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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 28 — Dec. 31, 2012
  • pp: 29217–29222
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Light-shift suppression in a miniaturized Mx optically pumped Cs magnetometer array with enhanced resonance signal using off-resonant laser pumping

Theo Scholtes, Volkmar Schultze, Rob IJsselsteijn, Stefan Woetzel, and Hans-Georg Meyer  »View Author Affiliations


Optics Express, Vol. 20, Issue 28, pp. 29217-29222 (2012)
http://dx.doi.org/10.1364/OE.20.029217


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Abstract

The performance of an optically pumped Mx magnetometer with miniaturized Cs cell at earth’s magnetic field strength (50μT) is investigated. Operation using detuned high intensity laser light is shown to be superior to the conventional resonant operation in terms of the projected shot-noise-limited ( 50 f T H z) and the actual noise-limited sensitivity using a noise compensation method. The Zeeman light shift effect, emerging due to the off-resonant circularly polarized laser radiation and leading to a strong orientational dependence of the measurement, is suppressed by averaging two identical magnetometer configurations pumped with oppositely circularly polarized light. A residual heading error within the range of 14nT, limited by the present experimental characterization setup, was achieved.

© 2012 OSA

1. Introduction

Optically pumped magnetometers (OPMs), despite being invented more than 50 years ago [1

1. W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1565 (1957). [CrossRef]

], have seen renewed interest and a rapid development in recent years [2

2. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3, 227 – 234 (2007). [CrossRef]

], now even surpassing SQUIDs as the most sensitive magnetic field sensors [3

3. H. B. Dang, A. C. Maloof, and M.V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97, 151110 (2010). [CrossRef]

]. An OPM relies on a measurable interaction of alkali atom vapor, usually kept in glass cells, with the external magnetic field B⃗0. One established setup, as applied here, uses a single narrow-band laser light beam resonant on the D1 transition of the alkali atom for both preparation of the atoms by optical pumping [4

4. W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972). [CrossRef]

], and for signal detection by monitoring the cell-transmitted light power [5

5. A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61–68 (1962). [CrossRef]

]. A suitably prepared alkali atom subject to an external static magnetic field starts to precess, thereby modulating its optical properties at the characteristic Larmor frequency ωL = γ|B⃗0|, where γ denotes the gyromagnetic ratio of the alkali atom. This modulation becomes resonantly enhanced and all the atoms precess phase-synchronized when the frequency of an additionally applied alternating magnetic field B1 matches the Larmor frequency, giving rise to the macroscopic measurement signal. Using a feedback loop keeping the B1 frequency equal to ωL a sensor can be built [6

6. S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38, 239–247 (2006). [CrossRef]

].

Basically, OPMs are inherently scalar sensors measuring the absolute value of B⃗0 independently of its spatial direction. However, several prominent effects like the dead zones of the Mx setup, the nonlinear Zeeman effect in mediate magnetic fields (leading to asymmetic Cs magnetic resonance lines) or light shifts (i.e. AC Stark shifts) due to off-resonantly tuned, circularly polarized light [7

7. B. S. Mathur, H. Tang, and W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11–19 (1968). [CrossRef]

] introduce an orientational dependence to the sensor’s readings that have to be considered and well controlled [8

8. E. B. Aleksandrov and A. K. Vershovskii, “Modern radio-optical methods in quantum magnetometry,” Phys. Usp. 52, 573–601 (2009). [CrossRef]

]. Operating the magnetometer in the light-narrowed (LN) mode (cf. Sec. 3), as published recently [9

9. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]

], requires the circularly polarized laser radiation frequency to be tuned away from the magnetic resonance (at the upper hyperfine groundstate level F = 4). Due to the high intensity of the detuned laser light a strong displacement of the detected Larmor frequency dependent on the relative orientation of the external magnetic field to the pumping light’s direction emerges. To remove this effect, an approach known for almost 40 years [10

10. T. Yabuzaki and T. Ogawa, “Frequency shifts of self-oscillating magnetometer with cesium vapor,” J. Appl. Phys. 45, 1342–1355 (1974). [CrossRef]

], using the average of two identical but oppositely circularly polarized pumped magnetometer channels, is reinvestigated. However, this approach is applied to our special case of severe laser detuning and a buffer-gas broadened cell absorption profile of overlapping hyperfine transitions. For this purpose, due to the need of as identical cells as possible, a microfabricated multi-channel array sharing a common reservoir is used.

After describing the experimental setup the sensitivity optimizations are presented, followed by the investigation of the light-shift suppression.

2. Experimental setup

The setup shown in Fig. 1(a) is similar to the one described in [9

9. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]

], extended to be capable of two-channel measurements. The central part of the sensor is the newly designed vapor cell array shown in Fig. 1(b) incorporating two measurement cells sharing one common Cs metal reservoir. The fabrication of the cells follows the procedure described in [11

11. S. Woetzel, V. Schultze, R. IJsselsteijn, T. Schulz, S. Anders, R. Stolz, and H.-G. Meyer, “Microfabricated atomic vapor cell arrays for magnetic field measurements,” Rev. Sci. Instrum. 82, 033111 (2011). [CrossRef] [PubMed]

]. The cells are illuminated by narrow-band (Δν < 5MHz) circularly polarized light of a DFB laser, that is optionally amplified by a tapered amplifier and tuned to the Cs D1 line (λ = 894.6nm). The intensity of the modulated cell-transmitted laser light is monitored by silicon PIN photo diodes. The cell array is temperature-controlled by far off-resonant (λ = 977nm) heating laser radiation that is fiber-coupled onto two sooted spots of the cell array’s silicon wafer parts. The relatively good heat conductivity of silicon leads to equal measurement cell temperatures and to a slightly smaller temperature at the bigger central reservoir cavity, ensuring that Cs condensation always occurs there [12

12. R. IJsselsteijn, M. Kielpinski, S. Woetzel, T. Scholtes, E. Kessler, R. Stolz, V. Schultze, and H.-G. Meyer, “A full optically operated magnetometer array: an experimental study,” Rev. Sci. Instrum. 83, 113106 (2012). [CrossRef] [PubMed]

]. Coils on printed circuit boards are attached to both sides of the cell array to supply B1 fields parallel to the pump laser’s direction being separately tunable for both channels. The B1 fields are driven by the lock-in’s integrated oscillators that are also being used as the photo signals demodulation references. Despite the encouraging results obtained most recently by the use of an all-optical light modulation technique [13

13. V. Schultze, R. IJsselsteijn, T. Scholtes, S. Woetzel, and H.-G. Meyer, “Characteristics and performance of an intensity-modulated optically pumped magnetometer in comparison to the classical Mx magnetometer,” Opt. Express 20, 14201–14212 (2012). [CrossRef] [PubMed]

], we here stick to the ”classical” B1 method, as with the present setup the maximum possible pump laser power is not sufficient to allow an investigation of all-optical LN operation. For future unshielded application, we characterize our sensor at earth’s magnetic field strength. The setup is placed inside a three-axis Helmholtz coil system, described more in detail in [14

14. V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]

]. The six coils are each fed by independently controllable current sources, to supply B0 = 50μT at an angle of 45° relative to the laser direction (used for the noise measurements) as well as enabling rotation of B⃗0 across a full half space for the orientation-dependent investigations. External fields and disturbances are shielded using a three-fold mu-metal barrel and reduced by a factor of not less than 500. The two channels can be used as independent magnetometers or one channel, made magnetically insensitive by switching off the B1 field, can serve to cancel technical noise [14

14. V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]

, 15

15. V. Gerginov, S. Knappe, V. Shah, L. Hollberg, and J. Kitching, “Laser noise cancellation in single-cell CPT clocks,” IEEE Trans. Instrum. Meas. 57, 1357 (2008). [CrossRef]

].

Fig. 1 (a) Experimental setup: The two magnetometer channels can be operated independently (switched to A) or channel 2 can be made magnetically insensitive to provide a noise subtraction signal for the magnetometer channel 1 (switched to B). (b) Used cell array assembly filled with 170mbar of nitrogen buffer gas.

