The origin corresponds to the capture space  50 . The y axis represents the magnitude of the magnetic field on the beam axis. The coil  44  for the Zeeman slower and coil  48  for the MOT device are formed symmetrically with respect to the beam axis. Accordingly, the magnetic field on the beam axis only has a component in the beam axis direction. On the beam axis, a position where the coil  282  of the coil  44  for the Zeeman slower is arranged, and a position where the MOT coil  302  of the coil  48  for the MOT device is arranged are indicated. Points on the graph indicate calculated values of the magnetic field. Narrow lines indicate the value of the magnetic field that is ideal for decelerating atoms toward the capture space  50  by the Zeeman slower. 
     The magnetic field becomes the maximum slightly downstream of the end of the coil  282  on the upstream side. On the slightly upstream side of the position of the maximum value, the value of the magnetic field abruptly decreases. On the further upstream side, the value gradually approaches zero. The ideal magnetic field has a distribution where the magnetic field outside of the coil  282  becomes zero, and no magnetic field leaks to the outside. However, generation of the magnetic field due to the current has a spatial extension. For example, in a case without an opposite directional coil compensating (canceling) the external magnetic field, the magnetic field outside of the coil  282  cannot be entirely zero. 
     On the downstream side of the position with the magnetic field of the maximum value, the magnetic field monotonically decreases. The number of turns of the coil has slight irregularities as described above. The monotonically decreasing magnetic field for Zeeman slower is created by the effect of the surrounding coil. The magnetic field having the gradient substantially coincides with the ideal magnetic field distribution for Zeeman slower, and indicates steady deceleration of atoms toward the capture space  50 . 
     The magnetic field abruptly decreases before the end of the downstream side of the coil  282 . The MOT coil part  286  therearound has a large number of turns. No coil resides on the further downstream side. Accordingly, the value of the magnetic field rapidly decreases. 
     The magnetic field decreases with a substantially constant slope, and becomes zero in the capture space  50 . Furthermore, the magnetic field decreases with the same slope, and becomes the minimum value (the negative value became strongest) around the MOT coil  302  of the coil  48  for the MOT device. This is because the MOT coil  302  causes the current to flow in the direction opposite to the coil  282 . A portion ranging from a portion around the MOT coil part  286  of the coil  282  to a portion around the MOT coil  302  approximately forms a Helmholtz-type coil. Accordingly, by causing the current to flow through the MOT coil  302  in the opposite direction, the magnetic field having a constant slope is allowed to be formed. Although not shown, the magnetic field having a constant slope is formed also in a direction perpendicular to the beam axis. The gradient magnetic field formed by the MOT device is irradiated with MOT optical beams in the respective three axes. Accordingly, the atoms are allowed to be captured in the capture space  50  at the origin. On the downstream side of the MOT coil  302 , the magnetic field gradually approaches zero. 
     As described above, the coil  44  for the Zeeman slower and the coil  48  for the MOT device are installed in the combined manner, and the length in the beam axis direction is allowed to be reduced in comparison with a case where the Zeeman slower and the MOT device are separately provided. The entire coil length can also be reduced, which could facilitate power savings and reduction in amount of heat generation. 
     Note that in a case where a background magnetic field is present, the position where the magnetic field is zero deviates from the capture space  50 . Accordingly, in the process of capturing the atoms, the triaxial magnetic field correction coil  96  or a bias coil for correcting the gradient magnetic field is adjusted, thus allowing generation of the compensation magnetic field that cancels the background magnetic field around the capture space  50 . 
     Next, by reference to  FIGS.  31 A and  32 B , an example of an increasing type coil  340  for a Zeeman slower is described.  FIG.  31 A  is a sectional view showing a state before the coil  340  for the Zeeman slower is attached to the inside of the vacuum chamber  20 .  FIG.  31 B  is a sectional view showing a state after the attachment. A coil  342  of the coil  340  for the Zeeman slower shown in  FIG.  31 A  serves as the Zeeman coil portion  344  whose greater part of the beam-axis upstream side has a function of a Zeeman coil. The furthest downstream side of the coil  342  serves as a MOT coil portion  346  where the function of the Zeeman coil and the function of the MOT coil reside in a combined manner. At the Zeeman coil portion  344 , the number of turns monotonically increases from the end of the upstream side to the downstream side. Around the end on the downstream side, irregularities are repeated, and subsequently the number of turns becomes the maximum on the most downstream side. For the sake of convenience, a portion with the maximum number of turns and therearound is called the MOT coil portion  346 . As described above, in view of functionality, the portion also plays a role of a Zeeman coil. 
