Patent Publication Number: US-10775450-B1

Title: Zero field parametric resonance magnetometer with triaxial sensitivity

Description:
The following is an application for patent under 35 USC 111 (a). This disclosure was made with government support under R44MH123492 awarded by the National Institutes of Health. The government has certain rights to the apparatus and method. 
    
    
     BACKGROUND 
     High sensitivity magnetometers, including zero-field paramagnetic resonance magnetometers (ZF-PRM) as described by Slocum and Reilly in 1963 (Slocum and Reilly 1963), have a wide range of applications including, but not limited to fundamental research, detecting biomagnetic signals such as those emanating from biological organisms including the human body, geophysical exploration and prospecting, navigation and space applications, and military uses such as ordinance and underground-underwater structure detection. Until recently, the most sensitive commercially available magnetometer for such applications was the superconducting quantum interference device (SQUID) (Weinstock 1996). However, zero-field paramagnetic resonance magnetometers (Dupont-Roc, Haroche, and Cohen-Tannoudji 1969; Marie-Anne et al. 1971; Vishal Shah et al. 2007), which have advanced to comparable sensitivity as SQUID systems, have recently gained popularity as a lower-cost, more robust alternative to SQUID magnetometers for many applications. 
     Significant developments in alkali atomic magnetometery (Budker and Romalis 2007) over the past decade have led to a variety of techniques and methods for sensing magnetic fields. In general, the different methods are based on the same fundamental physical sensing mechanism that exploits the energy structure of atoms and the perturbations that result in their energy levels, or spin state, from exposure to external magnetic fields. Atomic based magnetic sensors measure the direction and magnitude of an external magnetic field through the induced changes in the atomic spin polarization of an ensemble of atoms. 
     A zero field parametric resonance magnetometer (ZF-PRM) relies on detecting changes in optical transmission properties of spin polarized atomic vapor in a narrow magnetic field range centered on absolute zero magnetic field. The optical transmission properties of the polarized atomic vapor in ZF-PRM change substantially when magnetic field, in a direction perpendicular to the direction of the atomic spin polarization, changes. However, little or no change is observed when there is a change in magnetic field parallel to the direction of the atomic spins. Consequently, ZF-PRM is primarily sensitive to magnetic field in just one or two orthogonal directions perpendicular to the atomic spin polarization, and not sensitive to magnetic field in the third direction which is parallel to the direction of the atomic spin polarization. In many scientific, research, and biomedical applications, measurement of all three orthogonal vector components of the magnetic field is necessary. 
     SUMMARY 
     Here we disclose a simple apparatus capable of obtaining magnetic field measurement in all three directions with an improved ZF-PRM device. Further, we describe a method for measuring magnetic field in all three directions. The triaxial ZF-PRM of the present disclosure may simultaneously measure all three orthogonal vector components of a magnetic field with high sensitivity using a single atomic vapor cell. In addition, this ZF-PRM may operate to measure at least one direction, two directions, or the three orthogonal directions of the magnetic field at one time. The apparatus and method disclosed herein has the following advantages: (i) provides simultaneous measurement of all three vectors components at substantially the same location, (ii) measures all three components with equally high sensitivity, (iii) requires only a single light source and vapor cell, and (iv) is robust. 
     The present apparatus and method address a longstanding need recognized by those skilled in the art of building and operating ZF-PRMs. Slocum and Reilly (1963) described a method to operate a helium based ZF-PRM in triaxial mode using synchronous phase demodulation of rotating fields in two orthogonal directions. Slocum first applied a 90-degree phase offset modulation fields in the X (optical axis) and Y direction to obtain the magnitude of the magnetic field in the X and Y directions. Next, Slocum applied a 90-degress phase offset modulation in the X and Z direction to obtain the magnitude of the magnetic field in the X and Z directions. Slocum proposed alternating between XY and XZ modulation at a predefined rate to obtain magnetic field information in all three axes. The main drawback of Slocum&#39;s method is that it does not provide a simultaneous measurement of the magnetic field in all three axes. In addition, in Slocum, the sensitivity of the magnetometer in the X direction is lower compared to the sensitivity in the Y and Z directions. 
     Dong et al. and H. Huang et al. demonstrated that it is possible to operate a single beam ZF-PRM in triaxial mode by applying three separate orthogonal modulation fields at different frequencies or phases (H. C. Huang et al. 2015; H. Huang et al. 2016; Dong et al. 2012). The main downside of their approach is that the magnetometer sensitivity in the direction along the optical axis is much lower compared with the sensitivity obtained in directions perpendicular to the optical axis. Seltzer and Romalis (2004) described a similar modulation apparatus to obtain sensitivity along all three-axis using a two beam pump-probe configuration ZF-PRM. Although not explicitly highlighted in the publication, from their equation (5) it is evident that their magnetometer also suffers from reduced sensitivity in the direction of the pump beam. 