3. Magnetometer sensitivity optimization

The absorption spectrum of one magnetometer channel for different pump laser intensities is shown in Fig. 2(a). Due to buffer gas broadening the Cs D1 excited state hyperfine splitting is unresolved, the two ground state hyperfine levels F = 3 and F = 4 are partially overlapped. Tuning the narrow-band laser across the absorption profile results in changing the relative pumping ratio between the ground state levels. As described earlier [9

9. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]

] two different regimes can be observed: Pumping resonantly to F = 4 at a modest laser intensity has been labeled as the conventional operation mode, while strong pumping near the lower F = 3 level has been termed the light-narrowed (LN) operation mode, exhibiting a drastically improved shot-noise limited sensitivity compared to the conventional mode. The main effect responsible for improvement in sensitivity is the much higher signal strength due to repumping of the lower ground state level F = 3. Furthermore, due to the detuning of the high intensity laser in respect to the detected Zeeman resonances in the upper ground state level F = 4 the magnetic resonance gets not power-broadened to a large extent. On the other hand, the effect of “Light Narrowing” as suppression of spin-exchange broadening as described by Appelt et al. [16

16. S. Appelt, A. B. Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59, 2078–2084 (1999). [CrossRef]

], despite being overestimated at the time we published [9

9. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]

], still gives an extra contribution to the sensitivity improvement to justify the label ”light-narrowed”, in our opinion. To optimize the shot-noise-limited sensitivity in both regimes, automatically controlled measurements with variation of the operational parameters namely cell temperature, pump laser power and frequency and B1 field strength are carried out. The shot-noise-limited sensitivity of one channel is determined according to
Bsn=Gγ2eIdcdPqu/dν,
(1)
where dPqu/ is the steepness of the quadrature signal component at resonance, Idc the measured photo current and G the gain factor of the transimpedance amplifier. The results of the parameter scans shown in Fig. 2(b) correspond to overall optimum values at given cell temperatures. The optimal value for LN operation of Bsn=50fTHz is almost a factor of 4 better than the best conventional mode finding ( Bsn=185fTHz).

Fig. 2 (a) Cell absorption profile without B1 field, normalized to the F = 4 peak. Increasing the pump laser intensity results in reduced absorption for the F = 3 transitions caused by depletion of the lower hyperfine ground state level. Optimal laser frequency tuning points for conventional mode (black square) and LN mode (red triangle) are indicated. (b) Shot-noise-limited sensitivity optimized for each cell temperature in conventional (black squares) and LN (red triangles) operation mode.

As a second step the real noise values were acquired for each optimal parameter set by recording the noise spectra Vn of the quadrature component lock-in output and using
Bn=VnγdPqu/dν
(2)
to determine the actual sensor’s magnetic field sensitivity.

The noise level evaluated at 1kHz (what is within the magnetometer’s bandwidth) for single channel conventional mode operation lies about a factor of 2 above the calculated shot-noise limited value. By application of the noise compensation method [14

14. V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]

] the shot-noise limit is reached at high frequencies, which is a factor of 2 higher than without noise compensation due to the doubled light intensity. Noise measurements in the LN mode reveal a performance improvement by a factor of 2 compared to the conventional mode. However, in contrast to the conventional mode operation, despite the use of noise compensation, the shot-noise limit is not reached. Further investigations are necessary to shed light upon this issue.

4. Magnetometer orientational dependence

The most straightforward setup is to use the two oppositely circularly polarized pumped magnetometer channels of the cell array in parallel. However, this proved to be problematic for our experimental characterization method. Even though the measurement setup was trimmed to produce very homogenous magnetic fields at the place of the sensors, a residual distortion of about 2 · 10−3 still exists [14

14. V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]

]. Moreover, this resulting magnetic field gradient between the two cells of the integrated setup of Fig. 1(b) depends on the applied magnetic field orientation and the actual measurement history. In order to get rid of these problems, we chose another measurement procedure. Only one magnetometer cell was used, whose pumping light’s circular polarization sign was altered (σ±) by mechanically switching two λ/4-plates in and out the beam path. The retardation plates were carefully adjusted to give an equal minor-to-major axis ratio of the polarization ellipse of ≈ 0.98 for both positions. The magnitude of the light shift was trimmed to be identical in both configurations by carefully tuning the pump laser intensities, finally ending up with nearly equal detected photo current values. Each time before the magnetic field direction was changed, the shielding barrel was carefully demagnetized. Furthermore, to compensate for residual magnetization of the shielding barrel, imperfections of the coil system calibration and limited resolution of the magnetic field components due to the quantization limit of the coil’s current sources, the same B⃗0 orientation variation procedure was carried out twice. Starting in the conventional mode configuration, tuning the laser frequency to the point near the F = 4 absorption maximum, where no Zeeman light shift occurs, the Larmor frequency was measured in dependence of static magnetic field orientation. Then, by subtracting these values from the ones obtained in the LN mode all deviations due to experimental imperfections should be cancelled, leading to the measurement of the pure light-shift phenomenon.

