Abstract

A novel quintuplet spectrum is observed in  3He atoms’ metastable state 23S1, when linear polarized light is adopted to probe the alignment component of its F=3/2 hyperfine structure. Static and oscillating magnetic fields produce magnetic resonance and Rabi nutation in ground state 11S0, respectively. After Fourier transform, centre frequency of the metastable-state quintuplet spectrum coincidences with the ground state Larmor frequency, and frequency separations between the five peaks equal to that of ground state Rabi nutation. Similar quintuplet spectrum is observed in  4He metastable state mixed with  3He hybrid vapor.

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

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References

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  1. K. Pachucki and V. A. Yerokhin, “Reexamination of the helium fine structure,” Phys. Rev. A 79, 062516 (2009).
    [Crossref]
  2. G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
    [Crossref]
  3. M. Smiciklas and D. Shiner, “Determination of the Fine Structure Constant Using Helium Fine Structure,” Phys. Rev. Lett. 105, 123001 (2010).
    [Crossref] [PubMed]
  4. T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
    [Crossref]
  5. T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
    [Crossref]
  6. C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
    [Crossref]
  7. A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
    [Crossref]
  8. H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
    [Crossref]
  9. S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
    [Crossref] [PubMed]
  10. F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
    [Crossref]
  11. F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
    [Crossref]
  12. R. C. Greenhow, “Optical pumping in He3,” Phys. Rev. 136, A660–A662 (1964).
    [Crossref]
  13. M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms (Oxford University, 2010).
  14. P.-J. Nacher and M. Leduc, “Optical pumping in  3He with a laser,” J. Phys. 46, 2057–2073 (1985).
    [Crossref]
  15. R. B. Partridge and G. W. Series, “The transfer of coherence by collisions of  3He atoms,” Proc. Phys. Soc. 88, 983–993 (1966).
    [Crossref]
  16. H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
    [Crossref]
  17. C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
    [Crossref]
  18. K. Blum, Density Matrix Theory and Applications (Plemum, 1996).
    [Crossref]
  19. A. Weis and G. Bison, “Theory of double resonance magnetometers based on atomic alignment,” Phys. Rev. A 74, 033401 (2006).
    [Crossref]
  20. This equation is derived by simply implementing a ratotion on the zeroth component of the second order tensor. It can be easily done with the WignerD function in the ADM package of Mathematica, which can be found in http://rochesterscientific.com/ADM/AtomicDensityMatrix .
  21. J. Dupont-Roc, “Etude de quelques effets lié au pompage optique en champ faible,” Université Pierre et Marie Curie - Paris VI (1972).
  22. E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

2019 (1)

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

2018 (1)

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

2017 (3)

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

2015 (3)

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
[Crossref]

2014 (1)

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

2010 (2)

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

M. Smiciklas and D. Shiner, “Determination of the Fine Structure Constant Using Helium Fine Structure,” Phys. Rev. Lett. 105, 123001 (2010).
[Crossref] [PubMed]

2009 (1)

K. Pachucki and V. A. Yerokhin, “Reexamination of the helium fine structure,” Phys. Rev. A 79, 062516 (2009).
[Crossref]

2006 (1)

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

1996 (1)

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

1985 (1)

P.-J. Nacher and M. Leduc, “Optical pumping in  3He with a laser,” J. Phys. 46, 2057–2073 (1985).
[Crossref]

1966 (1)

R. B. Partridge and G. W. Series, “The transfer of coherence by collisions of  3He atoms,” Proc. Phys. Soc. 88, 983–993 (1966).
[Crossref]

1964 (1)

R. C. Greenhow, “Optical pumping in He3,” Phys. Rev. 136, A660–A662 (1964).
[Crossref]

1963 (1)

F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
[Crossref]

Alcouffe, F.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Auzinsh, M.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms (Oxford University, 2010).

Baessler, S.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Basler, C.

C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
[Crossref]

Beato, F.

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

Belorizky, E.

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

Berger, F.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Bertrand, F.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Bigelow, N.

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

Bison, G.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

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

Blum, K.

K. Blum, Density Matrix Theory and Applications (Plemum, 1996).
[Crossref]

Blümler, P.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Budker, D.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms (Oxford University, 2010).

Burghoff, M.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Cauffet, G.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Chupp, T. E.

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

Colegrove, F. D.

F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
[Crossref]

Corsi, M. C.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Dupont-Roc, J.

J. Dupont-Roc, “Etude de quelques effets lié au pompage optique en champ faible,” Université Pierre et Marie Curie - Paris VI (1972).