     In contrast to the present disclosure, in prior art pump-probe magnetometers (Seltzer and Romalis 2004; Fang and Qin 2012), the measurement volume that produces the magnetometer output is given by the region in which the pump and the probe beams overlap. 
     Other commercial ZF-PRM magnetometers, for example the QuSpin QZFM Gen-1 magnetometer (Osborne et al. 2018), are sensitive to magnetic fields in one or two axes. To obtain high sensitivity in all three directions with these sensors, two or more single or dual axis ZF-PRM sensors may be placed near each other at right angles to measure magnetic fields in all three complementary directions as described by Boto et al. (2018). The downside of this approach of combining multiple magnetometers to obtain triaxial field measurement is that such a device doubles or even triples the size, weight, power consumption, and cost of the combined magnetometer device. In addition, these combined single/dual axis magnetometers do not achieve measurement of all three components of magnetic field at the same location which creates measurement bias that can be difficult to remove. 
     A prior art single beam ZF-PRM  101 , as shown in  FIG. 1 , primarily consists of a light or light beam  20 , an alkali vapor cell  70  and a photodetector  90 . In summary, the light beam  20  is circularly polarized and its wavelength adjusted such that the light is resonant with the D1 line of alkali atoms  60  inside the vapor cell  70 . As shown in  FIG. 2 , in zero magnetic field, the alkali atoms  60  in the path of the light beam  20  are polarized by the circularly polarized light beam  20  such that the spins of the alkali atoms  60 A that the beam  20  falls on are aligned along the direction of the light beam. When the alkali spins are aligned with the beam, they absorb very little laser light. Therefore, the light beam  20  passes on to the photodetector or photodiode  90  substantially unaffected by the alkali atoms  60  inside the vapor cell  70 . 
     When a magnetic field orthogonal to the direction of the light beam is present, the orthogonal magnetic field applies a torque on the spins which rotates the orientation of spin polarized alkali atoms  60 A and causes a misalignment between the light beam and alkali spins. As a result of the misalignment, the alkali atoms start absorbing light from the beam which changes the amount of light falling on the photodetector. From a change in the amount of light falling on the photodetector, strength of the magnetic field in a direction orthogonal to the light beam is inferred by the ZF-PRM. However, when a magnetic field parallel to the light beam is present, no torque is applied on the alkali spins and consequently the orientation of alkali spins is unaffected by the magnetic field. Therefore, the ZF-PRM cannot sense magnetic field parallel to the direction of the light beam. 
     In the triaxial ZF-PRM apparatus of the present disclosure  FIG. 3, 301 , in addition to the circularly polarized light beam  20 , a second circularly polarized light beam  220 , which travels substantially orthogonal to the first beam  20 , is used. This second circularly polarized light beam  220  travels through the vapor cell  70 , falling on the alkali atoms  60  and is detected by a second photodetector  290 . The photodetector  90  can measure the perturbance of light from magnetic fields orthogonal to beam  20  (x and y directions) and photodetector  290  can measure the perturbance of light from magnetic field orthogonal to beam  220  (in y and z directions). Together the output of the two photodetectors  90 ,  290  utilizing the same vapor cell  70  provide a measurement of magnetic field in all three directions. 
     The magnetic field measurements in the x and/or y direction made using beam  20  and photodetector  90  does not require the presence of beam  220  or photodetector  290 . Similarly, the magnetic field measurements in the z and/or y direction made using beam  220  and photodetector  290  does not require the presence of either beam  20  or photodetector  90 . Therefore, the magnetic field measurements made using photodetector  90  and photodetector  290  are substantially independent of one another. 
     If the two beams  20  and  220  overlap inside the vapor cell, the alkali spin polarization is adversely affected in the overlap region, denoted VO, or volume of overlap, volume O, and therefore for optimal performance the beam overlap volume must be reduced to the greatest extent possible. To minimize beam overlap, techniques known to persons skilled in art may be employed including reducing the diameter of the beams  20  and  220  to minimize beam overlap, and/or positioning or engineering the beams to create a small gap between the beams  20  and  220  to further reduce beam overlap region inside the vapor cell. 
     Inasmuch, the apparatus described and claimed herein is a zero-field paramagnetic resonance magnetometer (ZF-PRM) able to simultaneously measure magnetic field in three orthogonal directions at substantially the same location comprising: a first circularly polarized light beam, a vapor cell filled with alkali atoms and a buffer gas, and a first photodetector to detect changes in the magnetic field in a first and optionally second direction, wherein the detected changes using the first photodetector define a first measurement set, and the first and second directions are mutually orthogonal and orthogonal to the direction of propagation of the first light beam through the vapor cell; a second circularly polarized light beam, the vapor cell filled with alkali atoms and the buffer gas, and a second photodetector to detect changes in the magnetic field in a third and optionally the first or the second direction, wherein the detected changes using the second photodetector define a second measurement set, and the third and first or second directions are mutually orthogonal and orthogonal to the direction of propagation of the second light beam through the vapor cell; wherein the first and second light beams pass through the vapor cell in substantially orthogonal directions; wherein the first and second measurement sets are not dependent on each other; and wherein the first and the second measurement sets together measure magnetic field in all three substantially orthogonal directions. 