The result of this subtraction is shown in Fig. 3(a). The strong dependence of the measured Larmor frequency difference on the B⃗0 field direction, caused by the light shift, can then be eliminated to a high degree by averaging the σ+ and σ light values. The residual variations, as shown in Fig. 3(b), are within the range of 14nT.

Fig. 3 (a) Measured Larmor frequency difference as a function of the angle of the magnetic field to the laser beam direction (−90°: antiparallel, 0°: perpendicular, 90° parallel) for the two oppositely circularly polarized configurations σ+ (red dots) and σ (black squares) and the average (blue triangles) of both measurements, magnified in (b).

Except for the measurements near the dead zones of the Mx magnetometer (±90° and 0°), where the measurement resolution gets poor, a systematic but asymmetric effect in the two hemispheres is visible. Thus, the deviation is most probably due to residual experimental imperfection of the magnetic field generation with the coil system inside the magnetic shielding. To overcome these experimental limits of the characterisation system, the rotation of a suitably constructed magnetometer system in a stable homogenous external field would be necessary. This would also offer the opportunity to study the impact of the nonlinear Zeeman effect and to investigate methods for its elimination. In the measurements shown here this systematic error is virtually absent as both the LN as well as the subtracted conventional mode values are shifted in a similar manner.

5. Conclusion

After optimizing the shot-noise limited sensitivity of an optically pumped magnetometer working both in the LN mode and the conventional mode at B0 = 50μT, the value of 50fTHz in the LN mode represents an improvement by a factor of 4 compared to the conventional mode performance. The drawback of having to operate with an off-resonant pump laser of circular polarization, which introduces an orientational dependence to the measurement by a strong Zeeman light shift, can be suppressed by averaging two channels pumped by light of inverse circular polarzation sense. With this method the residual error was made to be within the range of 14nT, experimentally limited by the reproducibility of the used characterisation setup.

Acknowledgments

We thank Alex Brown for carefully proofreading the article. This work was supported by the state of Thuringia/Germany under contract number B714-10043 with participation of the European Union Fund for Regional Development.

References and links

1.

W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1565 (1957). [CrossRef]

2.

D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3, 227 – 234 (2007). [CrossRef]

3.

H. B. Dang, A. C. Maloof, and M.V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97, 151110 (2010). [CrossRef]

4.

W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972). [CrossRef]

5.

A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61–68 (1962). [CrossRef]

6.

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38, 239–247 (2006). [CrossRef]

7.

B. S. Mathur, H. Tang, and W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11–19 (1968). [CrossRef]

8.

E. B. Aleksandrov and A. K. Vershovskii, “Modern radio-optical methods in quantum magnetometry,” Phys. Usp. 52, 573–601 (2009). [CrossRef]

9.

T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]

10.

T. Yabuzaki and T. Ogawa, “Frequency shifts of self-oscillating magnetometer with cesium vapor,” J. Appl. Phys. 45, 1342–1355 (1974). [CrossRef]

11.

S. Woetzel, V. Schultze, R. IJsselsteijn, T. Schulz, S. Anders, R. Stolz, and H.-G. Meyer, “Microfabricated atomic vapor cell arrays for magnetic field measurements,” Rev. Sci. Instrum. 82, 033111 (2011). [CrossRef] [PubMed]

12.

R. IJsselsteijn, M. Kielpinski, S. Woetzel, T. Scholtes, E. Kessler, R. Stolz, V. Schultze, and H.-G. Meyer, “A full optically operated magnetometer array: an experimental study,” Rev. Sci. Instrum. 83, 113106 (2012). [CrossRef] [PubMed]

13.

V. Schultze, R. IJsselsteijn, T. Scholtes, S. Woetzel, and H.-G. Meyer, “Characteristics and performance of an intensity-modulated optically pumped magnetometer in comparison to the classical Mx magnetometer,” Opt. Express 20, 14201–14212 (2012). [CrossRef] [PubMed]

14.

