Abstract:
Precise measurements of a precessional rate of noble gas in a magnetic field is obtained by constraining the time averaged direction of the spins of a stimulating alkali gas to lie in a plane transverse to the magnetic field. In this way, the magnetic field of the alkali gas does not provide a net contribution to the precessional rate of the noble gas.

Description:
STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0001]    -- 
       CROSS REFERENCE TO RELATED APPLICATION 
       [0002]    -- 
       BACKGROUND OF THE INVENTION 
       [0003]    The present invention relates to a method and apparatus for measuring the resonance of noble gas nuclei in a magnetic field, such as may be useful for constructing sensitive gyroscopes or magnetometers, and in particular to a resonator that reduces the effect of the magnetic fields of alkali atoms used to polarize and/or detect the noble gas spins. 
         [0004]    The nuclei of isotopes of noble gases such as xenon have a net spin which possesses a magnetic moment. These noble gases tend to be insensitive to environmental perturbations, except those which couple to the nuclear magnetic moments. Accordingly, if the nuclei of such atoms can be polarized and stimulated into precession, the frequency of precession can be used to precisely measure a magnetic field free from other influences. In this way, a precision magnetometer may be constructed. 
         [0005]    Alternatively, it will be understood that if the magnetic field is known and constant, deviations in the resulting frequency of precession, measured in the reference frame rotationally stationary with respect to the measurement of the precession, will indicate rotation of the observer about the axis of precession. In this way, a precision gyroscope may be constructed. 
         [0006]    The qualities of noble gas that make them relatively insensitive to environmental conditions other than the magnetic field may conversely make it difficult to enforce a net polarization of these atoms in the small magnetic fields typically at issue. Accordingly, spin-polarization of the noble gas may be accomplished in a two-step process in which alkali atoms such as rubidium are first spin-polarized by pumping them with a circularly polarized pump beam from a laser. The spin-polarization of the alkali atoms is then transferred to the noble gas isotopes by collision. 
         [0007]    In the construction of a gyroscope, the magnetic fields must be carefully controlled. Generally, the Earth&#39;s magnetic field has some variability, the influence of which may be reduced by magnetic shielding. In addition, the magnetic field produced by the magnetic moment of the alkali atoms adds a poorly known local component to the magnetic field. Both of these unknowns may be reduced by the use of two isotopes (for example 129-xenon and 131-xenon) as follows: 
         [0008]    Generally the two xenon isotopes will have different gyromagnetic constants γ 1  and γ 2  such that: 
         [0000]      ω 1 =γ 1 ( B   0   +B   A1 )±Ω  (1)
 
         [0000]      ω 2 =γ 2 ( B   0   +B   A2 )±Ω  (2)
 
         [0009]    where ω is the measured precessional frequency, B 0  is the magnetic field (a combination of all magnetic field influences including that of the alkali atoms), B A1  and B A2  are the magnetic field produced by the alkali atoms, and Ω is the angular rotational rate of the system to be determined. The sign of the gyromagnetic constants determines whether the rotation adds to or subtracts from the resonance frequency. For xenon, B A1 =B A2 , so that measurements of the two precession frequencies ω 1  and ω 2  allows the system of two independent equations to be solved for Ω reducing the influence of the unknown value of B 0  and B A  to the limits of the measurement precision. 
         [0010]    The use of xenon atoms has a drawback insofar as one xenon isotope (Xe 131) is subject to quadrupolar electric interaction causing it to be sensitive to electrical field gradients, and thus adds an extra term to one precession frequency violating the assumption that the noble gases are generally insensitive to environmental conditions other than magnetic field. The quadrupolar interaction can be eliminated through the use of a different noble gas such as a helium isotope, for example, 3-helium, which has no electrical quadrupole moment. Unfortunately, the helium atoms have a different value for B A  as compared to xenon, so the 3-helium/xenon mixture is far more influenced by the magnetic field of the alkali atoms used to promote spin polarization than the xenon isotopic mixture. Imperfect correction for the magnetic field of the alkali atoms imposes an error on the precision of the measurement of the precession of the helium or xenon atoms, largely negating any improvement obtained by replacing one xenon isotope with helium. 
