Abstract

Light shifts are an important source of noise and systematics in optically pumped magnetometers. We demonstrate that the long spin-coherence time in paraffin-coated cells leads to spatial averaging of the vector light shift over the entire cell volume. This renders the averaged vector light shift independent, under certain approximations, of the light-intensity distribution within the sensor cell. Importantly, the demonstrated averaging mechanism can be extended to other spatially varying phenomena in anti-relaxation-coated cells with long coherence times.

© 2016 Optical Society of America

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References

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  4. Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
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  5. E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
    [Crossref]
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  8. D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  24. S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
    [Crossref]
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    [Crossref] [PubMed]
  32. W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
    [Crossref]
  33. D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
    [Crossref]

2015 (1)

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

2014 (3)

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

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

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

2013 (2)

I. A. Sulai, R. Wyllie, M. Kauer, G. S. Smetana, R. T. Wakai, and T. G. Walker, “Diffusive suppression of AC-Stark shifts in atomic magnetometers,” