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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 22, Iss. 6 — Mar. 24, 2014
  • pp: 6837–6843
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Simultaneously improving the sensitivity and absolute accuracy of CPT magnetometer

Shang-Qing Liang, Guo-Qing Yang, Yun-Fei Xu, Qiang Lin, Zhi-Heng Liu, and Zheng-Xiang Chen  »View Author Affiliations


Optics Express, Vol. 22, Issue 6, pp. 6837-6843 (2014)
http://dx.doi.org/10.1364/OE.22.006837


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Abstract

A new method to improve the sensitivity and absolute accuracy simultaneously for coherent population trapping (CPT) magnetometer based on the differential detection method is presented. Two modulated optical beams with orthogonal circular polarizations are applied, in one of which two magnetic resonances are excited simultaneously by modulating a 3.4GHz microwave with Larmor frequency. When a microwave frequency shift is introduced, the difference in the power transmitted through the cell in each beam shows a low noise resonance. The sensitivity of 2pT/ Hz @ 10Hz is achieved. Meanwhile, the absolute accuracy of ± 0.5nT within the magnetic field ranging from 20000nT to 100000nT is realized.

© 2014 Optical Society of America

1. Introduction

An atomic magnetometer is a very promising instrument for detecting weak magnetic field. It can reach high sensitivity or absolute accuracy. However, it is very difficult to achieve high sensitivity and absolute accuracy simultaneously. For instance, atomic magnetometers based on electron spin such as Nonlinear Magneto Optical Rotation (NMOR), Spin Exchange Relaxation Free (SERF) and Mx optical pumping can reach very high sensitivity of few ft/Hz [1

1. P. D. D. Schwindt, L. Hollberg, and J. Kitching, “Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation,” Rev. Sci. Instrum. 76(12), 126103 (2005). [CrossRef]

3

3. V. Schultze, R. IJsselsteijn, and H. G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100(4), 717–724 (2010). [CrossRef]

], but they perform poor in absolute measurement. On the contrary, atomic magnetometers based on nuclear spin such as Overhauser (OVH) magnetometer, which is developed from the proton precession method, performs well in absolute measurement, but it’s sensitivity and sampling rate are not so high [4

4. V. Sapunov, J. Rasson, A. Denisov, D. Saveliev, S. Kiselev, O. Denisova, Y. Podmogov, and S. Khomutov, “Theodolite-borne vector Overhauser magnetometer: DIMOVER,” Earth Planets Space 58, 711–716 (2006).

]. The coupled dark state magnetometer (CDSM), which is proposed by Pollinger et al. [5

5. A. Pollinger, R. Lammegger, W. Magnes, M. Ellmeier, W. Baumjohann, and L. Windholz, “Control loops for a Coupled Dark State Magnetometer,” in Sensors (IEEE, 2010), 779–784.

,6

6. A. Pollinger, M. Ellmeier, W. Magnes, C. Hagen, W. Baumjohann, E. Leitgeb, and R. Lammegger, “Enable the inherent omni-directionality of an absolute coupled dark state magnetometer for e.g. scientific space applications,” in Instrumentation and Measurement Technology Conference (I2MTC) (IEEE, 2012), 33–36. [CrossRef]

], can reach high absolute accuracy as an atomic magnetometer based on electron spin. However, as a kind of CPT magnetometer, the sensitivity of the CDSM could not be high due to the low contrast and signal to noise ratio of the CPT resonance. In recent years, several methods have been put forward for improving the signal to noise ratio of CPT resonance such as lin ⊥ lin [7

7. P. Yun, B. Tan, W. Deng, J. Yang, and S. Gu, “Quasi-bichromatic laser for a lin⊥lin coherent population trapping clock produced by vertical-cavity surface-emitting lasers,” Rev. Sci. Instrum. 83(9), 093111 (2012). [CrossRef] [PubMed]

], lin Π lin [8

8. E. E. Mikhailov, T. Horrom, N. Belcher, and I. Novikova, “Performance of a prototype atomic clock based on lin ‖ lin coherent population trapping resonances in Rb atomic vapor,” J. Opt. Soc. Am. B 27(3), 417–422 (2010). [CrossRef]

,9

9. A. L. Yang, G. Q. Yang, Y. F. Xu, and Q. Lin, “High contrast atomic magnetometer based on coherent population trapping,” Chin. Phys. B. 23(2), 027601 (2014). [CrossRef]

], push-pull optical pumping [10

10. X. C. Liu, J. M. M’erolla, S. Gu’erandel, C. Gorecki, E. D. Clercq, and R. Boudot, “Coherent-population-trapping resonances in buffer-gas-filled Cs-vapor cells with push-pull optical pumping,” Phys. Rev. A 87(1), 013416 (2013). [CrossRef]

], differential detection by orthogonal polarization [11

11. M. Rosenbluh, V. Shah, S. Knappe, and J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]

], etc.. However, most of these methods are only effective in clock transition used in CPT clocks. For the transition of magnetic sublevels used in CPT magnetometers, few methods can guarantee high sensitivity and absolute accuracy simultaneously.