     The ZF-PRM described herein may further comprise a beam splitter, and the first and the second light beams may be generated by splitting light from a single light source. In the ZF-PRM of the present disclosure, the first and the second light beams may be generated by two separate light sources. 
     Further, the ZF-PRM described herein may be surrounded by a coil system that produces an oscillating magnetic field over the region of the vapor cell in two or more directions. The frequency of the oscillating magnetic field may be different in three mutually orthogonal directions. The oscillating magnetic field may be the same in at least two directions and different in a third direction. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions and the phase of the oscillating magnetic field is offset by an amount substantially equal to pi/2 in at least two mutually orthogonal directions. 
     In the ZF-PRM described herein the buffer gas in the vapor cell may have a pressure greater than 100 torr. In the ZF-PRM a volume of beam overlap inside the vapor cell is defined as the space where the beams overlap inside the vapor cell, and the volume of beam overlap is substantially less than the total volume of both the beams occupy inside the vapor cell. Alternately, the first and the second beams may not overlap inside the vapor cell. 
     In other words, a triaxial ZF-PRM of the present disclosure may comprise: two circularly polarized light beams resonant with the D1 line of a group of alkali atoms; a single vapor cell filled with the group of alkali atoms and at least one buffer gas, wherein the two light beams are directed through the vapor cell at substantially orthogonal directions, and wherein the light beams occupy a volume within the vapor cell, and wherein an overlap volume is defined by the volume where the beams overlap inside the vapor cell, and wherein the overlap volume is substantially smaller than the total beam volumes in the vapor cell; and two photodiodes, wherein a first photodiode measures magnetic field in one or two directions orthogonal to the propagation direction of the beam detected by the first photodiode, and a second photodiode measures magnetic field in one or two directions orthogonal to the propagation direction of the beam detected by the second photodiode. The triaxial ZF-PRM may further comprise a beam splitter, wherein the first and the second light beams are generated by splitting light from a single light source. 
     A method for measuring magnetic frequency in three directions simultaneously is described and claimed herein, the method comprising the steps of: propagating two circularly polarized light beams through a vapor cell containing alkali atoms and at least one buffer gas at substantially orthogonal directions to each other, and wherein the light beams occupy a volume within the vapor cell, and wherein an overlap volume is defined by the volume where the beams overlap inside the vapor cell, and wherein the overlap volume is substantially smaller than the total beam volumes in the vapor cell; and using two separate photodetectors to detect the two beams after they pass through the vapor cell. 
     The method described herein may further comprise creating an oscillating magnetic field over the region of the vapor cell in two or more directions. The frequency of the oscillating magnetic field may be different in three mutually orthogonal directions. The frequency of the oscillating magnetic field may be the same in at least two directions and different in the third direction. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions and the phase of the oscillating magnetic field is offset by an amount substantially equal to pi/2 in at least two mutually orthogonal directions. The method may further comprise pressurizing the vapor cell to a pressure greater than 100 torr. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic illustration of a prior art ZF-PRM. 
         FIG. 2  is a schematic illustration of how in zero magnetic field, the alkali atoms in the path of the light beam are polarized by the light beam. 
         FIG. 3  is a schematic illustration of a triaxial ZF-PRM of the present disclosure. 
         FIG. 4  schematic illustration of a magnetic field measurement from the X component direction. 
         FIG. 5  is a schematic illustration of a magnetic field measurement from the Y component direction. 
         FIG. 6  is a schematic illustration of a magnetic field measurement from the Z component direction. 
         FIG. 7A  is a schematic illustration of two light beams intersecting in the vapor cell of the present disclosure. 
         FIG. 7B  is a schematic illustration of two non-overlapping light beams passing through the vapor cell of the present disclosure. 
         FIGS. 8A, 8B, and 8C  are schematic illustrations of measurement in the x, y, and z directions (Bx, By, and Bz) with the first circularly polarized light beam of the triaxial ZF-PRM of the present disclosure. 
         FIGS. 9A, 9B, and 9C  are schematic illustrations of measurement in the x, y, and z directions with the second circularly polarized light beam passing through the vapor cell in an orthogonal direction from the first circularly polarized light beam. 
         FIG. 10  is a schematic illustration of how an error signal is generated. 
         FIG. 11  is a schematic illustration of an example triaxial ZF-PRM of the present description. 
         FIG. 12  is a schematic illustration of an example triaxial ZF-PRM of the present description. 
     