Feng, G.-P.

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

Fierlinger, P.

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

Fourcault, W.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Gemmel, C.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Gentile, T. R.

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

Gobbo, C.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Greenhow, R. C.

R. C. Greenhow, “Optical pumping in He3,” Phys. Rev. 136, A660–A662 (1964).
[Crossref]

Grujic, Z. D.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

Grujic, Z.D.

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Grzesiak, J.

C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
[Crossref]

Hehn, M.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Heil, W.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Helm, H.

C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
[Crossref]

Hu, S.-M.

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

Karpuk, S.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Kasprzak, M.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Kilian, W.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Knappe-Grüneberg, S.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Knowles, P.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Koch, H. C.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

Koch, H.-C.

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Kraft, A.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Labyt, E.

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Leduc, M.

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

P.-J. Nacher and M. Leduc, “Optical pumping in  3He with a laser,” J. Phys. 46, 2057–2073 (1985).
[Crossref]

Lenouvel, F.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Lenz, K.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Ludwig, C.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Maul, A.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Meyerhoff, M.

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

Morales, S.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Müller, W.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Nacher, P.-J.

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

P.-J. Nacher and M. Leduc, “Optical pumping in  3He with a laser,” J. Phys. 46, 2057–2073 (1985).
[Crossref]

Nikiel, A.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Otten, E.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Pachucki, K.

K. Pachucki and V. A. Yerokhin, “Reexamination of the helium fine structure,” Phys. Rev. A 79, 062516 (2009).
[Crossref]

Palacios-Laloy, A.

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

Partridge, R. B.

R. B. Partridge and G. W. Series, “The transfer of coherence by collisions of  3He atoms,” Proc. Phys. Soc. 88, 983–993 (1966).
[Crossref]

Pazgalev, A.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Prado, M. Le

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Ramsey-Musolf, M. J.

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

Rochester, S. M.

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms (Oxford University, 2010).

Saam, B.

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

Schearer, L. D.

F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
[Crossref]

Schnabel, A.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Schreiber, L.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Seifert, F.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Series, G. W.

R. B. Partridge and G. W. Series, “The transfer of coherence by collisions of  3He atoms,” Proc. Phys. Soc. 88, 983–993 (1966).
[Crossref]

Shiner, D.

M. Smiciklas and D. Shiner, “Determination of the Fine Structure Constant Using Helium Fine Structure,” Phys. Rev. Lett. 105, 123001 (2010).
[Crossref] [PubMed]

Singh, J. T.

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

Smiciklas, M.

M. Smiciklas and D. Shiner, “Determination of the Fine Structure Constant Using Helium Fine Structure,” Phys. Rev. Lett. 105, 123001 (2010).
[Crossref] [PubMed]

Sobolev, Y.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Stoltz, E.

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

Sun, Y. R.

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

Tastevin, G.

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

Terekhov, M.

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

Trahms, L.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Tullney, K.

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

Vanzetto, G.

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Voigt, J.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

Walker, T. G.

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

Walters, G. K.

F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
[Crossref]

Weis, A.

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

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

Yerokhin, V. A.

K. Pachucki and V. A. Yerokhin, “Reexamination of the helium fine structure,” Phys. Rev. A 79, 062516 (2009).
[Crossref]

Zheng, X.

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

Appl. Phys. B: Lasers Opt. (1)

E. Stoltz, M. Meyerhoff, N. Bigelow, M. Leduc, P.-J. Nacher, and G. Tastevin, “High nuclear polarization in  3He and  3He- 4He gas mixtures by optical pumping with a laser diode,” Appl. Phys. B: Lasers Opt. 63, 629–633 (1996).

Eur. Phys. J. D (4)

C. Gemmel, W. Heil, S. Karpuk, K. Lenz, C. Ludwig, Y. Sobolev, K. Tullney, M. Burghoff, W. Kilian, S. Knappe-Grüneberg, W. Müller, A. Schnabel, F. Seifert, L. Trahms, and S. Baessler, “Ultra-sensitive magnetometry based onfree precession of nuclear spins,” Eur. Phys. J. D 57, 303–320 (2010).
[Crossref]

A. Nikiel, P. Blümler, W. Heil, M. Hehn, S. Karpuk, A. Maul, E. Otten, L. Schreiber, and M. Terekhov, Ültrasensitive  3He magnetometer for measurements of high magnetic fields,” Eur. Phys. J. D 68, 330 (2014)
[Crossref]

H.-C. Koch, G. Bison, Z.D. Grujić, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Investigation of the intrinsic sensitivity of a  3He/Cs magnetometer,” Eur. Phys. J. D 69, 262 (2015).
[Crossref]