In this paper, a new method based on the differential detection in CPT magnetometer in order to get high sensitivity and absolute accuracy simultaneously is presented. The right circularly polarized optical beam (σ-) and the left circularly polarized one (σ+) excite magnetic sublevels of 87Rb atoms respectively. Each of the beams can excite two groups of magnetic sublevels, whose magnetic quantum numbers are mF=±1, and prepare two CPT states simultaneously by the method of modulating a 3.4GHz microwave with Larmor frequency. When a microwave frequency shift is introduced, the difference in the power transmitted through the cell in each beam shows a resonance with low noise. In this way, common-mode noise can be suppressed and the sensitivity of the magnetometer can be improved. Meanwhile, the influences of undesired frequency shift of magnetic sublevels can be restrained in principle and high absolute accuracy can be ensured. Compared to the traditional CPT magnetometer, not only the characteristics of no dead zone and all optical technique can be preserved, but also high sensitivity and absolute accuracy can be guaranteed. This kind of CPT magnetometer can be used as a high absolute accuracy magnetometer with high sensitivity.

2. Experimental setup

The experimental setup is shown in Fig. 1(a).
Fig. 1 (a) The experimental setup of magnetometer in this experiment. (b) 87Rb atom’s energy levels of D1 line in magnetic field and Λ-type configurations excited by σ+ laser (red lines) and σ- laser (green lines).
A Vertical Cavity Surface Emitting Laser (VCSEL) is used to provide 100MHz-bandwith, 80μW-intensity, linearly polarized laser at 795nm wavelength. Lens is used to collimate the light came from VCSEL. Isolator (ISO) is used to forbid optical feedback. The cylindrical vapor cell with 15mm-diameter and 25mm-length is filled with 87Rb and 10 Torr buffer gas and is set in a shielding cylinder with four layers. The magnetic field is provided by coils. PD1 and PD2 are balanced photo detectors for getting the same electro-optical properties. Lock-in Amplifier 1 (LIA1) and PI controller (PI) are used to frequency stabilization. The absorption spectrum is used to find and stabilize the frequency of laser needed for CPT states preparation. A microwave source of 3.417GHz is mixed into the current supply of the VCSEL for modulation. A Digital Signal Generator (DSG) which uses the technique of Direct Digital Synthesizer (DDS) modulates the microwave source at Larmor frequency through FM. Lock-in Amplifier 2 (LIA2) is used to demodulate the CPT resonances and the modulation frequency is 678Hz. The magnetic field is produced by a solenoid and the current of the solenoid is provided by a current source. It’s made by Agilent and its model is B2912A.

The laser of VCSEL goes through lens, ISO, λ/2 plate in turn and Polarizing Beam Splitter (PBS) splits the linearly polarized laser into two beams whose polarizations are orthogonal and intensities are equal. λ/2 plate is arranged for adjusting the intensity ratio of the two laser beams. λ/4 plate transforms polarizations of two beams into left circular polarization and right circular polarization separately. The two laser beams are separated spatially in the cell. The two CPT resonances are detected by the two photodiodes and processed by a subtractor. The vapor cell is heated to about 45°C.