    
    
     Before explaining the disclosed embodiments of the present apparatus and method in detail, it is to be understood that the disclosure is not limited in its application to the details of the particular arrangement shown, since the disclosed apparatus and method are capable of other embodiments. Also, the terminology used herein is for the purpose of description and not of limitation. 
     DETAILED DESCRIPTION OF THE INVENTION 
     Single beam zero field paramagnetic resonance magnetometers or ZF-PRM generally, as shown in prior art  FIG. 1 , are known in the art as described previously as in U.S. Pat. No. 3,629,697 to Bouchiat et al. and U.S. Pat. No. 4,005,355 to Flapper et al. The theory, construction, and operation of single beam ZF-PRMs is also described in prior art (Marie-Anne et al. 1971; W and E 1974). A ZF-PRM apparatus  101 , comprises a cell  70  containing alkali atoms  60 . The cell  70 , which can be made of glass, or some other transparent material, can also include a buffer gas  80 . The buffer gas may comprise a noble gas such as helium, argon, xenon or neon. Another gas such as nitrogen can also be used as buffer gas  80 . The buffer gas may comprise of a mixture of gases or a single component gas. The cell  70  may be heated to an elevated temperature to provide a density of alkali metal atom vapors, which can range from at least about 10 7  cm −3  to at least about 10 15  cm −3  or more. The exact temperature to which the cell  70  is heated will depend. in general, upon the atomic species, or atoms (e.g. sodium, potassium, rubidium, or cesium), which is used in the apparatus. As an example, when the alkali metal comprises rubidium-87, the cell  70  may be heated to about room temperature or up to about 200° C. The cell  70  may be heated by locating the cell within an oven (not shown) or by placing it within thermal proximity to a heating element. The alkali atoms  60  employed may include rubidium, cesium, potassium, sodium, and helium. 
     In the ZF-PRM  101 , a pump light beam  20 , which can be generated by a laser  10 , or a vapor lamp  10 , may be directed through a linear polarizer  40  to linearly polarize the pump light beam  20 . The linear polarizer  40  can be omitted if the pump light beam  20  is already linearly polarized. The pump light beam  20 , which can have an optical power level of up to a few microWatts (μW) or more depending upon the size and temperature of the cell  70 , can be expanded and substantially collimated by one or more lenses  30 . 
     After being expanded and substantially collimated by the lenses  30 , the pump light beam  20  may be directed through an optical waveplate  50 , having a fast axis which is oriented at 45° with respect to a direction, e.g. vertical out of the plane of  FIG. 1  or horizontal in the plane of  FIG. 1 , of the linear polarization of the pump light beam  20 . In this way, the optical waveplate  50  converts the pump light beam  20 , which was initially linearly polarized into being circularly polarized. The circularly polarized light in the beam  20  after passing through the optical waveplate  50  can be either right-handed circularly-polarized light or left-handed circularly-polarized light. After being transmitted through the optical waveplate  50 , the pump light beam  20  is directed through the cell  70  containing the alkali metal vapor  60  or other alkali atoms or vapors. The cell may have lateral dimensions of each side of generally about one millimeter (mm), two mm, or three mm, or larger. 
     The optical waveplate  50  functions as a quarter waveplate at the wavelength of the pump light beam  20 , which is substantially equal to the wavelength of a first or second D1 line atomic transition of the alkali metal vapor  60 . D1 line is defined herein as a transition from a n 2 S 1/2  ground state to a m 2 P 1/2  excited state of the alkali metal atoms in the vapor  60  where n and m are integers. The pump light beam  20  need not be exactly on line center of the D1 transition, but can be tuned off the line center and onto the wines of the D1 transition. 
     The buffer gas  80 , which may be helium, neon, or nitrogen, in the cell  70  is useful to slow down the rate at which the atoms of the alkali metal vapor  60  collide with the inner walls of the cell  70  which can randomize the spins of the alkali metal atoms. The buffer gas  80  pressure in the cell  70  can be, for example, in a range between about 50 torr or 100 torr and about 3000 torr, or higher. 
     The pump beam  20 , after passing through the vapor cell  70 , is collected by a photodetector  90 , which provides a measure of the amount of light transmitted through the cell  70 . Various types of photodetectors  90  may he used with detection capability in the wavelength range of the pump light beam  20 . The output of the photodetector may be subsequently amplified using suitable low noise electronic amplifiers. 
     The ZF-PRM apparatus  101 , the cell  70  alone, or a space or room where the ZF-PRM is housed, may be surrounded by a set of electrically activated magnetic coils  110 . The set of coils  110  being three coils, one generating field in the x-direction, one generating field in the y-direction, and one generating field in the z-direction. Further, each coil may be a single coil, or additional coils to generate a homogenous magnetic field around the cell  70  in each of the three directions. 
     When the alkali atoms  60  in the cell  70  are in a substantially zero magnetic field environment, the circular polarization of the pump light beam  20  produced by the optical waveplate  50  aligns the nuclear and electron spins of the individual alkali metal atoms in the alkali metal vapor  70  from optical pumping process (Happer and Mathur 1967). As shown in  FIG. 2 , the optical pumping process re-orients the spins of the individual alkali metal atoms  60 A so that they are in a magnetically polarized state aligned along the direction of the circularly polarized light beam  20 , i.e. defined here as the z-direction. 
     Summarizing the operation of a ZF-PRM  101 , illustrated by  FIG. 1 , the behavior of the spin polarization vector ({right arrow over (P)}) of alkali atoms  60  in a sensing cell  70  can be understood based on the Bloch equation (Allred et al. 2002): 
     
       
         
           
             
               
                 
                   
                     
                       
                         d 
                         ⁢ 
                         
                           P 
                           → 
                         
                       
                       dt 
                     
                     = 
                     
                       
                         γ 
                         ⁢ 
                         
                           P 
                           → 
                         
                         × 
                         
                           B 
                           → 
                         
                       
                       - 
                       
                         R 
                         ⁡ 
                         
                           ( 
                           
                             
                               P 
                               → 
                             
                             - 
                             
                               
                                 P 
                                 → 
                               
                               0 
                             
                           
                           ) 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   1 
                 
               
             
           
         
       
     
     where γ is the gyromagnetic ratio of the alkali atoms  60 , R is the combined optical pumping and relaxation rate, and {right arrow over (B)} is the magnetic field to which alkali atoms are exposed. A representation of a magnetic field may be detected as a change in transmission of the light or pump light beam through the alkali atoms by a photodetector. Because the light beam  20  propagates in the z-direction in  101 , the amount of light beam  20  transmitted through the vapor cell  70  is proportional to the steady state solution of the said equations along the z-direction, i.e.: 
                       P   z     =       P   0     ⁢         B   z   2     +       (     R   γ     )     2           B   x   2     +     B   y   2     +     B   z   2     +       (     R   γ     )     2             ,           Eq   .           ⁢   2               
where P z  is the component of the spin polarization vector, {right arrow over (P)}, in the z-direction.
 
     When the cell  70  is in a zero field (ZF) environment, i.e. Bx=By=Bz=0, scanning the magnetic field, Bx  140  , produces a narrow Lorentzian resonance, defined herein as the natural ZF resonance, which can be seen by monitoring the amplified output of the photodetector  90  on an oscilloscope. The resonance Rx, as shown in  FIG. 4 , is referred to in the prior art as the ZF resonance and has a height, Hx, and a width Wx. Because the photodetector output changes substantially as a function of the Bx field  140 , the magnetometer is highly sensitive to changes in the magnetic field in the x-direction. 
     Similarly, from Eq. 2, in ZF environment, scanning the magnetic field By  150  produces a narrow ZF resonance Ry of height Hy and width Wy as shown in  FIG. 5 . Therefore, because the photodetector output changes substantially as a function of the By field  150 , the magnetometer is also highly sensitive to changes in the magnetic field in the y-direction. 
     However, from Eq. 2, in ZF environment, scanning the magnetic field Bz  160  does not produce any change in the photodetector  90  output as shown in  FIG. 6 . Therefore, the magnetometer is not sensitive to changes in the magnetic field in the z-direction. And therefore, a traditional ZF-PRM cannot measure all three components in the same location at one time. 
     The ZF-PRM as described herein and essentially shown in  FIG. 3, 301 , is sensitive to changes in the magnetic field in all three directions, X, Y and Z. In the triaxial ZF-PRM  301 , two circularly polarized light beams  20 ,  220  are projected through a single vapor cell  70  housing a group of alkali atoms  60  and at least one buffer gas  80 . The cell may have lateral dimensions of each side of generally about one millimeter (mm), two mm, or three mm, or larger. In  301 , the light source  10  lens  30 , polarizer  40 , and waveplate  50  used in  FIG. 1 , and other optical components are not shown for clarity. The circularly polarized light beams  20 ,  220  may be produced by a single light source or multiple light sources. 
     In the ZF-PRM  301  of  FIG. 3 , two photodetectors  90 ,  290  measure optical power in light beams  20 ,  220  respectively after the circularly polarized light beams pass through the vapor cell  70  containing alkali atoms  60  and buffer gas  80 . The alkali atoms  60  employed may include rubidium, cesium, potassium and sodium. The buffer gas may comprise a noble gas such as helium, argon, xenon or neon. Another gas such as nitrogen can also be used as buffer gas  80 . The buffer gas may comprise of a mixture of gases or a single component gas. 
     The circularly polarized light beams  20 ,  220  are designed to both be resonant with the D1 transition of the alkali atoms  60  and both beams are substantially circularly polarized as described above for  FIG. 1 . The circularly polarized beams  20  and  220  may be derived from the same light source or from distinct light sources. The beams are projected through the vapor cell  70  containing the alkali atoms  60  and buffer gas  80  at substantially orthogonal or perpendicular directions from each other. Coils, not shown, may create magnetic fields in the x, y, and z directions. 
     Referring to the ZF-PRM of  FIG. 3, 301  the light beam  20  measures magnetic field in the x and 7 directions. The light beam  220  measures magnetic field if the y and z directions. When the beams are offset so as not to occupy the same space or volume, or in other words overlap each other inside the vapor cell, the beam and photodetector it falls on, beam  20  for instance, and photodetector  90 , or beam  220  and photodetector  290 , operate independently to each measure in two directions even if the other beam is interrupted or fails. This creates a robust apparatus that can measure in at least two directions with only one light beam being operational, but in three directions if both beams are functioning. This is in opposition to prior art pump-probe magnetometers wherein the linearly polarized light beam and circularly polarized light beam overlap and where if one fails or is interrupted no detection or signal may be derived from the other. 
     For the purposes of the present description, the term “modulation” is used to describe periodic variations in either a field or an electrical current that drives a coil. Similarly, the term “modulate” is defined herein to be the act of apply such modulation. Specifically, the terms “modulate” and “modulation” apply to periodic variations that enable error signal generation, as one example, through the lock-in detection technique. The term lock-in detection is known in the art. The term “scan” or “scanning” is used in conjunction with a parameter and is defined herein to mean the act of changing a parameter to make a manual (visual) or computer-aided observation. As an example, one may scan the field to observe the shape of the zero-field resonance using an oscilloscope. The “scan” need not be periodic as is required with “modulation”. The term “optimizing a zero-field resonance” is used herein in to describe the minimizing the width and maximizing the height of the ZF resonance. Further, the act of nulling a field, wherein in the field is effectively equal to zero, can occur when the width of the measured resonance is minimized and height is maximized, and is therefore said to be optimized. 
     Further, the one or more coils may be an additional single coil, or an additional two coils, or set of coils, or the sole coil, or coils, or set of coils of the magnetometer. Coils may be a means for generating an oscillating magnetic field. Further, the term “coil” is known in the art and defined to be an object that can produce a tunable magnetic field. One example of a coil is a wire that has been wound in a circular shape through which electrical current is passed to produce a magnetic field. Other geometries of a coil could include, but are not limited to a Helmholtz coil pair, a round solenoid, or a wire wrapped in rectangular-shaped windings. Herein the term “null” means to apply a field to cancel a component of the background field. As one example of the term “null”, an x-bias coil is positioned with the axis of the coil along the x-direction. 
     Orthogonal direction means perpendicular,or substantially perpendicular, or at a right angle to, at substantially a right angle to, wherein substantially may be defined as no more than about ten degrees from the ninety degree or right angle, or no more than about nine degrees, or no more than about eight degrees, or no more than about seven degrees, or no more than about six degrees, or no more than about five degrees, or no more than about four degrees, or no more than about three degrees, or no more than about two degrees, or no more than about one degree, or at ninety degrees or a right angle. For the purposes of the present application the term “field” when not accompanied by a qualifier is defined to mean magnetic field. A field has both direction and magnitude and herein the term “field component” refers to the field along a given direction. The terms photodiode and photodetector may be interchangeable. 
     Now referring to  FIG. 7A , the overlap of the beams inside the vapor cell  70 , should be minimized by methods known in the art which may be either a reduction of beam circumference or diameter, or offset of beams, in other words engineered to create space between where the beams fall inside the vapor cell. As illustrated in  FIG. 7A , circularly polarized light beam  20  derives its signal from the atoms it lands on inside the vapor cell  70 , defined as beam volume 1. Laser beam  220  derives its signal from the atoms it lands on, being beam volume 2. When the beams overlap, as in FIG. 7 A, a volume of overlap is created, volume O. Volume O is defined as the volume inside the vapor cell  70  where the two beams  20  and  220  overlap. 
     In the region in which the two beams overlap, volume O, the alkali atoms are partially depolarized, and the spin polarization axis is rotated. The reduction in spin polarization from beam overlap lowers the magnetometer sensitivity, and the changes in the spin polarization axis can introduce measurement inaccuracies. Such effects from beam overlap can be readily modeled using Bloch equation. It is therefore desirable to minimize the beam overlap volume, volume O, to the greatest extent possible. Ideally, the overlap volume, volume O, should be minimized, as such volume O, may be three-fourths the volume 1 or volume 2, or one-half the volume 1 or volume 2, or one-quarter, or less, being substantially zero. 
     The overlap region can be reduced by shaping the light beam cross-sections or by intentionally aligning the beams to not intersect such that the light beam overlap region is reduced to an extent that is practical.  FIG. 7B  illustrates a system where the beams have been aligned such that a gap exists between beams  20  and  220  wherein the light beam  20  passes through the vapor cell  70  and the light beam  220  passes through the vapor cell  70  and do not substantially intersect or cross each other. Laser beam  20  derives its signal from the atoms it lands on in the vapor cell  70 , defined as beam volume 1. Laser beam  220  derives its signal from the atoms it lands on, being beam volume 2. Because the beams have been offset, such that substantially no portion of the beams occupy the same space in the vapor cell  70 , the beam overlap volume, volume O, is reduced to essentially zero, thereby minimizing adverse effects from beam overlap. 
     In addition to reducing beam overlap, increasing the pressure of one or more buffer gases within the vapor cell  70  helps keep alkali atoms confined within the beam volume over a time scale comparable to the ground state coherence time of the alkali atoms. The pressure in the vapor cell may be increased to over 100 torr or higher, for example up to 3000 torr. The high pressure buffer gas helps confine spin polarized alkali atoms within the beam volume 1 and 2 and prevents migration of spin polarized atoms from one beam volume to another over a time scale comparable to the coherence time of the alkali atom ground states. 
     With the triaxial ZF-PRM  301  illustrated in  FIG. 3 , because the circularly polarized light beam  20  travels through the vapor cell in the z-direction, the photodetector  90  output is proportional to P z1 , where P z1  is given by 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       z 
                       ⁢ 
                       1 
                     