H. C. Koch, G. Bison, Z. D. Grujic, W. Heil, M. Kasprzak, P. Knowles, A. Kraft, A. Pazgalev, A. Schnabel, J. Voigt, and A. Weis, “Study of  3He Rabi nutations by optically-pumped cesium magnetometers,” Eur. Phys. J. D 71, 262 (2017).
[Crossref]

J. Phys. (1)

P.-J. Nacher and M. Leduc, “Optical pumping in  3He with a laser,” J. Phys. 46, 2057–2073 (1985).
[Crossref]

Phys. Med. Biol. (1)

S. Morales, M. C. Corsi, W. Fourcault, F. Bertrand, G. Cauffet, C. Gobbo, F. Alcouffe, F. Lenouvel, M. Le Prado, F. Berger, G. Vanzetto, and E. Labyt, “Magnetocardiography measurements with  4He vector optically pumped magnetometers at room temperature,” Phys. Med. Biol. 62, 7267–7279 (2017).
[Crossref] [PubMed]

Phys. Rev. (2)

F. D. Colegrove, L. D. Schearer, and G. K. Walters, “Polarization of  3He Gas by Optical Pumping,” Phys. Rev. 132, 2561–2572 (1963).
[Crossref]

R. C. Greenhow, “Optical pumping in He3,” Phys. Rev. 136, A660–A662 (1964).
[Crossref]

Phys. Rev. A (5)

C. Basler, J. Grzesiak, and H. Helm, “Radio-frequency-assisted electromagnetically induced transparency,” Phys. Rev. A 92, 013809 (2015).
[Crossref]

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

F. Beato, E. Belorizky, E. Labyt, M. Le Prado, and A. Palacios-Laloy, “Theory of a  4He parametric-resonance magnetometer based on atomic alignment,” Phys. Rev. A 98, 053431 (2018).
[Crossref]

K. Pachucki and V. A. Yerokhin, “Reexamination of the helium fine structure,” Phys. Rev. A 79, 062516 (2009).
[Crossref]

G.-P. Feng, X. Zheng, Y. R. Sun, and S.-M. Hu, “Laser-spectroscopy measurement of the fine-structure splitting 23P1−23P2 of  4He,” Phys. Rev. A, 91, 030502 (2015).
[Crossref]

Phys. Rev. Lett. (1)

M. Smiciklas and D. Shiner, “Determination of the Fine Structure Constant Using Helium Fine Structure,” Phys. Rev. Lett. 105, 123001 (2010).
[Crossref] [PubMed]

Proc. Phys. Soc. (1)

R. B. Partridge and G. W. Series, “The transfer of coherence by collisions of  3He atoms,” Proc. Phys. Soc. 88, 983–993 (1966).
[Crossref]

Rev. Mod. Phys. (2)

T. R. Gentile, P.-J. Nacher, B. Saam, and T. G. Walker, “Optically polarized  3He,” Rev. Mod. Phys. 89, 045004 (2017).
[Crossref]

T. E. Chupp, P. Fierlinger, M. J. Ramsey-Musolf, and J. T. Singh, “Electric dipole moments of atoms, molecules, nuclei, and particles,” Rev. Mod. Phys. 91, 015001 (2019).
[Crossref]

Other (4)

M. Auzinsh, D. Budker, and S. M. Rochester, Optically Polarized Atoms (Oxford University, 2010).

This equation is derived by simply implementing a ratotion on the zeroth component of the second order tensor. It can be easily done with the WignerD function in the ADM package of Mathematica, which can be found in http://rochesterscientific.com/ADM/AtomicDensityMatrix .

J. Dupont-Roc, “Etude de quelques effets lié au pompage optique en champ faible,” Université Pierre et Marie Curie - Paris VI (1972).

K. Blum, Density Matrix Theory and Applications (Plemum, 1996).
[Crossref]

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Figures (6)