       SUMMARY OF THE INVENTION 
       [0011]    The present invention further reduces the influence of the magnetic fields of the alkali atoms on the precession of noble gas nuclei by constraining the magnetic moments of the alkali atoms to have, on average, zero angular difference with the magnetic moments of the noble gas. In this way, the magnetic field of the alkali atoms does not affect the precession rate of the noble gas and the B A  terms in Eqs 1 and 2 do not appear (i.e. have a time average value of zero), leaving the noble gas precession rates dependent only on external magnetic fields and rotations. 
         [0012]    Specifically, the present invention may provide a magnetic resonator system having a chamber holding an inter-mixed noble gas and an alkali gas exposed to a magnetic field external to those generated by the gases and directed along a z-axis. A spin aligner acts on the alkali gas to promote a precession of a magnetic moment of the alkali gas about the z-axis so that a time averaged angular difference between the magnetic moment of the alkali gas and the magnetic moment of the noble gas is substantially zero and a monitor outputs a signal indicating the precession frequency of the noble gas. 
         [0013]    It is thus a feature of at least one embodiment of the invention to significantly reduce the effect of the magnetic field generated by the alkali atoms on the precession of the noble gas by constraining the magnetic moments of the alkali atoms to be, on average, parallel to the noble gas moments. The constrained magnetic moment of the alkali atoms ensures that there will be no time averaged component of the magnetic moment that can add to the external magnetic field and affect the noble gas precession. 
         [0014]    The spin aligner may promote a precession of the magnetic moment of the alkali gas about the z-axis without a substantial time-averaged z-component of the magnetic moment. 
         [0015]    It is thus a feature of at least one embodiment of the invention to prevent the alkali gas from having a time averaged magnetic moment along the z-axis that would change the precession rate of the noble gas about the z-axis. 
         [0016]    The monitor may detect z-axis excursions of the magnetic moment of the alkali gas as modulated by the noble gas to measure precession frequency of the noble gas. 
         [0017]    It is thus a feature of at least one embodiment of the invention to provide a simple method of measuring the noble gas precession free from interference from the process that produces and detects the noble gas polarization. 
         [0018]    The spin aligner may drive the magnetic moment of the alkali gas in two alternating directions along the x-axis at the frequency of precession of the noble gas. 
         [0019]    It is thus a feature of at least one embodiment of the invention to cancel the effect of z-axis excursions of the spin polarization caused by interactions between the noble gas and the alkali gas and to coordinate spin polarization of the alkali atoms with precession of the noble gas to maximize the spin polarization of the noble gas and hence the generated precession signal. 
         [0020]    The magnetic resonator system may include a detector detecting excursions of the magnetic moment of the alkali gas along the z-axis and the spin aligner may change a direction of polarization of the magnetic moment of the alkali gas at a predetermined excursion of the alkali gas along the z-axis. 
         [0021]    It is thus a feature of at least one embodiment of the invention to permit timing of the stimulation of the alkali gas using a z-axis monitor free from interference from the process that produces and detects the noble gas polarization. 
         [0022]    The spin aligner may receive a measure of the precession of the noble gas signal from the monitor for driving the magnetic moment of the alkali gas in two alternating directions along the x-axis at a frequency of precession of the noble gas. 
         [0023]    It is thus a feature of at least one embodiment of the invention to permit a single detection mechanism to be used both to detect precession of the noble gas and control the precession of the alkali gas magnetic moment. 
         [0024]    The spin aligner may include at least one magnetic coil providing a second magnetic field aligned with the z-axis and a pump laser aligned along the x-axis, the second magnetic field modulated to provide a time-averaged alignment of the magnetic moment of the alkali gas along the x-axis. 
         [0025]    It is thus a feature of at least one embodiment of the invention to provide a simple method of modulating the precession of the alkali gas. By providing a modulating field having an average value of zero, the magnetic field may be free from interfering with the precessional frequency of the noble gas. 