     The coil  340  for the Zeeman slower internally includes a bobbin. A flange  350  is provided at the end on the upstream side. A flange  352  is provided at the middle of the coil  342  around the end on the downstream side. A flange  354  is provided on the end on the downstream side. The flanges  350 ,  352  and  354  are welded to the bobbin. 
     A mirror supporter, not shown, is attached to the furthest upstream flange  350 . The optical mirror  76  is fixed to the mirror supporter. 
     The downstream flanges  352  and  354  are linked to each other at portions other than the bobbin, and improve the strength. The flange  352  is a large disk that is thin and has a large radius. The flange  352  is attached to a circular ring supporter  370  made to have a ring shape. The ring of the circular ring supporter  370  internally includes a water-cooling tube  372  through which cooling water flows, and cools the coil  342  through the flange  352 . Right and left beams  374  are attached to an upper portion of the circular ring supporter  370 . Right and left beams  376  also serving as water-cooling tubes are attached to a lower part of the circular ring supporter  370 . The beams  374  and  376  are attached to the rear circular wall  28  of the main body  22  of the vacuum chamber  20 , and support the entire part including the coil  340  for the Zeeman slower. The beams  374  and  376  serve as exhaust heat paths for transmitting heat of the coil  342  to the rear circular wall  28 . Note that cooling water flowing through the beams  376  is allowed to be circulated to the radiator plate  58   b  of the refrigerator  58 . 
     This configuration assumes that a coil  380  for the MOT device is attached to the rear circular wall  28  by a separately provided support member. The coil  340  for the Zeeman slower is assumed to be positioned with the coil  380  for the MOT device by a positioning mechanism. 
       FIG.  32    is a diagram corresponding to  FIG.  30   , and shows the magnetic distribution in a case where the increasing type coil  340  for the Zeeman slower and the coil  380  for the MOT device are adopted. The magnetism gradually increases from the downstream side of the coil  342  of the coil  340  for the Zeeman slower, and becomes the maximum value before the MOT coil part  346 . The increase in magnetism well coincides with a target curve required to achieve the Zeeman slower. On the downstream side of the position with the maximum value, the magnetism rapidly decreases. Before and after the capture space  50  serving as the origin, the magnetism decreases from positive to negative at a substantially constant slope, and becomes zero in the capture space  50 . The magnetic field becomes the minimum around the coil  380  for the MOT device, and subsequently gradually approaches zero. 
     At a portion constituting the MOT device before and after the capture space  50 , the slope of the magnetic field becomes abrupt in comparison with the case of the decreasing type in  FIG.  30   . This is because the number of turns of the MOT coil  346  at the coil  342  is large, and the number of turns of the facing coil  380  for the MOT device is also large. By making the slope of the magnetic field steep, atoms can be captured with a short distance in the beam axis direction. 
     The increasing type coil  340  for the Zeeman slower shown in  FIG.  32    can have a shortened length as compared with the decreasing type coil  44  for the Zeeman slower in  FIG.  30   . This is because the increasing type can efficiently decelerate atoms. The increasing type can suppress the magnetic field required to decelerate the atoms and achieve power savings in comparison with the decreasing type. 
     On the other hand, in the increasing type coil  340  for the Zeeman slower, the side of the capture space  50  is heavier. Accordingly, it is difficult to support the coil in the vacuum chamber  20 . The increasing type has the greater number of turns on the capture space  50  side. Accordingly, problems are caused in that the amount of heat generation is a large amount of heat generation around the center of the vacuum chamber  20  and it is difficult to cool. However, as described above, the coil  340  for the Zeeman slower is supported around the center of the vacuum chamber  20  by the circular ring supporter  370  having the cooling function. Accordingly, these problems are not caused. 
     The mode of attaching the increasing type coil  340  for the Zeeman slower shown in  FIGS.  31 A and  31 B  is only an example. Another mode may be adopted. By reference to  FIGS.  33 A and  33 B , a modified example is described. 
       FIG.  33 A  is a perspective view showing a state before the coil  390  for the Zeeman slower is attached to the inside of the vacuum chamber  20 .  FIG.  33 B  is a perspective view showing a state after the attachment. A coil  392  of the coil  390  for the Zeeman slower is wound in a manner similar to that of the coil  340  for the Zeeman slower. The configuration including a bobbin and flanges  394 ,  396 , and  398  is also almost the same. However, in the coil  390  for the Zeeman slower, the shape of the flange  396  provided close to the lower end in the beam direction is a semicircular shape that is substantially about the lower half. A portion that supports the flange  396  serves as a substantially U-shaped semicircular ring supporter  400  obtained by halving a circular ring. The semicircular ring supporter  400  is provided with a water-cooling tube  402 . 
     In the mode shown in  FIGS.  33 A and  33 B , the flange  396  has a semicircular shape. The cooling performance in a case where the cooling water circulation is equivalent decreases slightly. On the other hand, in the coil  390  for the Zeeman slower, a space is present above the flange  396 . Accordingly, in the vacuum chamber  20 , access is facilitated from the optical resonator  46  toward the atomic oven  40 . Presence of the space above the semicircular ring supporter  400  facilitates removal of the optical resonator  46 . Furthermore, since the distance of the water-cooling tube in the vertical direction is reduced, the disturbance of the flow caused by convection in the water-cooling tube can be easily prevented. Note that the flange  396  shown in  FIGS.  33 A and  33 B  can be appropriately provided pores in its surface. In the case of providing the pores, the efficiency of thermal conduction decreases, but reduction in weight can be achieved. Likewise, the flange  352  shown in  FIGS.  31 A and  31 B  could be appropriately provided with pores in its surface. 
       FIG.  34    is a sectional view of a coil  410  for an increasing type Zeeman slower according to another embodiment. The coil  410  for the Zeeman slower included a bobbin  412  having a thickness varying in the beam direction. The cylindrical-shaped bobbin  412  has a constant inner diameter, but an outer diameter that gradually decreases stepwise from the upstream to the downstream in the beam direction. A coil  414  wound around the bobbin  412  has a greater number of turns on the downstream side in the beam axis direction. Accordingly, the outer diameter of the coil  414  is substantially constant in the beam axis direction. 
     According to the configuration shown in  FIG.  34   , increase in the outer diameter of the bobbin  412  increases the contact area between the bobbin  412  and the coil  414 . Accordingly, the thermal conduction efficiently from the coil  414  to the bobbin  412  improves. A covered conductor wire can be wound using the steps of the bobbin  412 , thus facilitating installation of the coil  414 . 
     Note that this embodiment is not necessarily limiting; instead of a round wire having a round section, a rectangular flat wire having a rectangular section may be used for the covered conductor wire included in the coil  414 , which can further improve the thermal conduction efficiently with the bobbin  412  and the like. As described below, in a case where the periphery of the coil  414  is covered with a thermal conductive cover, the outer diameter of the coil  414  is constant, which facilitates bringing the cover into close contact with the coil  414 , and removing heat through the cover. 
     The example of installing the Zeeman slower in the vacuum chamber  20  has been described so far. The cooling mechanism of removing Joule heat caused by the coil is provided, which enables thermally stable installation of the Zeeman slower in the vacuum chamber  20 . Hereinafter, as another example, an example of sealing part or the entirety of the coil with a cover (i.e., encapsulation) is described. 
       FIGS.  35 A and  35 B  are side sectional views showing a coil  420  for a Zeeman slower and a cover  440 .  FIG.  35 A  shows a state before the cover  440  is attached to the coil  420  for the Zeeman slower.  FIG.  35 B  shows a state after the attachment. The coil  420  for the Zeeman slower is of the decreasing type, where the number of turns of the coil gradually decreases in the beam axis direction. 
