Abstract

Light-shift caused by the interaction between atoms and detuned light can be equivalent to the phenomena that atoms are coupled to an external magnetic or electric field. A fictitious magnetic or electric field is used to describe the effect of light-shift. Whether fictitious magnetic or electric field should be used depends on the polarization state of the detuned light. The fictitious fields can shift Zeeman sublevels and excite transitions between different sublevels. We study the magneto-optical double resonance of optically polarized 4He atoms driven by the detuned light with either circular or linear polarization states, model the light-shift with effective Hamiltonian, and the polarized 4He metastable state with density matrix calculations. Our proposed theoretical explanations based on the fictitious fields show good agreement with experimental results, especially for amplitude and frequency shifts of the signals at Larmor frequency and double Larmor frequency driven by the fictitious electric field.

© 2017 Optical Society of America

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References

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  1. E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).
  2. A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
    [Crossref]
  3. W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science & Business Media, 2013).
  4. W. Happer and B. Mathur, “Effective operator formalism in optical pumping,” Phys. Rev. 163, 12 (1967).
    [Crossref]
  5. C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968 (1972).
    [Crossref]
  6. B. Mathur, H. Tang, and W. Happer, “Light shifts in the alkali atoms,” Phys. Rev. 171, 11 (1968).
    [Crossref]
  7. D. Budker and M. Romalis, “Optical magnetometry,” Nature Phys. 3, 227 (2007).
    [Crossref]
  8. B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
    [Crossref] [PubMed]
  9. 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]
  10. T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
    [Crossref]
  11. M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).
  12. M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
    [Crossref]
  13. Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
    [Crossref]
  14. A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database (ver. 5.3), [On-line]. Available: http://physics.nist.gov/asd [2016, December 27]. National Institute of Standards and Technology, Gaithersburg, MD. (2015).
  15. D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2004).
  16. D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).
    [Crossref]
  17. B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
    [Crossref]
  18. T. Scholtes, V. Schultze, R. IJsselsteijn, S. Woetzel, and H.-G. 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 (2012).
    [Crossref]
  19. A. L. Bloom, “Principles of operation of the rubidium vapor magnetometer,” Appl. Opt. 1, 61 (1962).
    [Crossref]
  20. T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
    [Crossref]
  21. A. Ben-Kish and M. Romalis, “Dead-zone-free atomic magnetometry with simultaneous excitation of orientation and alignment resonances,” Phys. Rev. A 105, 193601 (2010).

2016 (1)

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

2015 (1)

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

2014 (2)

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

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)

2010 (2)

A. Ben-Kish and M. Romalis, “Dead-zone-free atomic magnetometry with simultaneous excitation of orientation and alignment resonances,” Phys. Rev. A 105, 193601 (2010).

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

2009 (2)

B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
[Crossref]

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

2007 (1)

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

2006 (1)

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
[Crossref]

1996 (1)

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

1972 (1)

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968 (1972).
[Crossref]

1968 (1)

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

1967 (1)

W. Happer and B. Mathur, “Effective operator formalism in optical pumping,” Phys. Rev. 163, 12 (1967).
[Crossref]

1962 (1)

Alexandrov, E.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Auzinsh, M.

M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

Balabas, M.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Ben-Kish, A.

A. Ben-Kish and M. Romalis, “Dead-zone-free atomic magnetometry with simultaneous excitation of orientation and alignment resonances,” Phys. Rev. A 105, 193601 (2010).

Bison, G.

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
[Crossref]

Bloom, A. L.

Brown, A. W.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Budker, D.

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

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,” Nature Phys. 3, 227 (2007).
[Crossref]

M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2004).

D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968 (1972).
[Crossref]

DeMille, D. P.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2004).

Demtröder, W.

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science & Business Media, 2013).

Dupont-Roc, J.

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968 (1972).
[Crossref]

Fukuda, Y.

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Guo, H.

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

Happer, W.

B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
[Crossref]

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

W. Happer and B. Mathur, “Effective operator formalism in optical pumping,” Phys. Rev. 163, 12 (1967).
[Crossref]

Hovde, D.

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

IJsselsteijn, R.

Jackson Kimball, D. F.

D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).
[Crossref]

Jau, Y.-Y.

B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
[Crossref]

Kimball, D. F.

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2004).

Kohmoto, T.

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Koyama, Y.