                   
                   ∝ 
                   
                     
                       
                         B 
                         z 
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             R 
                             γ 
                           
                           ) 
                         
                         2 
                       
                     
                     
                       
                         B 
                         x 
                         2 
                       
                       + 
                       
                         B 
                         y 
                         2 
                       
                       + 
                       
                         B 
                         z 
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             R 
                             γ 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     Similarly, because the circularly polarized light beam  220  travels through the vapor cell in the x-direction, the photodetector  290  output is proportional to P x2 , where P x2  is given by 
     
       
         
           
             
               
                 
                   
                     P 
                     
                       x 
                       ⁢ 
                       2 
                     
                   
                   ∝ 
                   
                     
                       
                         B 
                         x 
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             R 
                             γ 
                           
                           ) 
                         
                         2 
                       
                     
                     
                       
                         B 
                         x 
                         2 
                       
                       + 
                       
                         B 
                         y 
                         2 
                       
                       + 
                       
                         B 
                         z 
                         2 
                       
                       + 
                       
                         
                           ( 
                           
                             R 
                             γ 
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     From Eqn. 3, in ZF, scanning the magnetic field in the X-direction produces the ZF resonance Rx 1  as shown in  FIG. 8A . Similarly, scanning magnetic field in the y-direction produces resonance Ry 1  as seen in  FIG. 8B . However, scanning the magnetic field in the Z-direction does not change the photodiode output and zero field resonance is not observed,  FIG. 8C . Thus, the output of the photodiode  90  is sensitive to magnetic fields in the X and Y directions, but not the Z direction. 
     Similarly, from eqn. 4, as shown in  FIG. 9B , in ZF, scanning the magnetic field in the Y-direction produces a magnetic resonance Ry 2  and scanning the magnetic field in the z-direction produces resonance Rz 2    FIG. 9C . Thus, the output of the photodiode  290  is sensitive to magnetic fields in the Y and Z directions, but not the X direction, as shown in  FIG. 9A . 
     By utilizing the photodetector  FIG. 3, 90  output to sense magnetic fields in the X and Y direction, and by using the photodetector  FIG. 3, 290  to sense the magnetic field in the Z and Y direction, the triaxial ZF-PRM magnetometer  301  can sense magnetic field in all three orthogonal directions with high sensitivity at the same time and in substantially the same location. 
     Signal processing techniques are generally used to obtain a response that is linearly proportional to the background magnetic field. In ZF magnetometers, a commonly used technique to obtain a linear output proportional to magnetic field is using phase sensitive detection with a lock-in amplifier to generate a dispersive line shape, or error signal, from the Lorentzian shaped ZF resonance signal as shown in  FIG. 4  for example, where Rx is the ZF resonance obtained by scanning magnetic field in the x-direction and Ex is the error signal generated from Rx using signal processing (Schwindt and Johnson 2012). The reason error signal is used as the output of the magnetometer is because the error signal has a steep linear slope about zero field, where as the ZF resonance has quadratic slope about zero field. It is well known in the art that the error signal can be generated by first applying a magnetic field modulation in the direction of the desired magnetic field sensitive axis, and then demodulating the photodiode output using synchronous phase detector such as a lock-in amplifier. 
     For example, the error signal Ex 1  can be generated as follows as shown schematically in  FIG. 10 . First, an oscillating electrical current is applied to coils  110   x  using coil driver  810  to produce an oscillating magnetic field at the location of the vapor cell  70 . The oscillating electrical current generated by the coil driver  810  CD x  can be a periodic waveform of frequency f x  and phase Φ x . Example waveforms include but not limited to sine wave or square wave. The oscillating magnetic field causes the spin polarization of the alkali atoms  60  inside the vapor cell  70  to oscillate, which in turn produces an oscillation in the amount of light  20  transmitted through vapor cell and measured by the photodiode  90 . Using the waveform used to generate the oscillating magnetic field in the x-direction as the reference input, and the photodiode  90  output as the input signal to the lock-in amplifier  820 , the error signal Ex 1  is produced by the lock-in amplifier  820 . 
     In an identical fashion, the error signal Ez 2  be generated by applying a modulation field in the z-direction and then demodulating the photodetector  290  output using a separate lock in amplifier. Similarly, the error signal Ey 1  and Ey 2  can be produced by applying a modulation field in the y-direction and then demodulating the photodiode  90  output using a locking amplifier to produce Ey 1  and/or using output of the other photodetector  290  to produce Ey 2 . A sum or linear combination of the both photodetector signals can also be used to produce y-error signal output which gives the sum or linear combination of Ey 1  and Ey 2 . The error signals Ex 1 , Ez 2 , and either Ey 1  or Ey 2  or linear combination of Ey 1  and Ey 2  are the three outputs of the triaxial magnetometer. 
     Coils or other means may be employed to generate oscillating magnetic field over the region of the vapor cell in two or more directions. The frequency of the oscillating magnetic field may be different in three mutually orthogonal directions. The frequency of the oscillating magnetic field may be the same in at least two directions and different in the third direction. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions. The frequency of the oscillating magnetic field may be the same in all three mutually orthogonal directions and the phase of the oscillating magnetic field is offset by an amount substantially equal to π/2 in at least two mutually orthogonal directions. 