         [0026]    The magnetic resonator system may further include a second monitor detecting transverse excursions of the magnetic moment of the alkali gas along a transverse axis perpendicular to the z-axis and the spin aligner may communicate with the second monitor to control the second magnetic field to modify precession of the alkali gas about the z-axis to provide a time averaged alignment of the magnetic moment of the alkali gas along the x-axis. 
         [0027]    It is thus a feature of at least one embodiment of the invention to provide effective controlled alignment of the magnetic moments of the alkali gas. 
         [0028]    The noble gas may be a helium isotope or any other noble gas isotope with spin-½. 
         [0029]    It is thus a feature of at least one embodiment of the invention to provide improved accuracy in the measurement of precessional frequency of the noble gas by selecting a noble gas with no quadrupole interaction. 
         [0030]    The magnetic resonator system may further include a processor receiving the precession frequency and converting it to a magnetic field strength of the magnetic field and/or converting it to a rotational orientation. 
         [0031]    It is thus a feature of at least one embodiment of the invention to provide an improved gyroscope or magnetometer. 
         [0032]    These particular objects and advantages may apply to only some embodiments falling within the claims and thus do not define the scope of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0033]      FIG. 1  is a simplified perspective view of a magnetic resonator system of the present invention showing orientation of a stimulating laser, magnetic field coils, and orthogonal sensing lasers about a gas chamber holding a noble gas and alkali gas; 
           [0034]      FIG. 2  is a simplified perspective view of the precession of the magnetic moment of the atoms of the alkali gas stimulated into precession in the x-y plane at a changing precession rate plotted against time; 
           [0035]      FIG. 3  is a vector diagram showing orientation of the magnetic moment of the alkali gas in the x-y plane as weighted by incremental dwell time at each angle, per the time plot of  FIG. 2 , illustrating a magnetic moment of the alkali gas having a time averaged upward vertical orientation; 
           [0036]      FIG. 4  is a graph and vector diagram similar to those of  FIG. 3  and  FIG. 2 , showing a precession rate providing magnetic moment of the alkali gas having a time averaged downward vertical orientation; 
           [0037]      FIGS. 5-8  are corresponding perspective, x-y plane and x-z plane depictions of the magnetic moments of the noble gas and alkali gas during transverse plane precession of the magnetic moments of the noble gas population as induced by switching between the modulation patterns producing upward and downward magnetic moment for the alkali gas; 
           [0038]      FIG. 9  is a plot of the signal received by a z-axis sensing laser such as provides a measure of precession of the noble gas about the z-axis; 
           [0039]      FIG. 10  is a functional block diagram of a control system for the present invention; and 
           [0040]      FIG. 11  is a representation of an alternative chamber of  FIG. 1  holding multiple species of atoms for providing a gyroscope output less sensitive to the external magnetic field. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
       [0041]    Referring now to  FIG. 1 , a magnetic resonator system  10 , per one embodiment of the present invention, may include a chamber  12  holding an alkali gas  14  and noble gas  16 . In one embodiment, the alkali gas  14  may be rubidium (Rb) and the noble gas  16  may be a helium isotope (3-He). Each of the atoms of the alkali gas  14  and the noble gas  16  has magnetic moments  15  and  17 , respectively, represented by directional arrows in the figure. 
         [0042]    The chamber  12  may have transparent walls allowing a laser beam  18  of a first Faraday rotational probe  21  to pass through the chamber  12  along a z-axis of a Cartesian coordinate system having its z-axis aligned with an external magnetic field  20  (B 0 ). This laser beam  18  may be emitted from a laser source  22  and received by a polarimeter  24  positioned on opposite sides of the chamber  12  along the z-axis from the laser source  22 . As will be understood in the art, this first Faraday rotational probe  21  provides a measure of a z-axis component of the magnetic moment  15  of the population of alkali gas  14 . 
         [0043]    A set of magnetic coils  23  (for example a Helmholtz coil pair flanking the chamber and aligned along the z-axis) may provide an alternating or pulsed magnetic field (B 1 ) aligned along the z-axis. As will be discussed below, this field provides a means for controlling the time-averaged alkali spin precession in the presence of an external field B 0 . In particular, the field B 1  will be modulated to moderate the naturally faster precession rate of the alkali gas  14  in the external magnetic field B 0  to be aligned along the pump laser  32  direction. 