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Lin, Z.

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

MacFarlane, D. L.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Mathur, B.

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

W. Happer and B. Mathur, “Effective operator formalism in optical pumping,” Phys. Rev. 163, 12 (1967).
[Crossref]

McGregor, D. D.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

McGuyer, B.

B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
[Crossref]

Meyer, H.-G.

Moriyasu, T.

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Nomoto, D.

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Pasgalev, A.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Patton, B.

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

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]

Pazgalev, A. S.

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
[Crossref]

Peng, X.

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

Plante, M. K.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Rochester, S.

M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

Romalis, M.

A. Ben-Kish and M. Romalis, “Dead-zone-free atomic magnetometry with simultaneous excitation of orientation and alignment resonances,” Phys. Rev. A 105, 193601 (2010).

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

Sampson, W. M.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Scholtes, T.

Schultze, V.

Slocum, R. E.

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Tang, H.

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

Vershovskii, A.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Wang, H.

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

Weis, A.

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
[Crossref]

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]

Woetzel, S.

Wu, T.

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

Yakobson, N.

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Zhivun, E.

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

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]

Appl. Opt. (1)

Appl. Phys. Lett. (2)

B. McGuyer, Y.-Y. Jau, and W. Happer, “Simple method of light-shift suppression in optical pumping systems,” Appl. Phys. Lett. 94, 251110 (2009).
[Crossref]

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]

Laser Phys. (1)

E. Alexandrov, M. Balabas, A. Pasgalev, A. Vershovskii, and N. Yakobson, “Double-resonance atomic magnetometers: from gas discharge to laser pumping,” Laser Phys. 6, 244 (1996).

Nature Phys. (1)

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

Opt. Express (1)

Phys. Rev. (2)

W. Happer and B. Mathur, “Effective operator formalism in optical pumping,” Phys. Rev. 163, 12 (1967).
[Crossref]

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

Phys. Rev. A (4)

A. Ben-Kish and M. Romalis, “Dead-zone-free atomic magnetometry with simultaneous excitation of orientation and alignment resonances,” Phys. Rev. A 105, 193601 (2010).

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968 (1972).
[Crossref]

A. Weis, G. Bison, and A. S. Pazgalev, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
[Crossref]

M. K. Plante, D. L. MacFarlane, D. D. McGregor, R. E. Slocum, W. M. Sampson, and A. W. Brown, “Generalized theory of double-resonance optical pumping of 4He,” Phys. Rev. A 82, 013837 (2010).
[Crossref]

Phys. Rev. Lett. (2)

B. Patton, E. Zhivun, D. Hovde, and D. Budker, “All-optical vector atomic magnetometer,” Phys. Rev. Lett. 113, 013001 (2014).
[Crossref] [PubMed]

T. Moriyasu, D. Nomoto, Y. Koyama, Y. Fukuda, and T. Kohmoto, “Spin manipulation using the light-shift effect in rubidium atoms,” Phys. Rev. Lett. 103, 213602 (2009).
[Crossref]

Rev. Sci. Instrum. (2)

Z. Lin, H. Wang, X. Peng, T. Wu, and H. Guo, “Laser pumped 4He magnetometer with light shift suppression,” Rev. Sci. Instrum. 87, 115111 (2016).
[Crossref]

T. Wu, X. Peng, Z. Lin, and H. Guo, “A dead-zone free 4He atomic magnetometer with intensity-modulated linearly polarized light and a liquid crystal polarization rotator,” Rev. Sci. Instrum. 86, 103105 (2015).
[Crossref]

Other (5)

A. Kramida, Yu. Ralchenko, J. Reader, and NIST ASD Team, NIST Atomic Spectra Database (ver. 5.3), [On-line]. Available: http://physics.nist.gov/asd [2016, December 27]. National Institute of Standards and Technology, Gaithersburg, MD. (2015).

D. Budker, D. F. Kimball, and D. P. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2004).

D. Budker and D. F. Jackson Kimball, Optical Magnetometry (Cambridge University, 2013).
[Crossref]

M. Auzinsh, D. Budker, and S. Rochester, Optically Polarized Atoms: Understanding Light-Atom Interactions (Oxford University, 2010).