     While various embodiments have been described in detail, it is apparent that modifications and adaptations of those embodiments will occur to those skilled in the art. However, is to be expressly understood that such modifications and adaptations are within the spirit and scope of the present disclosure. 
     EXAMPLES 
     Example 1 
     In this example illustrated in  FIG. 11 , a 795 nm laser  10  tuned to the D1 transition of the  87 Rb atoms was used to generate light for optical pumping. The beam  20  exiting the laser may be collimated using an optical lens (not shown) if the initial output from the laser has high divergence or convergence. The full width at half maximum (FWHM) beam diameter was about 1 mm for example in this case. The beam diameter can be bigger or smaller but preferably less than half the inside height, width or depth dimensions of the vapor cell  70 . 
     The light beam  20  was converted to circular polarization using a 795 nm quarter waveplate  50 . The light beam  20  was then split into two parts  201 ,  202  using a 50:50 optical beam splitter  1010 . The beam  201  was reflected using a mirror  1020  such that it passed through the vapor cell  70  travelling in the z-direction. After passing through the vapor cell, the beam  201  was captured by a photodiode  90  sensitive to light at 795 nm. The photodiode converted the laser light falling on the photodetector to an electrical current. 
     Similarly, the beam  202  was reflected using mirror  1030  such that it passed through the vapor cell  70  travelling in the x-direction. After passing through the vapor cell  70 , the beam  202  was captured by the photodiode  290 . 
     The vapor cell  70  was 3×3×3 mm in this example and filled with a droplet of enriched  87 Rb and nitrogen at a pressure over 100 torr. Helium could be used instead of nitrogen. The buffer gas minimizes the diffusion of  87 Rb atoms from one beam  201 ,  202  to another over the timescale of  87 Rb ground state coherence, being 1 millisecond (ms). But could be as little as 0.1 ms or as long as 10 ms. 
     A small modulating current was added to each of the three coil pairs  110   x ,  110   y , and  110   z . The modulation currents produced an oscillating magnetic field at the location of the vapor cell  70 . For example, coil  110   x  was modulated such that it produces a magnetic field Bm x =A x  Sin(2πf x +f x ) oscillating in the x-direction, coil  110   y  produces a magnetic field Bm y =A y  Sin(2πf y +f y ) oscillating in the y-direction, and coil  110   z  produces magnetic field Bm z =A z  Sin(2πf z +f z ) oscillating in the z-direction. The amplitude and the frequency of the modulation field were chosen to maximize error signal generation as well as to reduce technical low frequency noise (Shah and Romalis 2009). For example, A x , A y  and A z  can range from 1 to 1000 nT and the f x , f y , f z  can be in the range of 100 Hz to 10 kHz. The phase f x , f y , f z  can be in the range of 0 to 2π. The modulation function can be any periodic function such as but not limited to sine wave, square wave, triangle wave. 
     To generate an error signal from the photodetector output, synchronous phase sensitive detection was used. Following is the description of one method to generate the three error signals corresponding to the three open-loop outputs of the triaxial magnetometer. Additional ways exist for generating error signals that are well known to people skilled in art. 
     We refer to the amplified current-to-voltage converted output of the photodetector  90  to be PD 90 . Similarly, we refer to the amplified current-to-voltage converted output of the photodetector  290  to be PD 290 . 
     The error signal Ez 2  was generated by multiplying PD 290  with a periodic function of frequency f z . For example, PD 290  can be multiplied with Sin (2πf z +f Lz ), where f Lz  is chosen to maximize the amplitude and slope of the error signal, Ez 2 . Example f Lz =f z +π/2. The multiplied output was then low pass filtered with the filter cutoff frequency set to be less than f z . The filtered output was the error signal Ez 2 . The photodiode output PD 290  was chosen to generate Ez 2  because beam  202  travels through the vapor cell in the x-direction which is orthogonal to the z-direction and therefore the ZF resonance in the z-direction was observed using PD 290 . 
     Similarly, the error signal Ex 1  was generated by multiplying PD 90  with a periodic function of frequency f x . For example, PD 90  is multiplied with Sin (2πf x +f Lx ), where f Lx  was chosen to maximize the amplitude and slope of the error signal, Ex 1 . Example f Lx =f x +π/2. The multiplied output was then low pass filtered with the filter cutoff frequency set to be less than f x . The filtered output was the error signal Ex 1 . The photodiode output PD 90 was chosen to generate Ex 1  because beam  201  travels in the z-direction through the vapor cell, which is orthogonal to the x-direction and therefore Ex 1  was observed using PD 90 . 
     A procedure similar to Ex 1  and Ez 2  was used to generate the error signal Ey1 or Ey2, wherein the photodiode output was first multiplied with a periodic function of frequency f y , and then a low pass filter was applied to the multiplied product with low pass filter cutoff less than f y . In the case of error signal for the y direction, because the y-direction is orthogonal to the propagation direction of both beams  201 ,  202  through the vapor cell, either of the two photodiode outputs PD 90  or PD 290  or a linear combination of PD 90  and PD 290  can be used to generate the error signal in the y direction. 
     The error signal Ey 1  (Ey 2 ) was generated by multiplying PD 90  (PD 290 ) with a periodic function of frequency f y . For example, PD 90  (PD 290 ) was multiplied with Sin (2πf y +f Ly ), where f Ly  is chosen to maximize the amplitude and slope of the error signal, Ey 1  (Ey 2 ). Example f Ly =f y +π/2. The multiplied output was then low pass filtered with the filter cutoff frequency set to be less than f y . The filtered output was the error signal Ey 1  (Ey 2 ). Either Ey 1  or Ey 2  can be used as the y-axis output of the magnetometer. A sum or a linear combination of Ey 1 or Ey2 may also be used at the y-axis magnetometer output. The main difference between Ey1 and Ey2 is that Ey1 is produced from sampling of the atoms in volume 1 by beam  201  and Ey2 is produced from sampling of the atoms in volume 2 by beam  202 . 
     Modulation frequencies f x , f y , f z  and the phase Φ x , Φ y , Φ z  can be chosen to be the same or distinct based on technical constraints of the setup as well as to reduce crosstalk between the outputs. Crosstalk is defined as the response in the j th  error signal output when magnetic field changes in the i th  direction. For example, when magnetic field changes in the x-direction, only Ex is ideally expected to reflect this field change. However, any response observed in Ey or Ez error signal is referred to as the crosstalk between x and y axis or between x and z axis. 
     A few advantageous configurations are the following.
         Case 1. f x ≠f y ≠f z      Case 2. f x =f z ≠f y      Case 3. f x =f z =f y          