         [0044]    A second Faraday rotational probe  27  may include a laser source  26  directing a laser beam  30  along the y-axis through the chamber  12  to a corresponding receiving polarimeter  28  on the other side of the chamber  12 . This second Faraday rotational probe  27  provides a measure of the y-axis component of the magnetic moment  15  of the population of alkali gas  14 . 
         [0045]    A “pump” laser  32  may direct a laser beam  33  along the x-axis through the chamber  12  after passing through a polarization modulator  34 . The pump laser  32  and polarization modulator  34  may “spin-polarize” the magnetic moment  15  of the alkali gas  14  to align in either of two directions along the x-axis (upward or downward as depicted) according to a modulation signal  36  received by the polarization modulator  34 . This polarization occurs by transfer of the angular momentum of the polarized photons of the laser beam  33  to the alkali gas  14  as will be generally understood in the art. 
         [0046]    It will be understood that the various laser sources  22 ,  26 , and  32  in various combinations may be derived from one or more light sources. 
         [0047]    Signals from the polarimeters  28  and  24  may be provided as electrical signal input to a control system  40  to be processed as will be described below. The control system  40  may in turn output the modulation signal  36  to the polarization modulator  34 . The control system  40  may also output the modulation signal  37  to the magnetic coils  23 . The control system  40  may be constructed of discrete components or functional blocks such as lock-in amplifiers, frequency counters and the like as will be described below or these elements may be implemented in software in an electronic computer  42  as depicted, or in dedicated hardware including an application-specific integrated circuit or digital signal processor, or as a combination of different elements in a hybrid configuration. In the case of implementation in a computer  42 , the computer  42  may execute a stored program  44  and may communicate with user input devices  46  such as a keyboard and/or mouse and may provide output for example through a graphic display screen  48  or other functionally similar device. Alternatively, or in addition, the control system  40  may provide a control output  50 , for example, providing a gyro output (e.g., angle or angular rate about the z-axis) or a magnetometer output (e.g. Gauss) use for control of an ancillary device such as aircraft or the like. 
         [0048]    Referring also to  FIG. 2 , during operation of the magnetic resonator system  10 , the control system  40  will control the laser beam  33  and the applied magnetic field B 1  to drive the magnetic moment of the population of alkali gas  14  into precession substantially within the x-y plane. This precession is invoked by illuminating the alkali gas  14  with photons having alternate upward and downward angular momentum indicated by arrows  52 . The momentum of the photons is then transferred to the alkali gas  14  to align the magnetic moment  15  of the alkali gas  14  with the photon angular momentums. Ongoing precession of the alkali gas  14  is then controlled by varying the B 1  field by control signal  37 . The y-axis component of this precession of the magnetic moment  15  of the alkali gas  14  may be detected by the beam  30  of the second Faraday rotational probe  27   
         [0049]    Control of the B 1  will be such that the precession  54  of the magnetic moment  15  of the alkali gas  14  in the x-y plane will not be at a uniform angular rate such as would be detected as a sinusoidal waveform by the second Faraday rotational probe  27 , but rather, as an irregular angular rate processing, relatively slower in the upper half cycle such as will produce a compressed precession waveform  56 . The compressed precession waveform  56  represents the y-axis component of an angular rate having a greater dwell time  29  of the magnetic moment  15  of the alkali gas  14  during precession when the magnetic moment of the alkali gas  14  is facing in an upward rather than the downward direction. 
         [0050]    This compressed precession waveform  56  may be produced by modulating the B 1  field to a low relatively constant negative value  31  to substantially offset the B 0  field during the time  29  (greatly reducing the precession when the magnetic moment  15  is facing upward) for most of the period 1/ω of the normal precession of the alkali gas  14  in field B 0  The field B 1  may then be maximized during a short time remaining in 1/ω by providing a positive pulse of amplitude  41  augmenting the field B 0  to promote rapid precession of the alkali gas  14  by 360 degrees back to the upward orientation. The field B 1  is controlled to have no direct current (that is areas  53  and  55  during times  29  and the remainder of 1/ω are equal and opposite) so that it has no net effect on the precession frequency of the alkali gas  14  or noble gas  16 . 
         [0051]    Referring momentarily to  FIG. 3 , a diagram of the alkali magnetic moment  15  at various points in time as an angular vector having a length proportional to the incremental dwell time at each angle, it traces an oval outline  35  reflecting the increased time weighting of the magnetic moment in the upward direction. The centroid of this outline  35  may illustrate the time-averaged magnetic moment  15  as a stationary upward magnetic moment  15   a . The compressed precession waveform  56  which still retains the normal precession rate of the alkali gas  14  in the magnetic field B 0  boosts the length of the average magnetic moment  15  over that which might be provided by a sinusoidal B 1  field by a significant amount (for example 10 times) greatly increasing the effect on the noble gas  16 . In addition, effective neutralization of the B 0  field during time  29  comprising most of the precession cycle, substantially reduces dephasing of the precession due to spin-exchange between atoms of the alkali gas  14 . This stationary magnetic moment  15   a  represents moment experienced by the noble gas  16  during its precession during the irregular precession of the alkali gas  14 , the latter of which generally has precession rate as much is 1000 times higher the precession rate of the noble gas  16 . 
         [0052]    Referring now to  FIG. 4 , it will be understood that the same waveform  56  with an inversion of signal  36  received by the polarization modulator  34  will produce a precession waveform  60  producing a time averaged magnetic moment  15   b  facing downward along the x-axis. Accordingly, by switching signal  36 , an effective upward or downward magnetic moment  15   a  or  15   b  of the alkali gas  14  may be generated within the transverse x-y plane. 
         [0053]    Referring now to  FIG. 5 , the laser beam  33  from the pump laser  32  and the coils  23  initially may be modulated to produce the upward directed time averaged magnetic moment  15   a  causing the magnetic moments  17  of the population of noble gas to align therewith along the x-axis. Referring also to  FIG. 9 , at this time a z-component signal  62  from the first Faraday rotational probe  21  will show no z-axis component as indicated at waveform value  64 . 
         [0054]    Referring now to  FIG. 6 , a short time later, the magnetic moments  17  of the noble gas will have precessed away from a vertical orientation along the x-axis caused by the influence of the external magnetic field B 0 . The divergence of the magnetic moments  15   a  and  17  causes a torque on the magnetic moment  15   a  pushing the magnetic moment  15   a  by an angle β out of the x-y plane in the direction of B 0 . This excursion of the magnetic moment  15   a  out of the x-y plane applies a slight additional z-axis magnetic field to the noble gas (adding to field B 0 ) causing the noble gas  16  to increase slightly in precession. A similar torque will be applied to the magnetic moment  17  which will be neglected at this time. 
         [0055]    Referring now to  FIG. 7 , after an additional time, the magnetic moment  17  of the noble gas  16  will have precessed to be aligned with the y-axis so that the magnetic moments  15   a  and  17  are nearly perpendicular. In this state, the magnetic moment  17  produces its maximum torque on magnetic moment  15   a , which will afterwards begin to decrease as the magnetic moment  17  passes below the y-axis. Referring to  FIG. 9 , accordingly, at this time the z-component signal  62  is at a maximum waveform value  70  of zero slope. This point of zero slope may be used to change the polarization of the laser beam  33  to change the asymmetrical angular rotation of the alkali gas  14  to the pattern shown in  FIG. 4 , with the result of flipping the angle of the magnetic moment  15   a  to  15   b  so that it is facing vertically downward as depicted in  FIG. 7 . 
         [0056]    As shown in  FIG. 9 , at this time the z-component signal  62  is at a negative waveform value  72  caused by a corresponding reversal of the torque on magnetic moment  15   b  from magnetic moment  17  still on the y-axis. This torque now causes the magnetic moment  15   a  to be deflected by an angle −β from the x-y plane but in a direction counter to that of B 0 . This negative deflection of the magnetic moment  15   b  produces a negative z-axis component that slows the precession of the magnetic moment  17  by an amount offsetting the previously described increase in precession, resulting in no net effect on the magnetic moment  17  by the magnetic moments  15   a  and  15   b  of the alkali gas  14 . 