V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]

15.

V. Gerginov, S. Knappe, V. Shah, L. Hollberg, and J. Kitching, “Laser noise cancellation in single-cell CPT clocks,” IEEE Trans. Instrum. Meas. 57, 1357 (2008). [CrossRef]

16.

S. Appelt, A. B. Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59, 2078–2084 (1999). [CrossRef]

OCIS Codes
(020.0020) Atomic and molecular physics : Atomic and molecular physics
(020.6580) Atomic and molecular physics : Stark effect
(020.7490) Atomic and molecular physics : Zeeman effect
(230.0230) Optical devices : Optical devices

ToC Category:
Atomic and Molecular Physics

History
Original Manuscript: October 10, 2012
Revised Manuscript: November 15, 2012
Manuscript Accepted: November 29, 2012
Published: December 17, 2012

Citation
Theo Scholtes, Volkmar Schultze, Rob IJsselsteijn, Stefan Woetzel, and Hans-Georg Meyer, "Light-shift suppression in a miniaturized Mx optically pumped Cs magnetometer array with enhanced resonance signal using off-resonant laser pumping," Opt. Express 20, 29217-29222 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-28-29217


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References

  1. W. E. Bell and A. L. Bloom, “Optical detection of magnetic resonance in alkali metal vapor,” Phys. Rev. 107, 1559–1565 (1957). [CrossRef]
  2. D. Budker and M. Romalis, “Optical magnetometry,” Nat. Phys. 3, 227 – 234 (2007). [CrossRef]
  3. H. B. Dang, A. C. Maloof, and M.V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97, 151110 (2010). [CrossRef]
  4. W. Happer, “Optical pumping,” Rev. Mod. Phys. 44, 169–249 (1972). [CrossRef]
  5. A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61–68 (1962). [CrossRef]
  6. S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38, 239–247 (2006). [CrossRef]
  7. B. S. Mathur, H. Tang, and W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11–19 (1968). [CrossRef]
  8. E. B. Aleksandrov and A. K. Vershovskii, “Modern radio-optical methods in quantum magnetometry,” Phys. Usp. 52, 573–601 (2009). [CrossRef]
  9. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. Meyer, “Light-narrowed optically pumped Mx magnetometer with a miniaturized Cs cell,” Phys. Rev. A 84, 043416 (2011). [CrossRef]
  10. T. Yabuzaki and T. Ogawa, “Frequency shifts of self-oscillating magnetometer with cesium vapor,” J. Appl. Phys. 45, 1342–1355 (1974). [CrossRef]
  11. S. Woetzel, V. Schultze, R. IJsselsteijn, T. Schulz, S. Anders, R. Stolz, and H.-G. Meyer, “Microfabricated atomic vapor cell arrays for magnetic field measurements,” Rev. Sci. Instrum. 82, 033111 (2011). [CrossRef] [PubMed]
  12. R. IJsselsteijn, M. Kielpinski, S. Woetzel, T. Scholtes, E. Kessler, R. Stolz, V. Schultze, and H.-G. Meyer, “A full optically operated magnetometer array: an experimental study,” Rev. Sci. Instrum. 83, 113106 (2012). [CrossRef] [PubMed]
  13. V. Schultze, R. IJsselsteijn, T. Scholtes, S. Woetzel, and H.-G. Meyer, “Characteristics and performance of an intensity-modulated optically pumped magnetometer in comparison to the classical Mx magnetometer,” Opt. Express 20, 14201–14212 (2012). [CrossRef] [PubMed]
  14. V. Schultze, R. IJsselsteijn, and H.-G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100, 717–724 (2010). [CrossRef]
  15. V. Gerginov, S. Knappe, V. Shah, L. Hollberg, and J. Kitching, “Laser noise cancellation in single-cell CPT clocks,” IEEE Trans. Instrum. Meas. 57, 1357 (2008). [CrossRef]
  16. S. Appelt, A. B. Baranga, A. R. Young, and W. Happer, “Light narrowing of rubidium magnetic-resonance lines in high-pressure optical-pumping cells,” Phys. Rev. A 59, 2078–2084 (1999). [CrossRef]

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