Abstract

We investigate a new method that enables the direct measurement of the density ratio of a K-Rb hybrid vapor cell, using the spin-exchange collision mixing of the K and Rb light shifts. The densities for each alkali metals can be further determined using Raoult’s law. The mixture of the light shifts in both magnetometers and comagnetometers is formulated using Bloch equations and explained by considering the fast spin-exchange interaction. The relationship between the density ratio and the mixed light shifts is both formulated and simulated. The method was performed on several K-Rb magnetometer- and K-Rb-21Ne comagnetometer-cells at different temperatures, pump light powers, and mole fractions of K. The method was further verified by the conventional laser-absorption-spectroscopy method. The new approach has the advantage to measure the density ratio of the optically-thick hybrid alkali atoms, while requiring no additional magnetic field necessary for conventional magnetic-field induced Faraday-rotation techniques. It also has the advantage of in-situ measuring the density ratio under exactly the normal operation of the devices, which means that the errors caused by the heating-effect of the strong pump light and the temperature drift during long-term operation can be real-time monitored.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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    [Crossref]
  2. J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
    [Crossref] [PubMed]
  3. E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
    [Crossref] [PubMed]
  4. R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
    [Crossref]
  5. M. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105, 243001 (2010).
    [Crossref]
  6. E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
    [Crossref]
  7. W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
    [Crossref]
  8. J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
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  9. T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
    [Crossref] [PubMed]
  10. Y. Ito, D. Sato, K. Kamada, and T. Kobayashi, “Optimal densities of alkali metal atoms in an optically pumped K − Rb hybrid atomic magnetometer considering the spatial distribution of spin polarization,” Opt. Express 24, 15391–15402 (2016).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  12. M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
    [Crossref]
  13. E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
    [Crossref]
  14. H. Zhang, S. Zou, X. Chen, M. Ding, G. Shan, Z. Hu, and W. Quan, “On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation,” Opt. Express 24, 17234–17241 (2016).
    [Crossref] [PubMed]
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    [Crossref]
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  17. E. D. Babcock, “Spin exchange optical pumping with alkali metal vapors,” Ph.D. thesis, University of WisconsinMadison (2008).
  18. B. S. Mathur, H. Tang, and W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11–19 (1968).
    [Crossref]
  19. E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
    [Crossref]
  20. Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
    [Crossref]
  21. I. M. Savukov and M. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).
    [Crossref]
  22. R. K. Ghosh and M. V. Romalis, “Measurement of spin-exchange and relaxation parameters for polarizing 21Ne with K and Rb,” Phys. Rev. A 81, 043415 (2010).
    [Crossref]
  23. S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. thesis, Princeton University (2008).
  24. J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K −3 He comagnetometer,” Ph.D. thesis, Princeton University (2011).
  25. W. Quan, K. Wei, and H. R. Li, “Precision measurement of magnetic field based on the transient process in a K − Rb −21 Ne comagnetometer,” Opt. Express 25, 8470–8483 (2017).
    [Crossref] [PubMed]
  26. W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
    [Crossref]
  27. M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
    [Crossref]
  28. R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
    [Crossref]
  29. J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.
  30. R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
    [Crossref]

2018 (5)

J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
[Crossref] [PubMed]

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

K. Nishi, Y. Ito, and T. Kobayashi, “High-sensitivity multi-channel probe beam detector towards meg measurements of small animals with an optically pumped K − Rb hybrid magnetometer,” Opt. Express 26, 1988–1996 (2018).
[Crossref] [PubMed]

2017 (1)

2016 (5)

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

Y. Ito, D. Sato, K. Kamada, and T. Kobayashi, “Optimal densities of alkali metal atoms in an optically pumped K − Rb hybrid atomic magnetometer considering the spatial distribution of spin polarization,” Opt. Express 24, 15391–15402 (2016).
[Crossref] [PubMed]

H. Zhang, S. Zou, X. Chen, M. Ding, G. Shan, Z. Hu, and W. Quan, “On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation,” Opt. Express 24, 17234–17241 (2016).
[Crossref] [PubMed]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

2014 (1)

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

2012 (1)

R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[Crossref]

2010 (2)

R. K. Ghosh and M. V. Romalis, “Measurement of spin-exchange and relaxation parameters for polarizing 21Ne with K and Rb,” Phys. Rev. A 81, 043415 (2010).
[Crossref]

M. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105, 243001 (2010).
[Crossref]

2007 (2)

W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
[Crossref]

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

2005 (2)

T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[Crossref] [PubMed]

I. M. Savukov and M. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).
[Crossref]

2003 (1)

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

2002 (2)

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

2001 (1)

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

1998 (1)

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

1977 (1)

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

1968 (1)

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

Allred, J. C.