     A bobbin  422  of the coil  420  for the Zeeman slower is provided with a flange  424  at the end of the upstream side of the beam axis, and also with a flange  426  at a middle position on the downstream side. Similar to the example described above, the bobbin  422  and the flanges  424  and  426  are made of copper or the like, which secures high thermal conductivity. The outer periphery of the flanges  424  and  426  are provided respectively with sealing members  428  and  430  made of indium. The sealing members  428  and  430  are formed to have a ring-shaped, relatively thin sheet shape, or a ring-shaped thick shape. Indium has a characteristic enabling achievement of stable vacuum sealing even with large temperature variation. The flange  426  is provided with a hermetic connector  432  that is a vacuum-resistant connector. 
     A coil  434  is wound around the bobbin  422  between the flange  424  and the flange  426 . A coil  436  is wound on the downstream side of the flange  426 . The coils  434  and  436  are each formed of a covered conductor wire including copper insulated with a resin. The coil  434  and the coil  436  are electrically connected via the hermetic connector  432 . 
     The cover  440  is formed to have a cylindrical shape. The cover  440  is made of copper, which is the same as that of the bobbin  422 , the flanges  424  and  426 , and the coils  434  and  436 , and prevents deformation due to thermal expansion. 
     The cover  440  is installed for coverage from the flange  424  to the flange  426 . That is, part of the inner periphery of upstream end of the cover  440  encloses part of the outer periphery of the flange  424 , and is sealed with the sealing member  428 . Part of the inner periphery of downstream end of the cover  440  encloses part of the outer periphery of the flange  426 , and is sealed with the sealing member  430 . The cover  440  is formed so as to have a positive tolerance from the length from the flange  424  to the flange  426 , and can securely enclose both the flanges. 
     The atmospheric pressure can be freely set in the cover  440  only if the sealing members  428  and  430  can securely achieve shieling. For example, air at the atmospheric pressure may be enclosed, or a roughly pumped vacuum may be used. The roughly pumped vacuum is a state of being rarefied using a turbopump or the like, and is set to about 1 to 0.1 Pa, for example. In the case where the inside of the cover  440  is the roughly pumped vacuum, the pressure difference between the inside and the outside of the cover  440  is small in a state where the vacuum chamber  20  is in a vacuum. Accordingly, the sealing surfaces by the sealing members  428  and  430  can be strongly prevented from being separated from each other. 
     An inert gas, such as nitrogen or helium, may be enclosed in the cover  440 . A gas having low reactivity with a resin used for the coil when the coil  434  is at a high temperature is selected as the inert gas. The pressure of the inert gas is not specifically limited, and may be one atmosphere, or a roughly pumped vacuum. The inside of the cover  440  may be filled with, for example, a lightweight resin, such as urethane foam. In this case, the strength of the cover  440  can be improved. 
     The coil  420  for the Zeeman slower becomes a high temperature due to Joule heat during energization. The coil  434  with the larger number of turns generates more Joule heat than the coil  436  with the smaller number of turns. Accordingly, the coil  434  tends to become a high temperature. When the temperature becomes higher, a minute amount of gas (this gas is called outgas) contained in the resin of the covered conductor wire included in the coil  434  is discharged. However, in the coil  420  for the Zeeman slower, the coil  434  is sealed by the bobbin  422 , the flanges  424  and  426 , and the cover  440 . Accordingly, no outgas leaks into the vacuum chamber  20 . This prevents an error of the clock transition that would otherwise be caused by the outgas. Consequently, the coil  420  for the Zeeman slower sealed by the cover  440  functions as a vacuum installation coil having high usability in a case of installation in a vacuum. 
     The cover  440  also serves as a thermal conduction medium between the flange  424  and the flange  426 . That is, thermal conduction between the flange  424  and the flange  426  is not only through the bobbin  422  but also through the cover  440 . Accordingly, there is also an advantageous effect of cooling the coils  434  and  436 . 
     The above description assumes that the cover  440  covers the outer peripheries of the flanges  424  and  426 , but is not in contact with the coil  434 . However, the cover  440  may be in contact with part or the entirety of the outer peripheral surface of the coil  434 . In this case, heat from the coil  434  is directly transferred to the cover  440 , which improves the heat radiation efficiently. In particular, in the case where the coil  414  has a constant outer diameter as with the coil  414  shown in  FIG.  34   , it is easy to achieve close contact with the inner periphery of the cover  440 . If it is difficult to form a shape bringing the cover  440  into contact with the outer peripheral surface of the coil  434 , a thermal conductive member may be inserted between the cover  440  and the coil  434 . 
     In the embodiment shown in  FIGS.  35 A and  35 B , the coil  434  is not covered with the cover  440 . This is because the number of turns of the coil  434  is small, and the necessity of addressing outgas discharge is low. The coil  434  is a portion including the MOT coil included in the MOT device, and the optical resonator  46  and the like are arranged adjacent to this portion. Accordingly, increase in diameter due to coverage of the coil  434  with the cover is prevented. However, if interference with the surrounding devices and components can be avoided, the entire part including the coil  434  may be covered with the cover and encapsulated. 
     In the example in  FIGS.  35 A and  35 B , the decreasing type coil  420  for the Zeeman slower is exemplified. However, even in the case of the increasing type, part or the entirety of what includes a portion having the large number of turns can be encapsulated. 
     Note that the above description assumes that the cover  440  is in close contact with the flanges  424  and  426  using the indium sealing members  428  and  430 , and the inside is made hermetic. Alternatively, sealing members made of another material instead of indium may be adopted. In the case of using the sealing members, the cover  440  may be detachably attached to the flanges  424  and  426  using fixation screws, for example. Alternatively, for example, the cover  440  and the flanges  424  and  426  may be brought into close contact with each other by a semipermanent sealing method, such as welding or vacuum brazing, and the inside may be made hermetic. 
     The above description exemplifies the optical lattice clock. However, those skilled in the art can apply each technology of this embodiment to other than the optical lattice clock. Specifically, the technology is also applicable to atomic clocks other than the optical lattice clock, and an atom interferometer that is an interferometer using atoms. Furthermore, this embodiment is applicable also to various types of quantum information processing devices for atoms (including ionized atoms). Here, the quantum information processing devices are devices that perform measurement, sensing, and information processing using the quantum states of atoms and light, and may be, for example, a magnetic field meter, an electric field meter, a quantum computer, a quantum simulator, a quantum repeater, and the like besides an atomic clock and an atom interferometer. The physics package of the quantum information processing device can achieve miniaturization or transportability by using the technology of this embodiment, similar to the physics package of the optical lattice clock. It should be noted that in such devices the clock transition space is not a space for clock measurement but is sometimes dealt with simply as a space for causing clock transition spectroscopy. 
     In such device, for example, by providing the triaxial magnetic field correction coil according to the embodiment, improvement in the accuracy of the device can possibly be achieved. By providing the three axes according to the embodiment in the vacuum chamber, miniaturization, transportability, or improvement in accuracy of the physical package can possibly be achieved. Furthermore, by introducing the magnetic field compensation module, the magnetic field distribution can be controlled with high accuracy. In the physics package using the vacuum chamber, installation of the vacuum installation coil is effective. 
     In the above description, for facilitating understanding, the specific aspects are described. However, these exemplify the embodiments, and may be variously embodied in other modes. 
     Hereinafter supplements of the embodiments are described. 
     (Supplement 1) 
     A magnetic field compensation module, including: 
     a current device that is provided in a vacuum chamber that encloses a clock transition space in which atoms are arranged, and allows current for the device to flow therethrough and generates a stray magnetic field; 
     a compensation coil that is provided adjacent to the current device, and allows current for the coil to flow therethrough; and 
     control means for dynamically changing current for the coil that is to flow through the compensation coil, and compensates the stray magnetic field with respect to the clock transition space. 
     (Supplement 2) 
     The magnetic field compensation module according to supplement 1, 
     wherein the current device is a Peltier element that cools an isothermal cryostat reservoir that maintains the clock transition space at a predetermined low temperature, and the control means changes the current for the coil in accordance with the temperature of the isothermal cryostat reservoir, or current for the device that is to flow through the Peltier element. 