         [0057]    Referring now to  FIG. 8 , the magnetic moment  17  continues to precess until it is aligned with magnetic moment  15   b  directed downward along the x-axis. The torque between these magnetic moments  15   b  and  17  drops to zero. Referring to  FIG. 9 , z-component signal  62  returns to a zero value at waveform value  74 . 
         [0058]    It will be appreciated that the zero crossings  64  and  74  of waveform  62  may alternatively be used for synchronization of the modulation. 
         [0059]    It will also be appreciated that the amount of deflection of the magnetic moment  15   a  and  15   b  out of the x-y plane is symmetrical not only in its peak value but also in its decline to have no net effect on the time average value of the precession of the magnetic moment  17 . 
         [0060]    Referring to  FIG. 9 , it will be understood that the periodicity of z-component signal  62  over one complete cycle represents the inverse of the precession frequency of the noble gas  16  without influence by the alkali gas  14  and can therefore be used to accurately measure the precession of the population of the noble gas  16  without additional sensing structure. 
         [0061]    It should be noted that the magnetic moment  17  of the noble gas will also be affected by the torque caused by magnetic moments  15   a  and  15   b  of the alkali gas but again generally this deflection along the z-axis will be positive during a first-half cycle of the precession of the magnetic moment  15  and negative during a second-half cycle of that precession to be fully offset over one cycle. 
         [0062]    Referring now to  FIG. 10 , the control system  40  may implement a number of functional blocks either through discrete components or software or a combination of the same as described above. In one embodiment, precession waveform  56  from the polarimeter  28  representing the y-axis component of the precession of the alkali gas  14  may be received at a phase comparator  80  of a phase locked loop type lock-in amplifier  82 . The phase comparator  80  may also receive an output of a voltage controlled oscillator  84  divided by a divider  86 , and may operate to lock the phase and frequency of the voltage controlled oscillator  84  with the phase of the precession waveform  56  representing the precession of the magnetic moment  15  of the alkali gas  14 . 
         [0063]    The undivided high-frequency output of the voltage controlled oscillator may then be used to drive a synthesizer  87  synchronized to the precession waveform  56  providing a desired waveform implementing the modulation signal for driving the coils providing B 1 . The synthesized modulation signal  37  for coils  23  may be back-calculated from the desired precession waveforms  56  or  60 , as will be understood by those of ordinary skill in the prior art, to maintain the time averaged alkali spin along the x-axis at substantially the frequency of the freely processing alkali gas  14  in field B 0 . Generally the amplifier  82  thus adjusts the phase and frequency of the synthesized modulation signal  37  for the coils  23  to match the natural precession frequency of the alkali gas  14   
         [0064]    As noted, the synthesized modulation signal  36  may be selected to generate either the upward magnetic moment  15   a  or the downward magnetic moment  15   b  and this synthesized waveform may be selected by an input signal  93  to the synthesizer  87 . This input signal  93  may be generated from the z-component signal  62  from polarimeter  24  of the first Faraday rotational probe  21  (shown in  FIG. 9 ) by detecting the zero slope waveform value  70  of the positive peak of the z-component signal  62 , for example, using a differentiator  92  and zero crossing detector  94  triggering a toggle or flip-flop  96 . The flip-flop  96  provides a binary output producing the input signal  93  to switch the magnetic moment  15  of the alkali gas  14  appropriately using the polarization modulator  34 . 
         [0065]    In an alternative embodiment, the precession of the noble gas  16  may be measured directly using the Faraday rotational probe  27  which may be used to control the polarization modulator  34 . 
         [0066]    A frequency counter  90  may be used to produce a count signal  100  over a period of time, which may be scaled or otherwise processed by scaler  102  to provide for a display on display screen  48  indicating the precession frequency of the noble gas  16  or to provide the control output  50  for use as a gyroscope or magnetometer. 
         [0067]    Referring now to  FIG. 11 , it will be appreciated that these principles and techniques described above may be extended to a chamber  12  holding a first and second isotope of noble gas  16   a  and  16   b  having magnetic moments  17   a  and  17   b  respectively with different gyromagnetic constants. The use of these two different isotopes permits the production of a control output  50  for a gyroscope that is largely indifferent to the value of the external magnetic field B 0  using the equations (1) (2) as discussed above. In such a system, the waveforms needed for each species of the isotope may be combined by multiplication and the sign of the product used to provide the signal to the polarization modulator  34 . Frequency demultiplexing techniques may be used to extract the individual signals from the waveforms from the Faraday rotational probes  21  and  27 . The control output  50  will then reveal the rotation of a coordinate system fixed with respect to the reference frame used to determine the precession of the noble gas  16 , e.g. the reference frame of the Faraday rotational probe  21 . 
         [0068]    It will be appreciated that the present invention may be used, for example, with a magnetic shield  11  (shown in  FIG. 1 ) to moderate the influence of external magnetic fields that may have variability, when a gyroscope is being constructed. In addition the invention may be used with nulling coils to provide a field B 2  generally aligned with the z-axis to null or control the B 0  field. The laser detectors shown may be replaced by other magnetic detectors including for example pickup coils. It will be understood that the gas mixtures described may include other gaseous elements and the invention may also use noble gases with quadrupole interactions. In addition, it is contemplated that the invention may work with hybrid spin-exchange optical pumping in which there are two species of alkali atoms and one interacts with the laser and the other works as a spin-bath to exchange angular momentum between the first alkali and the noble gas. 
         [0069]    Generally, the term “magnetic field” as used herein should be understood to refer to both or either of the classical magnetic field and a quantum mechanical term that looks like a magnetic field, as context would require. The terms “alkali” and “alkali gas” as used herein should be understood to refer to “alkali-metal atom” or “alkali-metal gas” or “alkali-metal magnetic moment” as context would require per the understanding of those of ordinary skill in the art. 
         [0070]    Certain terminology is used herein for purposes of reference only, and thus is not intended to be limiting. For example, terms such as “upper”, “lower”, “above”, and “below” refer to directions in the drawings to which reference is made. Terms such as “front”, “back”, “rear”, “bottom” and “side”, describe the orientation of portions of the component within a consistent but arbitrary frame of reference which is made clear by reference to the text and the associated drawings describing the component under discussion. Such terminology may include the words specifically mentioned above, derivatives thereof, and words of similar import. Similarly, the terms “first”, “second” and other such numerical terms referring to structures do not imply a sequence or order unless clearly indicated by the context. 
         [0071]    When introducing elements or features of the present disclosure and the exemplary embodiments, the articles “a”, “an”, “the” and “said” are intended to mean that there are one or more of such elements or features. The terms “comprising”, “including” and “having” are intended to be inclusive and mean that there may be additional elements or features other than those specifically noted. It is further to be understood that the method steps, processes, and operations described herein are not to be construed as necessarily requiring their performance in the particular order discussed or illustrated, unless specifically identified as an order of performance. It is also to be understood that additional or alternative steps may be employed. 
         [0072]    References to “a controller” and “a processor” or “the microprocessor” can be understood to include one or more microprocessors that can communicate in a stand-alone and/or a distributed environment(s), and can thus be configured to communicate via wired or wireless communications with other processors, where such one or more processor can be configured to operate on one or more processor-controlled devices that can be similar or different devices. Furthermore, references to memory, unless otherwise specified, can include one or more processor-readable and accessible memory elements and/or components that can be internal to the processor-controlled device, external to the processor-controlled device, and can be accessed via a wired or wireless network. 
         [0073]    It is specifically intended that the present invention not be limited to the embodiments and illustrations contained herein and the claims should be understood to include modified forms of those embodiments including portions of the embodiments and combinations of elements of different embodiments as come within the scope of the following claims. All of the publications described herein, including patents and non-patent publications, are hereby incorporated herein by reference in their entireties.