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

Almasi, A.

J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
[Crossref] [PubMed]

Anderson, L. W.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Babcock, E.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

Babcock, E. D.

E. D. Babcock, “Spin exchange optical pumping with alkali metal vapors,” Ph.D. thesis, University of WisconsinMadison (2008).

Barnes, G.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Bestmann, S.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Boto, E.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Bowtell, R.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Brookes, M.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Brown, J. M.

J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K −3 He comagnetometer,” Ph.D. thesis, Princeton University (2011).

Budker, D.

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

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

Chann, B.

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

Chen, W. C.

W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
[Crossref]

Chen, X.

Chen, Y.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

Citron, M. L.

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

DeJoseph, C. A.

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

Ding, M.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

H. Zhang, S. Zou, X. Chen, M. Ding, G. Shan, Z. Hu, and W. Quan, “On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation,” Opt. Express 24, 17234–17241 (2016).
[Crossref] [PubMed]

Driehuys, B.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

Duan, L.

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

Erickson, C. J.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Fan, W.

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Fang, J.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

Fu, C.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Gabel, C. W.

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

Ganguly, B. N.

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

Gentile, T. R.

W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
[Crossref]

Gerginov, V.

J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.

Ghosh, R. K.

R. K. Ghosh and M. V. Romalis, “Measurement of spin-exchange and relaxation parameters for polarizing 21Ne with K and Rb,” Phys. Rev. A 81, 043415 (2010).
[Crossref]

T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[Crossref] [PubMed]

Gray, H. R.

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

Happer, W.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

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

Hersman, F. W.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

Holmes, N.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Hu, Z.

Ito, Y.

Ji, W.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Jiang, L.

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

Kadlecek, S.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Kamada, K.

Kitching, J.

R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[Crossref]

J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.

Knappe, S.

R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[Crossref]

J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.

Kobayashi, T.

Kornack, T. W.

T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[Crossref] [PubMed]

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

Lee, J.

J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
[Crossref] [PubMed]

Leggett, J.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Li, H. R.

Li, R.

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Li, Y.

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

Lu, Y.

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

Lyman, R. N.

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

Ma, D.

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

Mathur, B. S.

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

Meyer, S.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Mhaskar, R.

R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[Crossref]

Millard, M. W.

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

Mullinger, K.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Muñoz, L. D.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Nelson, I.

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

Nishi, K.

Patton, B.

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

Preusser, J.

J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.

Quan, W.

W. Quan, K. Wei, and H. R. Li, “Precision measurement of magnetic field based on the transient process in a K − Rb −21 Ne comagnetometer,” Opt. Express 25, 8470–8483 (2017).
[Crossref] [PubMed]

H. Zhang, S. Zou, X. Chen, M. Ding, G. Shan, Z. Hu, and W. Quan, “On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation,” Opt. Express 24, 17234–17241 (2016).
[Crossref] [PubMed]

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

Roberts, G.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Romalis, M.

J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
[Crossref] [PubMed]

M. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105, 243001 (2010).
[Crossref]

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

I. M. Savukov and M. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).
[Crossref]

T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[Crossref] [PubMed]

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

Romalis, M. V.

R. K. Ghosh and M. V. Romalis, “Measurement of spin-exchange and relaxation parameters for polarizing 21Ne with K and Rb,” Phys. Rev. A 81, 043415 (2010).
[Crossref]

Sato, D.

Savukov, I. M.

I. M. Savukov and M. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).
[Crossref]

Seltzer, S. J.

S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. thesis, Princeton University (2008).

Shah, V.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Shan, G.

Stroud, C. R.

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

Tang, H.

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

Tierney, T.

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Vliegen, E.

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Walker, T. G.

W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
[Crossref]

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Wei, K.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

W. Quan, K. Wei, and H. R. Li, “Precision measurement of magnetic field based on the transient process in a K − Rb −21 Ne comagnetometer,” Opt. Express 25, 8470–8483 (2017).
[Crossref] [PubMed]

Wickenbrock, A.

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

Xiao, Z.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Yan, H.

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Yaney, P. P.

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

Yao, H.

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

Zhang, H.

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

H. Zhang, S. Zou, X. Chen, M. Ding, G. Shan, Z. Hu, and W. Quan, “On-site monitoring of atomic density number for an all-optical atomic magnetometer based on atomic spin exchange relaxation,” Opt. Express 24, 17234–17241 (2016).
[Crossref] [PubMed]

Zhao, J.

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

Zhivun, E.

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

Zou, S.

Appl. Phys. Lett. (2)

E. Zhivun, A. Wickenbrock, B. Patton, and D. Budker, “Alkali-vapor magnetic resonance driven by fictitious radiofrequency fields,” Appl. Phys. Lett. 105, 192406 (2014).
[Crossref]

R. Mhaskar, S. Knappe, and J. Kitching, “A low-power, high-sensitivity micromachined optical magnetometer,” Appl. Phys. Lett. 101, 241105 (2012).
[Crossref]

Eur. Phys. J. D (1)

R. Li, Y. Li, L. Jiang, W. Quan, M. Ding, and J. Fang, “Pressure broadening and shift of K D1 and D2 lines in the presence of 3He and 21Ne,” Eur. Phys. J. D 70, 139 (2016).
[Crossref]

Meas. Sci. Technol. (1)

H. Yao, H. Zhang, D. Ma, J. Zhao, and M. Ding, “In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers,” Meas. Sci. Technol. 29, 6 (2018).
[Crossref]

Nat. Phys. (1)

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

Nature (1)

E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. Meyer, L. D. Muñoz, K. Mullinger, T. Tierney, S. Bestmann, G. Barnes, R. Bowtell, and M. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555, 657–661 (2018).
[Crossref] [PubMed]

Nucl. Instruments Methods Phys. Res. A (1)

E. Vliegen, S. Kadlecek, L. W. Anderson, T. G. Walker, C. J. Erickson, and W. Happer, “Faraday rotation density measurements of optically thick alkali metal vapors,” Nucl. Instruments Methods Phys. Res. A 460, 444–450 (2001).
[Crossref]

Opt. Express (4)

Phys. Rev. (1)

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

Phys. Rev. A (7)

M. L. Citron, H. R. Gray, C. W. Gabel, and C. R. Stroud, “Experimental study of power broadening in a two-level atom,” Phys. Rev. A 16, 1507 (1977).
[Crossref]

B. Chann, E. Babcock, L. W. Anderson, and T. G. Walker, “Measurements of 3He spin-exchange rates,” Phys. Rev. A 66, 032703 (2002).
[Crossref]

Y. Chen, W. Quan, L. Duan, Y. Lu, L. Jiang, and J. Fang, “Spin-exchange collision mixing of the K and Rb ac stark shifts,” Phys. Rev. A 94, 052705 (2016).
[Crossref]

I. M. Savukov and M. Romalis, “Effects of spin-exchange collisions in a high-density alkali-metal vapor in low magnetic fields,” Phys. Rev. A 71, 023405 (2005).
[Crossref]

R. K. Ghosh and M. V. Romalis, “Measurement of spin-exchange and relaxation parameters for polarizing 21Ne with K and Rb,” Phys. Rev. A 81, 043415 (2010).
[Crossref]

R. Li, W. Fan, L. Jiang, L. Duan, W. Quan, and J. Fang, “Rotation sensing using a K − Rb −21 Ne comagnetometer,” Phys. Rev. A 94, 032109 (2016).
[Crossref]

W. C. Chen, T. R. Gentile, and T. G. Walker, “Spin-exchange optical pumping of 3He with Rb − K mixtures and pure K,” Phys. Rev. A 75, 013416 (2007).
[Crossref]

Phys. Rev. Lett. (6)