     (Supplement 3) 
     The magnetic field compensation module according to supplement 1, 
     wherein a magnetic field shield made of a high permeability material is provided around the current device, and 
     the compensation coil compensates the stray magnetic field straying from the magnetic field shield. 
     (Supplement 4) 
     The magnetic field compensation module according to supplement 1, 
     wherein the control means includes a distributor wire that distributes the current for the coil from the current for the device, and distributes the current for the coil in accordance with the current for the device. 
     (Supplement 5) 
     A physics package system for an optical lattice clock, the system including the magnetic field compensation module according to supplement 1. 
     (Supplement 6) 
     A physics package system for an atomic clock, the system including the magnetic field compensation module according to supplement 1. 
     (Supplement 7) 
     A physics package system for an atom interferometer, the system including the magnetic field compensation module according to supplement 1. 
     (Supplement 8) 
     A physics package system for a quantum information processing device for atoms or ionized atoms, the system including the magnetic field compensation module according to supplement 1. 
     (Supplement 9) 
     A physics package system, including: 
     the magnetic field compensation module according to supplement 1; and 
     at least one atomic laser cooling technology device among a Zeeman slower, a magneto-optical trap, and an optical lattice trap that guide the atoms into the clock transition space. 
     (Supplement 10) 
     A physics package, including: 
     a vacuum chamber; and 
     a Zeeman slower that includes a bobbin that is formed to have a cylindrical shape and allows an atom beam to flow along a beam axis in the cylinder, and a series of coils wound around the bobbin, and forms a magnetic field caused to have a spatial gradient in the cylinder, 
     wherein the bobbin is provided with a flange at which an outer surface of the cylinder is radially enlarged at an intermediate position in a direction of the beam axis, 
     the series of coils are wound around the bobbin beyond the flange, and 
     the Zeeman slower is installed in the vacuum chamber so that the flange is attached directly or indirectly to the vacuum chamber. 
     (Supplement 11) 
     The physics package according to supplement 10, 
     wherein the series of coils is of an increasing type where the number of turns is greater on a downstream side than that on an upstream side of the atom beam, and 
     the flange is provided on the downstream side of the bobbin. 
     (Supplement 12) 
     The physics package according to supplement 11, 
     wherein the vacuum chamber is formed to have a substantially cylindrical shape having a central axis in parallel with the beam axis, and 
     the flange is attached to a cylindrical wall on a downstream side of the atom beam in the vacuum chamber, indirectly using a support member. 
     (Supplement 13) 
     The physics package according to supplement 12, 
     wherein the flange is formed to have a substantially circular shape, 
     the support member includes a substantially circular ring-shaped supporter that supports an outer edge of the flange, and 
     the substantially circular ring-shaped supporter is provided with a cooling mechanism that flows a liquid coolant through a tube and cools the flange. 
     (Supplement 14) 
     The physics package according to supplement 12, 
     wherein the flange is formed to have a substantially sectoral shape being enlarged along a direction including a vertically downward component, 
     the support member includes a substantially U-shaped supporter that supports an outer edge of the flange, and 
     the substantially U-shaped supporter is provided with a cooling mechanism that flows a liquid coolant through a tube and cools the flange. 
     (Supplement 15) 
     The physics package according to supplement 10, 
     wherein the bobbin and the flange are made of a metal, and 
     the physics package is provided with a cooling mechanism that directly or indirectly cools the flange. 
     (Supplement 16) 
     The physics package according to supplement 10, further including 
     an opposite coil wound around the beam axis at a position apart on a downstream side of the atom beam from the Zeeman slower, 
     wherein the series of coils and the opposite coil form a MOT magnetic field between the series of coils and the opposite coil. 
     (Supplement 17) 
     A physics package for an optical lattice clock, the package including the physics package according to supplement 10. 
     (Supplement 18) 
     A physics package for an atomic clock, the package including the physics package according to supplement 10. 
     (Supplement 19) 
     A physics package for an atom interferometer, the package including the physics package according to supplement 10. 