W. Demtröder, Laser Spectroscopy: Basic Concepts and Instrumentation (Springer Science & Business Media, 2013).

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Figures (6)

Fig. 1
Fig. 1 Relevant energy levels of 4He and three transition lines (not to scale) with transition frequency values in vacuum [14].
Fig. 2
Fig. 2 Experimental setup. FL, fiber laser; BE, beam expander; WP, half- or quarter-wave plate; PBS, polarization beam splitter; MS, magnetic shield; PD, photodiode; LIA, lock-in amplifier; AOM, acousto-optic modulator; FG, function generator.
Fig. 3
Fig. 3 Magneto-optical double resonance signals of four cases: CPCD, CPLD, LPCD, LPLD. Here the linearly polarized light polarization is perpendicular to the static magnetic field about 2456 nT (The Larmor frequency is 68829 Hz for 4He metastable state 23S1) and the wavelength of driving light is 1083.195 nm.
Fig. 4
Fig. 4 The dependence of the MODR signals on the polarization angle θ of driving light with respect to the static magnetic field. F1 and F2 (F1-T and F2-T) are experimental (theoretical) data of resonant frequency of Larmor frequency signals and double Larmor frequency signals, respectively. A1 and A2 (A1-T and A2-T) are experimental (theoretical) data of peak value of Larmor frequency signals and double Larmor frequency signals, respectively. The Larmor frequency of the static magnetic field is 68829 Hz and the wavelength of driving light is 1083.195 nm.
Fig. 5
Fig. 5 The amplitude of double Larmor frequency signals contour map under different light detuning. The double Larmor frequency of the static magnetic field is about 137658 Hz.
Fig. 6
Fig. 6 Light-shift of D0 line A0(ω′)/6, D1 line −A1(ω′)/4, D2 line A2(ω′)/12 and these three lines sum A0(ω′)/6 − A1(ω′)/4 + A2(ω′)/12. Zero detuning point is at D0 transition wavelength (1083.205 nm).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

ρ C s = I 3 + 1 2 J z C ( 1 2 J z + 1 6 T 0 ) = diag [ 1 3 + 2 J z C 3 , 1 3 J z C 3 , 1 3 J z C 3 ] ,
ρ L s = I 3 + 1 2 ( T 0 L T 0 + T 2 L T 2 + T 2 L T 2 ) = [ 1 3 + T 0 L 6 0 T 2 L 0 1 3 2 T 0 L 6 0 T 2 L 0 1 3 + T 0 L 6 ] ,
δ ε C z = J = 0 J = 2 A J ( ω ) ( α J ( 0 ) I + α J ( 1 ) J z + α J ( 2 ) T 0 ) ,
A J ( ω ) = k I L 0 ω ω v 1 + τ 2 ( ω ω v ) 2 exp ( ω J ω v ) 2 σ d ω v ,
δ ε C = J = 0 J = 2 A J ( ω ) { α J ( 0 ) I + α J ( 1 ) 2 ( J + + J ) 6 α J ( 2 ) 2 [ 1 6 T 0 1 2 ( T 2 + T 2 ) ] } .
δ ε L ( θ ) = J = 0 J = 2 A J ( ω ) { α J ( 0 ) I 6 α J ( 2 ) 2 [ ( 1 + 3 cos 2 θ ) 6 T 0 i sin 2 θ ( T 1 + T 1 ) sin 2 θ ( T 2 + T 2 ) ] } ,
δ ε C 1 12 A 0 ( ω ) [ 1 2 1 2 2 2 1 2 1 ] .
δ ε L ( π 2 ) 1 12 A 0 ( ω ) [ 2 0 2 0 0 0 2 0 2 ] .
δ ε L ( θ ) + γ B 0 J z [ 1 6 A 0 ( ω ) sin 2 θ + γ B 0 1 6 2 i A 0 ( ω ) sin 2 θ 1 6 A 0 ( ω ) sin 2 θ 1 6 2 i A 0 ( ω ) sin 2 θ 1 3 A 0 ( ω ) cos 2 θ 1 6 2 i A 0 ( ω ) sin 2 θ 1 6 A 0 ( ω ) sin 2 θ 1 6 2 i A 0 ( ω ) sin 2 θ 1 6 A 0 ( ω ) sin 2 θ γ B 0 ] ,
( 1 6 A 0 ( ω ) 1 4 A 1 ( ω ) + 1 12 A 2 ( ω ) ) ( T 2 + T 2 ) .

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