J. C. Allred, R. N. Lyman, T. W. Kornack, and M. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89, 130801 (2002).
[Crossref] [PubMed]

T. W. Kornack, R. K. Ghosh, and M. Romalis, “Nuclear spin gyroscope based on an atomic comagnetometer,” Phys. Rev. Lett. 95, 230801 (2005).
[Crossref] [PubMed]

J. Lee, A. Almasi, and M. Romalis, “Improved limits on spin-mass interactions,” Phys. Rev. Lett. 120, 161801 (2018).
[Crossref] [PubMed]

M. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105, 243001 (2010).
[Crossref]

E. Babcock, I. Nelson, S. Kadlecek, B. Driehuys, L. W. Anderson, F. W. Hersman, and T. G. Walker, “Hybrid spin-exchange optical pumping of 3He,” Phys. Rev. Lett. 91, 123003 (2003).
[Crossref]

W. Ji, Y. Chen, C. Fu, M. Ding, J. Fang, Z. Xiao, K. Wei, and H. Yan, “New experimental limits on exotic spin-spin-velocity-dependent interactions by using smco5 spin sources,” Phys. Rev. Lett. 121, 261803 (2018).
[Crossref]

Plasma Sources Sci. Technol. (1)

M. W. Millard, P. P. Yaney, B. N. Ganguly, and C. A. DeJoseph, “Diode laser absorption measurements of metastable helium in glow discharges,” Plasma Sources Sci. Technol. 7, 389–394 (1998).
[Crossref]

Other (4)

S. J. Seltzer, “Developments in alkali-metal atomic magnetometry,” Ph.D. thesis, Princeton University (2008).

J. M. Brown, “A new limit on Lorentz- and CPT-violating neutron spin interactions using a K −3 He comagnetometer,” Ph.D. thesis, Princeton University (2011).

E. D. Babcock, “Spin exchange optical pumping with alkali metal vapors,” Ph.D. thesis, University of WisconsinMadison (2008).

J. Preusser, V. Gerginov, S. Knappe, and J. Kitching, “A microfabricated photonic magnetometer,” Proc. IEEE Sensors Conf. (IEEE, 2008) pp. 344–346.

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Figures (10)

Fig. 1
Fig. 1 Vector diagram illustrating the mixture of light shifts due to rapid spin-exchange collision.
Fig. 2
Fig. 2 Schematic of the experimental setup. TA, tapered amplifier; BE, beam expander; GT, Glan-Thompson polarizer; PD, photo detector; PBS, polarization beam splitter; PEM, photo elastic modulator.
Fig. 3
Fig. 3 Simulation of light shifts in the K-Rb magnetometer under different conditions.
Fig. 4
Fig. 4 The effective light shift as a function of pump light frequency detuning. The point data were obtained at different light intensities, while the corresponding curves are fitted lines. The zero point of the horizontal axis is the D1 line of K in vacuum, 770.108 nm. Inset: The compensating magnetic field Bz as a function of light intensity Iz.
Fig. 5
Fig. 5 (a) The light shift of Rb L z Rb as a function of light intensity, (b) Fitted linewidths and the frequency detunes for Lz = 0, plotted against the left Y-axis, while the plotted frequency detunes are scaled up 10-fold for clarity. The calculated density ratios are plotted against the right Y-axis.
Fig. 6
Fig. 6 The effective light shift as a function of the pump light frequency detuning. The data points were measured at different temperatures, while the corresponding curves are fitted lines. The inset shows the laser absorption spectra of the pure K vapor cell (black triangles) and the cell Mag1 (red squares). The zero point of the horizontal axis is the D2 line of K in vacuum 766.701 nm, while the vertical axis represents the log base e of the transmitted light intensity. The black triangles and red squares are fitted with y = 4119/[(x − 0.3039)2 + 30.722] − 1.811 and y = 1315/[(x + 0.0709)2 + 31.252] − 1.796 based on Eq. (14).
Fig. 7
Fig. 7 Density ratios at different temperatures plotted against the left Y-axis. The fitted linewidths and the frequency detunes for Lz = 0 at different temperatures plotted against the right Y-axis. The shaded areas are the estimation errors of the calculated density ratios. (a): Data for the cell Mag1. The plotted frequency detunes are scaled up 10-fold for clarity. (b) Data for the cell Mag2. The plotted frequency detunes are scaled by a factor of five for clarity.
Fig. 8
Fig. 8 The response signals Δ S x e of a By square wave modulation for different δBz and pump light frequencies. The dots are measured signals, while the solid lines are fitted lines.
Fig. 9
Fig. 9 Effective light shift Lz as a function of the pump light frequency detuning. The zero point of the horizontal axis is the K D1 line in vacuum, 770.108 nm. Inset: The absorption curve of K atoms in the cell at 443 K. The zero point of the horizontal axis is the D2 line of K in vacuum (766.701 nm), while the vertical axis is the log base e of the transmitted light intensity. (a) Data for cell Comag1. The black dots in the inset are fitted using y = 284.7/[(x +7.411)2 +14.522]−1.597 based on Eq. (14). (b) Data for cell Comag2. The black dots in the inset are fitted using y = 195.9/[(x +6.511)2 + 16.942] − 1.425 based on Eq. (14).
Fig. 10
Fig. 10 Measurement of the optical heating effect. (a). The absorption curves of K atoms at 443 K with different light intensities. The zero point of the horizontal axis is the D2 line of K in vacuum (766.701 nm), while the vertical axis is the log base e of the transmitted light intensity. The dots are measured data, and solid curves are corresponding fitting curves based on Eq. (14). (b). The cell temperature increments derived from the absorption curves is plotted on the left-Y-axis-bottom-X-axis. The simulated relationship between the saturated vapor density ratio Dr0 and temperature is plotted on the right-Y-axis-top-X-axis.