As shown in Fig. 1(b), each of the two beams excites these two groups of ground states |F=1,mF=1>, |F=2,mF=1> (group one) and |F=1,mF=1>, |F=2,mF=1> (group two) simultaneously to prepare CPT states in Λ-type configurations by using two modulations mentioned before. In the first modulation by microwave source, the frequency ν0 of microwave source is stationary and its value is 3.417341305GHz which is half of the frequency difference of hyperfine structures of 87Rb D1 line. In the second modulation by DSG, the frequency νmod is variable. The result of the two modulations is a multichromatic laser field and its frequency components are shown in Eqs. (1):
ν22=νL(ν0+νmod)ν20=νLν0ν22=νL(ν0νmod)νL=νLν12=νL+(ν0νmod)ν10=νL+ν0ν12=νL+(ν0+νmod)
(1)
where νL is the laser frequency. ν22, ν22, ν12 and ν12 are the important frequency components as shown in Fig. 1(b). When only the linear Zeeman effect is considered and νmod is equal to Larmor frequency, the multichromatic laser (σ+ laser or σ- laser) which contains the frequency components of ν22, ν22, ν12 and ν12 can prepare CPT states by exciting two groups of ground states simultaneously. In fact, the magnetic sublevels are affected by many factors such as atom collisions, AC Stark effect and nonlinear Zeeman splitting. So the magnetic sublevels will shift and the value of shift can be regard as Δν. It’s important for our system that the values and the directions of frequency shift of two groups are the same instead of the accurate value and direction of frequency shift of single sublevel. So the magnetic sublevels after considering frequency shift can be indicated qualitatively as dotted lines in Fig. 1(b). In addition, ν22, ν22, ν12 and ν12 should be changed for the purpose of preparing CPT states and is shown in Eq. (2):
ν22=νL(ν0+νLarmor)Δνν22=νL(ν0νLarmor)Δνν12=νL+(ν0νLarmor)+Δνν12=νL+(ν0+νLarmor)+Δν
(2)
where νLarmor is the Larmor frequency. It means that the center frequency of CPT resonance of group one is νLarmorΔν while the one of group two is νLarmor+Δν. Due to optical pumping of circularly polarized laser which leads to atoms in noncoherent dark states [12

12. J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” Phys. Rev. A 67(6), 065801 (2003). [CrossRef]

], the amplitudes of CPT resonances in the two groups of ground states are not the same. For σ+ laser, the amplitude of CPT resonance with resonance frequency νLarmorΔν is much smaller than the one with resonance frequency νLarmor+Δν. Due to the result of two modulations, the single detector finally detects the superposed signal of CPT resonances of the two groups excited by one beam. So the center frequency of the final signal will be closer to νLarmor+Δν rather than νLarmorΔν for σ+ laser. For σ- laser, however, the center frequency of the signal will be closer to νLarmorΔν rather than νLarmor+Δν. Therefore, the final signals of CPT resonances detected by two detectors are separated. Due to the frequency difference between the CPT resonances constructed by group one and two, the CPT resonance detected by single detector is broader than the one constructed by single group.

3. Experimental result and discussion

3.1 Sensitivity

The CPT resonances detected by PD1 and PD2 are shown in Fig. 2(a) and Fig. 2(b).
Fig. 2 (a) CPT resonance excited by σ- laser. (b) CPT resonance excited by σ+ laser. (c) CPT signal after differential detection.
After differential detection, the signal is shown in Fig. 2(c). All the signals are obtained after averaging 128 times. It is obvious that the noise of CPT resonances is suppressed.

In order to get high sensitivity, LIA is needed to improve the signal to noise ratio of CPT resonance. Figure 3 shows the signals demodulated by LIA.
Fig. 3 The Lock-in signals after differential detection (blue line) and of single photo detector (red line). The peak-peak noise of the signal after differential detection is about 10mVp-p while the other one is about 100mVp-p.

The linewidth of the CPT resonance of the single photo detector is about 3KHz and the peak-peak noise is about 100mVp-p. However, the linewidth of CPT resonance after differential detection is about 2KHz and the peak-peak noise is about 10mVp-p. The sensitivity of a magnetometer can be evaluated by using the Eq. (3) [13

13. R. Jiménez-Martínez, W. C. Griffith, Y. J. Wang, S. Knappe, J. Kitching, K. Smith, and M. D. Prouty, “Sensitivity Comparison of Mx and Frequency-Modulated Bell–Bloom Cs Magnetometers in a Microfabricated Cell,” in Instrumentation and Measurement (IEEE, 2010), 372–378.

]:
δB=1γΔνSN
(3)
where γ is the gyromagnetic ratio, Δν is the linewidth of CPT resonance, S is the amplitude of the signal of CPT resonance and N is the noise. Here, ΔνS represents the slope of the CPT resonance. As is shown in Fig. 3, the slopes of the signals are almost the same (in fact, the slope of the CPT resonance after differential detection is a little steeper), but the noise after differential detection is suppressed about one order than the one of single photo detection. So the sensitivity can be improved about one order by using this method.