     Case 1 uses three separate modulation frequencies which is expected to produce the lowest crosstalk. The phases f x , f y , f z  in this case can be chosen to optimize slope and amplitude of individual error signals. 
     Case 2 has the benefit of requiring only two separate frequencies. In case 2, choosing f x =f z +π/2 is expected to result in the lowest crosstalk from simulations using Bloch equations. 
     Case 3 is particularly advantageous configuration because it allows all coils to be modulated at the same frequency which reduces interference from beat notes between frequencies f x , f y , f z . To minimize crosstalk, the modulation phase for example can be chosen to be Φ z =Φ x =Φ y +π/2. 
     In Case 2 and Case 3 in which the modulation frequency is the same in two or more directions, it is understood that an equivalent magnetic field pattern can be created using fewer coils. For example, a single coil with a correct orientation can generate the same magnetic field pattern that is created when modulation currents at the same frequency are separately applied to coils  110   x ,  110   x  and  110   z.    
     Example 2 
     In this example, as shown in  FIG. 12 , two separate 795 nm lasers  10 ,  1040  tuned to the D1 transition of the  87 Rb atoms, are used to generate light beams  201 , 202  for optical pumping. Besides the use of the two lasers  10 ,  1040  the apparatus and method for measuring the three magnetic components were the same and followed the same method as presented in Example 1. 
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