     (Supplement 20) 
     A physics package for a quantum information processing device for atoms or ionized atoms, the package including the physics package according to supplement 10. 
     (Supplement 21) 
     A vacuum installation coil, the coil including: 
     a coil that is installed in a vacuum chamber, is wound around a beam axis in which an atom beam flows, and forms a magnetic field caused to have a spatial gradient; and 
     a sealing member that hermetically encloses part or an entirety of the coil. 
     (Supplement 22) 
     The vacuum installation coil according to supplement 21, 
     wherein the sealing member is made of a metal. 
     (Supplement 23) 
     The vacuum installation coil according to supplement 21, 
     wherein the sealing member includes: 
     a cylindrical shaped bobbin which is provided on an inner peripheral side of the coil and around which the coil is wound; 
     two flanges that are enlarged outer surfaces of the cylinder of the bobbin, and enclose side surfaces of the coil in a direction of the beam axis; and 
     a cover that encloses an outer peripheral side of the coil between the two flanges. 
     (Supplement 24) 
     The vacuum installation coil according to supplement 23, 
     wherein the cover encloses at least part of outer peripheries of the two flanges. 
     (Supplement 25) 
     The vacuum installation coil according to supplement 23, 
     wherein the cover is in direct contact with part or an entirety of an outer peripheral side of the coil, or in indirectly contact therewith via a thermally conductive member inserted into a space enclosed by the sealing member. 
     (Supplement 26) 
     The vacuum installation coil according to supplement 21, 
     wherein the number of turns of the coil varies in a direction of the beam axis, and 
     a range enclosed by the sealing member includes a portion having the maximum number of turns in the coil. 
     (Supplement 27) 
     The vacuum installation coil according to supplement 21, 
     wherein a space enclosed by the sealing member is kept more rarefied than an atmosphere. 
     (Supplement 28) 
     The vacuum installation coil according to supplement 21, 
     wherein an inert gas is enclosed in a space enclosed by the sealing member. 
     (Supplement 29) 
     The vacuum installation coil according to supplement 21, 
     wherein a space enclosed by the sealing member is filled with a foamed resin. 
     (Supplement 30) 
     The vacuum installation coil for an optical lattice clock according to supplement 21, 
     wherein the sealing member includes a vacuum-resistant connector, and 
     wherein a portion of the coil hermetically enclosed by the sealing member and a not enclosed portion are electrically connected through the vacuum-resistant connector. 
     (Supplement 31) 
     A physics package, including: 
     the vacuum installation coil according to supplement 21; and 
     a vacuum chamber. 
     (Supplement 32) 
     The physics package according to supplement 31, 
     wherein the coil is a decreasing type coil having a relatively small number of turns on a downstream side of the atom beam, 
     the physics package includes an opposite coil wound around the beam axis at a position apart on a downstream side of the atom beam from the decreasing type coil, 
     the decreasing type coil and the opposite coil form a gradient magnetic field for a MOT device between the decreasing type coil and the opposite coil, and 
     the sealing member hermetically encloses a portion including a furthest upstream side of the beam axis in the coil, and does not enclose a portion including a furthest downstream side. 
     (Supplement 33) 
     The physics package according to supplement 31, 
     wherein the coil is an increasing type coil having the relatively large number of turns on a downstream side of the atom beam, 
     the physics package includes an opposite coil wound around the beam axis at a position apart on a downstream side of the atom beam from the increasing type coil, 
     the increasing type coil and the opposite coil form a gradient magnetic field for a MOT device between the increasing type coil and the opposite coil, and 
     the sealing member hermetically encloses a portion including a furthest downstream side of the beam axis in the coil. 
     (Supplement 34) 
     A physics package for an optical lattice clock, the package including the physics package according to supplement 31. 
     (Supplement 35) 
     A physics package for an atomic clock, the package including the physics package according to supplement 31. 
     (Supplement 36) 
     A physics package for an atom interferometer, the package including the physics package according to supplement 31. 
     (Supplement 37) 
     A physics package for a quantum information processing device for atoms or ionized atoms, the package including the physics package according to supplement 31. 