The magnetometer noise is presented in Fig. 4 for the purpose of quantitatively analyzing sensitivity.
Fig. 4 Magnetometer noise. The red line represents the noise of single photo detector while the blue line represents the noise after differential detection.
It is found that the noise @ 10Hz (the bandwidth of the system) is reduced from 25pT/Hz (single beam detection) to 2pT/Hz (dual beam detection). The calculated maximum long term drift of magnetic field is about ± 4.6nT and the noise is about 0.457nT from 0.1Hz~1Hz because the current source’s accuracy of the magnetic field coils is ± 0.02% of the output current and the noise is less than 600nA from 0.1Hz~1Hz when the output current is about 30mA. The maximum long term drift of magnetic field can be calculated, considering that the magnetic field is proportional to the current. Thanks to the method of differential detection, the magnetometer noise is out of the influence of common-mode noise while the magnetometer noise of single photo detector is affected. The level of the photon shot noise can be calculated by the Eq. (4) [3

3. V. Schultze, R. IJsselsteijn, and H. G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100(4), 717–724 (2010). [CrossRef]

]:
ΔVSN=2eIdc·G
(4)
where e is 1.6×1019C, Idc is the dc current of the photo detector, G is the transimpedance amplification factor of the measured photo current. In our system, the level of the photon shot noise is about 1.55μV/Hz.

In our system, the common-mode noise mainly consists of laser induced noise such as laser amplitude noise and FM-AM noise [14

14. Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38(11), 5652–5659 (1988). [CrossRef] [PubMed]

16

16. J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on VCSEL driven dark line resonances in CS vapor,” IEEE Trans. Instrum. Meas. 49(6), 1313–1317 (2000). [CrossRef]

]. The main FM-AM noise comes from the low-frequency fluctuations of the laser frequency owing to the noise of DC current supply, temperature controller, modulation which is used for frequency stabilization and the signal of 50Hz picked up from the power lines. For the single beam detection, laser induced noise cannot be cancelled out while this kind of noise can be eliminated for dual beam detection. This is because the two beams from the same laser with equal intensity go through the same vapor cell. It means that the two beams have the same absorption spectrum, intensity fluctuation and frequency fluctuation. So the two beams have the same laser induced noise. After differential detection, this kind of noise can be suppressed effectively and the sensitivity can be improved.

3.2 Absolute accuracy

We have compared the CPT magnetometer which uses differential detection with an Overhauser magnetometer so as to evaluate the absolute accuracy. The two magnetometers are compared from 20000nT to 100000nT magnetic field with step 20000nT. The results are shown in Table 1.

Table 1. Comparison between Overhausera and CPT magnetometer

table-icon
View This Table
The absolute accuracy of the CPT magnetometer is about ± 0.5nT from 20000nT to 100000nT magnetic field comparable to the Overhauser magnetometer. For the Overhauser magnetometer of model GSM-19 made by GEM, its absolute accuracy is ± 0.1nT. So our CPT magnetometer achieves a high absolute accuracy which is close to that of the Overhauser magnetometer. Although the Overhauser magnetometer has higher absolute accuracy than the CPT magnetometer, its sensitivity is limited by 0.01nT and sampling rate is lower than the CPT magnetometer [4

4. V. Sapunov, J. Rasson, A. Denisov, D. Saveliev, S. Kiselev, O. Denisova, Y. Podmogov, and S. Khomutov, “Theodolite-borne vector Overhauser magnetometer: DIMOVER,” Earth Planets Space 58, 711–716 (2006).

]. Additionally, different from the Overhauser magnetometer, the CPT magnetometer uses all optical techniques. So it is not suffered from electromagnetic disturbing when it is working.

The reason why the method of differential detection can improve the absolute accuracy is that the two CPT resonances used in differential detection are constructed by two groups of magnetic sublevels. In this case, the two CPT resonances have the opposite frequency shift by the method of double FM when the real magnetic sublevels are depicted as the dotted lines in Fig. 1(b). Consequently, the differential signal is out of influences caused by undesired frequency shift which are harmful for absolute measure.

4. Conclusions

In conclusion, we have put forward a new method based on differential detection to improve the sensitivity and absolute accuracy of CPT magnetometer simultaneously. The sensitivity can be improved about one order of magnitude. The reason is that the common-mode noise is canceled out. The absolute accuracy can be ensured owing to the suppression of the frequency shift of final CPT resonance. This kind of CPT magnetometer with high absolute accuracy and high sensitivity will find important applications in the future.