Fig. 1
Fig. 1 Energy-level diagram for 3He atoms (not in scale). The nuclear spin for 3He is 1/2. There is no electronic spin or orbit angular momentum for the ground state 11 S0. For the metastable state 23 S1, the electronic spin is 1 and the orbit angular momentum is 0. For the excited state 23 P0 the electronic spin is 1 and angular momentum is 0. The ground-state atoms can be excited to the metastable state by RF discharge, and atomic polarization canbe exchanged between the ground state and the metastable state by metastability-exchange collisions (MECs). The gyromagnetic ratios for the ground and the metastable states are different, i.e., γg= -32 Hz/μT, γμ= -38 kHz/μT, and γ μ = -19 kHz/μT for the ground state and the two metastable hyperfine levels F = 1/2 and F = 3/2, respectively [11]. Atoms in the metastable state can be optically pumped or detected by C8 or C9 line with a 1083.353 nm or 1083.326 nm wavelength laser beam [14].
Fig. 2
Fig. 2 Experimental setup. PBS, polarization beam splitter; QWP, quarter wave plate; HWP, half wave plate; BE, beam expander; BT, beam trap and PD, photo detector.
Fig. 3
Fig. 3 Frequency spectrums for C8- or C9-line probe. Black dots are the experimental data, and red lines are the connecting lines of adjacent data points. (a) and (b) are probed with C8 line, and (c) and (d) are probed with C9 line. The probe beams for (a) and (c) are circularly polarized, and for (b) and (d) are linearly polarized.
Fig. 4
Fig. 4 Quintuplet spectrums for linearly polarized probe laser beams with different polarization directions. Black dots in (c) and (d) are the experimental data, red lines in (c) are the connecting lines of adjacent data points, and blue line in (d)is a mathematical curve. (a) the polarization direction of the linearly polarized laser beam; it rotates in the z - y plane and θ is the titled angle with respect to y axis. (b) and (c) show the heights of the quintuplet spectrum at different angles. (d) The heights of the central peaks at differen angles; the black dots is the measured and normalized value and the blue line is a mathematical curve with function sin (2θ). The static magnetic field is ∼41 μT.
Fig. 5
Fig. 5 Quintuplet spectrums at different oscillating magnetic field. (a) the oscillating magnetic field’s frequency is tuned to Larmor frequency while changing its amplitude; (b) the oscillating magnetic field’s amplitude is fixed at 3 μT while changing its detuning. Larmor frequency is equal to ∼1300 Hz.
Fig. 6
Fig. 6 Frequency spectrums for 4He atoms in a hybrid atomic vapor cell mixed with 3He atoms. All the experimental conditions are similar to that of the pure 3He atomic vapor, except for that, the metastable 4He atoms are optically pumped and probed rather than the 3He. The 3He atoms are polarized via MECs with the 4He atoms. Black dots are the experimental data, and red lines are the connecting lines of adjacent data points. (a) triplet spectrum probed with circularly polarized laser beam; (b) quintuplet spectrum probed with linearly polarized laser beam. Both the pump and probe laser beams are tuned to D0 line and the pump beam is circular polarized.

Equations (13)

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

ρ m = F P F ( ρ g Tr n ρ m   ' ) P F ,
d d t 3 / 2 F = 4 9 τ 3 / 2 F + 10 9 τ 1 / 2 F + 10 9 τ I f ,
d d t 1 / 2 F = 1 9 τ 3 / 2 F 7 9 τ 1 / 2 F 1 9 τ I f ,
ρ m = k q m k , q T q ( k ) ,
m k , q = T q ( k ) = Tr ( ρ m T q ( k ) ) ,
T q ( k ) = M M ( 1 ) F M F , M , F , M | k , q | F , M F , M | ,
S C 0 m 2 , 0 ( 1 + 3 cos  2 α ) + C 1 ( m 2 , 1 + m 2 , 1 ) sin  2 α + C 2 ( m 2 , 2 + m 2 , 2 ) sin 2 α .
d d t 3 / 2 Q i j   m = 2 3 τ 3 / 2 Q i j   m + 1 9 τ ( 3 I i   f S j   m + I j   f S i   m 2 I f S m ) ,
I f = 1 3 [   3 / 2 F 1 / 2 F ] ,
S m = 2 3 [   3 / 2 F + 2 1 / 2 F ] ,
d d t 3 / 2 Q i j   m = 2 3 τ 3 / 2 Q i j   m + 1 9 τ [   3 / 2 F i   3 / 2 F j + 3 / 2 F i   1 / 2 F j + 3 / 2 F j   1 / 2 F i 4 1 / 2 F i   1 / 2 F j 3 2 9 (   3 / 2 F 2 + 3 / 2 F 1 / 2 F 2 1 / 2 F 2 ) ] .
S QS sin  2 α ( m 2 , 1 + m 2 , 1 ) .
T ± 1 ( 2 ) ( 3 / 2 F ) [ (   3 / 2 F x 3 / 2 F z + 3 / 2 F z 3 / 2 F x ) ± i (   3 / 2 F y 3 / 2 F z + 3 / 2 F z 3 / 2 F y ) ] ,

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