     (Supplement 38) 
     A sealing member sealing a coil that is installed in a vacuum chamber, is wound around a beam axis in which an atom beam flows, and forms a magnetic field caused to have a spatial gradient, 
     wherein an area between the sealing member and the coil side is sealed with indium formed to have a ring sheet shape or thick shape, and hermetically encloses part or the entirety of the coil. 
     REFERENCE SIGNS LIST 
     
         
         
           
               10  optical lattice clock,  12  physics package,  14  optical system device,  16  control device,  18  PC,  20  vacuum chamber,  22  main body,  24  cylindrical wall,  26  front circular wall,  28  rear circular wall,  30  protruding portion,  32  cylindrical wall,  34  front circular wall,  38  leg,  40  atomic oven,  42  atom beam,  44  coil for Zeeman slower,  44   a  flange,  46  optical resonator,  48  coil for MOT device,  48   a  flange,  50  capture space,  52  clock transition space,  54  cryostat reservoir,  56  thermal link member,  58  refrigerator,  58   a  Peltier element,  58   b  radiator plate,  58   c  heat-insulating member,  58   d ,  58   e  permalloy magnetic field shield,  60  vacuum pump main body,  62  vacuum pump cartridge,  64 ,  66  vacuum-resistant optical window for optical lattice,  68  vacuum-resistant optical window for MOT light,  70 ,  72  vacuum-resistant optical window for MOT light,  74 ,  76  optical mirror,  80  optical lattice optical beam,  82  Zeeman slower optical beam,  84 ,  86   a ,  86   b  MOT optical beam,  90  cooler for atomic oven,  92  cooler for Zeeman slower,  94  cooler for MOT device,  96  triaxial magnetic field correction coil,  98  vacuum-resistant electric connector,  102  individual magnetic field compensation coil for refrigerator,  104  individual magnetic field compensation coil for atomic oven,  120  first coil group,  122 ,  124  coil,  130  second coil group,  132 ,  134  coil,  136 ,  138  arrow,  140  first coil group,  142  composite coil,  143 ,  144  Coil,  145  composite coil,  146 ,  147  coil,  150  second coil group,  152 ,  154  coil,  160  first coil group,  162  composite coil,  163 ,  164  coil,  165  composite coil,  166 ,  167  coil,  170  second coil group,  172 ,  174  coil,  180  holder,  182 ,  184 ,  186  frame,  190  correction coil,  192  current path,  194  insulator,  196  wiring path,  198  terminal connector,  199  boundary portion,  200 ,  202 ,  203 ,  204 ,  206 ,  208  current path,  210  correction coil,  212 ,  214  current path,  218  physics package,  220  vacuum chamber,  222  main body,  224 ,  230  triaxial magnetic field correction coil,  240  atom population,  242  correction space,  243  fluorescent observation space,  244  fluorescent light,  246  optical receiver,  250  atom population,  252   a ,  252   b ,  252   c ,  252   d ,  252   e  fluorescent light,  254  CCD camera,  260  temperature sensor,  262  control device,  264  temperature sensor,  266  current path,  268  current path,  270  stray magnetic field,  272  compensation magnetic field,  280  bobbin,  282  coil,  284  Zeeman coil part,  286  MOT coil part,  288  upstream flange,  290 ,  292  downstream flange,  300  bobbin,  302  MOT coil,  304 ,  306  flange,  312  upper support member,  314  lower support member,  320  Zeeman coil,  322  portion,  330  Zeeman coil,  332  portion,  340  coil for Zeeman slower,  342  coil,  344  Zeeman coil part,  346  MOT coil part,  350 ,  352 ,  354  flange,  370  circular ring supporter,  372  water-cooling tube,  374 ,  376  beam,  380  coil for MOT device,  390  coil for Zeeman slower,  392  coil,  394 ,  396 ,  398  flange,  400  semicircular ring supporter,  402  water-cooling tube,  410  coil for Zeeman slower,  412  bobbin,  414  coil,  420  coil for Zeeman slower,  422  bobbin,  424 ,  426  flange,  428 ,  430  sealing member,  432  hermetic connector,  434 ,  436  coil,  440  cover.