Acknowledgments

This work is supported by the 973 Program (2013CB329501), the National Natural Science Foundation of China (11104243), the 863 Program (2013AA063901) and the Fundamental Research Funds for the Central Universities (2012FZA3001).

References and links

1.

P. D. D. Schwindt, L. Hollberg, and J. Kitching, “Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation,” Rev. Sci. Instrum. 76(12), 126103 (2005). [CrossRef]

2.

I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596–599 (2003). [CrossRef] [PubMed]

3.

V. Schultze, R. IJsselsteijn, and H. G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100(4), 717–724 (2010). [CrossRef]

4.

V. Sapunov, J. Rasson, A. Denisov, D. Saveliev, S. Kiselev, O. Denisova, Y. Podmogov, and S. Khomutov, “Theodolite-borne vector Overhauser magnetometer: DIMOVER,” Earth Planets Space 58, 711–716 (2006).

5.

A. Pollinger, R. Lammegger, W. Magnes, M. Ellmeier, W. Baumjohann, and L. Windholz, “Control loops for a Coupled Dark State Magnetometer,” in Sensors (IEEE, 2010), 779–784.

6.

A. Pollinger, M. Ellmeier, W. Magnes, C. Hagen, W. Baumjohann, E. Leitgeb, and R. Lammegger, “Enable the inherent omni-directionality of an absolute coupled dark state magnetometer for e.g. scientific space applications,” in Instrumentation and Measurement Technology Conference (I2MTC) (IEEE, 2012), 33–36. [CrossRef]

7.

P. Yun, B. Tan, W. Deng, J. Yang, and S. Gu, “Quasi-bichromatic laser for a lin⊥lin coherent population trapping clock produced by vertical-cavity surface-emitting lasers,” Rev. Sci. Instrum. 83(9), 093111 (2012). [CrossRef] [PubMed]

8.

E. E. Mikhailov, T. Horrom, N. Belcher, and I. Novikova, “Performance of a prototype atomic clock based on lin ‖ lin coherent population trapping resonances in Rb atomic vapor,” J. Opt. Soc. Am. B 27(3), 417–422 (2010). [CrossRef]

9.

A. L. Yang, G. Q. Yang, Y. F. Xu, and Q. Lin, “High contrast atomic magnetometer based on coherent population trapping,” Chin. Phys. B. 23(2), 027601 (2014). [CrossRef]

10.

X. C. Liu, J. M. M’erolla, S. Gu’erandel, C. Gorecki, E. D. Clercq, and R. Boudot, “Coherent-population-trapping resonances in buffer-gas-filled Cs-vapor cells with push-pull optical pumping,” Phys. Rev. A 87(1), 013416 (2013). [CrossRef]

11.

M. Rosenbluh, V. Shah, S. Knappe, and J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]

12.

J. Vanier, M. W. Levine, D. Janssen, and M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” Phys. Rev. A 67(6), 065801 (2003). [CrossRef]

13.

R. Jiménez-Martínez, W. C. Griffith, Y. J. Wang, S. Knappe, J. Kitching, K. Smith, and M. D. Prouty, “Sensitivity Comparison of Mx and Frequency-Modulated Bell–Bloom Cs Magnetometers in a Microfabricated Cell,” in Instrumentation and Measurement (IEEE, 2010), 372–378.

14.

Th. Haslwanter, H. Ritsch, J. Cooper, and P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38(11), 5652–5659 (1988). [CrossRef] [PubMed]

15.

J. C. Camparo, “Conversion of laser phase noise to amplitude noise in an optically thick vapor,” Opt. Soc. Am. B 15(3), 1177–1186 (1998). [CrossRef]

16.

J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, and W. Weidemann, “A microwave frequency reference based on VCSEL driven dark line resonances in CS vapor,” IEEE Trans. Instrum. Meas. 49(6), 1313–1317 (2000). [CrossRef]

OCIS Codes
(020.1670) Atomic and molecular physics : Coherent optical effects
(020.7490) Atomic and molecular physics : Zeeman effect

ToC Category:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 15, 2014
Revised Manuscript: February 28, 2014
Manuscript Accepted: February 28, 2014
Published: March 17, 2014

Citation
Shang-Qing Liang, Guo-Qing Yang, Yun-Fei Xu, Qiang Lin, Zhi-Heng Liu, and Zheng-Xiang Chen, "Simultaneously improving the sensitivity and absolute accuracy of CPT magnetometer," Opt. Express 22, 6837-6843 (2014)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-22-6-6837