Equations (14)

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P K t = γ e Q ( P K ) ( B + L K + λ K Ne M 0 n P n ) × P K + R p S p + R se Rb K ( P Rb P K ) Q ( P K ) P K { T 1 K , T 2 K , T 2 K } ,
P Rb t = γ e Q ( P Rb ) ( B + L Rb + λ Rb Ne M 0 n P n ) × P Rb + R se K Rb ( P K P Rb ) Q ( P Rb ) P Rb { T 1 Rb , T 2 Rb , T 2 Rb } ,
P n t = γ n ( B + λ Rb Ne M 0 Rb P Rb ) × P n Ω × P n + R se Rb Ne ( P Rb P n ) P n { T 1 n , T 2 n , T 2 n } .
P K 0 e P Rb 0 e D r R p D r R p + 1 / T 1 Rb .
P Rb x mag = P Rb 0 e B y R tot Rb / γ e + B x B z R tot Rb 2 / γ e 2 + B x 2 + B y 2 + ( B z + L z ) 2 ,
S Rb x comag = k P Rb x comag = k P Rb 0 e R tot Rb / γ e R tot Rb 2 / γ e 2 + ( L z + δ B z ) 2 × ( Ω y γ n + Ω x γ e ( L z + δ B z ) γ n R tot Rb B y δ B z B n n ) .
L z = L z Rb + D r L z K ,
L z K = r e c f D 1 K Φ S p γ e ν ν D 1 K ( ν ν D 1 K ) 2 + ( Γ D 1 K / 2 ) ,
L z Rb = r e c Φ S p γ e ( f D 1 Rb 1 ν ν D 1 Rb + 1 2 f D 2 Rb 1 ν ν D 2 Rb ) ,
D r = L z Rb L z K = 1.025 ν D 2 Rb ν D 1 Rb ( ν ν D 1 Rb ) ( ν ν D 2 Rb ) ( ν ν D 1 K ) 2 + ( Γ D 1 K / 2 ) 2 ν ν D 1 K ,
P Rb x mag P Rb 0 e B x mod sin ( ω x t ) ( B z + B z res + L z ) γ e / R tot Rb R tot Rb 2 / γ e 2 + ( B z + B z res + L z ) 2 ,
Δ S x e = k Δ P x e = k P z e γ e R tot Rb R tot Rb 2 / γ e 2 ( L z + δ B z ) 2 δ B z B n n Δ B y ,
OD = ln ( I / I 0 ) ,
OD = n L r e c f Γ L / 2 ( ν ν 0 ) 2 + ( Γ L / 2 ) 2 .

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