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References

  1. P. D. D. Schwindt, L. Hollberg, J. Kitching, “Self-oscillating rubidium magnetometer using nonlinear magneto-optical rotation,” Rev. Sci. Instrum. 76(12), 126103 (2005). [CrossRef]
  2. I. K. Kominis, T. W. Kornack, J. C. Allred, M. V. Romalis, “A subfemtotesla multichannel atomic magnetometer,” Nature 422(6932), 596–599 (2003). [CrossRef] [PubMed]
  3. V. Schultze, R. IJsselsteijn, H. G. Meyer, “Noise reduction in optically pumped magnetometer assemblies,” Appl. Phys. B 100(4), 717–724 (2010). [CrossRef]
  4. V. Sapunov, J. Rasson, A. Denisov, D. Saveliev, S. Kiselev, O. Denisova, Y. Podmogov, S. Khomutov, “Theodolite-borne vector Overhauser magnetometer: DIMOVER,” Earth Planets Space 58, 711–716 (2006).
  5. A. Pollinger, R. Lammegger, W. Magnes, M. Ellmeier, W. Baumjohann, and L. Windholz, “Control loops for a Coupled Dark State Magnetometer,” in Sensors (IEEE, 2010), 779–784.
  6. A. Pollinger, M. Ellmeier, W. Magnes, C. Hagen, W. Baumjohann, E. Leitgeb, R. Lammegger, “Enable the inherent omni-directionality of an absolute coupled dark state magnetometer for e.g. scientific space applications,” in Instrumentation and Measurement Technology Conference (I2MTC) (IEEE, 2012), 33–36. [CrossRef]
  7. P. Yun, B. Tan, W. Deng, J. Yang, S. Gu, “Quasi-bichromatic laser for a lin⊥lin coherent population trapping clock produced by vertical-cavity surface-emitting lasers,” Rev. Sci. Instrum. 83(9), 093111 (2012). [CrossRef] [PubMed]
  8. E. E. Mikhailov, T. Horrom, N. Belcher, I. Novikova, “Performance of a prototype atomic clock based on lin ‖ lin coherent population trapping resonances in Rb atomic vapor,” J. Opt. Soc. Am. B 27(3), 417–422 (2010). [CrossRef]
  9. A. L. Yang, G. Q. Yang, Y. F. Xu, Q. Lin, “High contrast atomic magnetometer based on coherent population trapping,” Chin. Phys. B. 23(2), 027601 (2014). [CrossRef]
  10. X. C. Liu, J. M. M’erolla, S. Gu’erandel, C. Gorecki, E. D. Clercq, R. Boudot, “Coherent-population-trapping resonances in buffer-gas-filled Cs-vapor cells with push-pull optical pumping,” Phys. Rev. A 87(1), 013416 (2013). [CrossRef]
  11. M. Rosenbluh, V. Shah, S. Knappe, J. Kitching, “Differentially detected coherent population trapping resonances excited by orthogonally polarized laser fields,” Opt. Express 14(15), 6588–6594 (2006). [CrossRef] [PubMed]
  12. J. Vanier, M. W. Levine, D. Janssen, M. Delaney, “Contrast and linewidth of the coherent population trapping transmission hyperfine resonance line in 87Rb: Effect of optical pumping,” Phys. Rev. A 67(6), 065801 (2003). [CrossRef]
  13. R. Jiménez-Martínez, W. C. Griffith, Y. J. Wang, S. Knappe, J. Kitching, K. Smith, and M. D. Prouty, “Sensitivity Comparison of Mx and Frequency-Modulated Bell–Bloom Cs Magnetometers in a Microfabricated Cell,” in Instrumentation and Measurement (IEEE, 2010), 372–378.
  14. Th. Haslwanter, H. Ritsch, J. Cooper, P. Zoller, “Laser-noise-induced population fluctuations in two- and three-level systems,” Phys. Rev. A 38(11), 5652–5659 (1988). [CrossRef] [PubMed]
  15. J. C. Camparo, “Conversion of laser phase noise to amplitude noise in an optically thick vapor,” Opt. Soc. Am. B 15(3), 1177–1186 (1998). [CrossRef]
  16. J. Kitching, N. Vukicevic, L. Hollberg, S. Knappe, R. Wynands, W. Weidemann, “A microwave frequency reference based on VCSEL driven dark line resonances in CS vapor,” IEEE Trans. Instrum. Meas. 49(6), 1313–1317 (2000). [CrossRef]

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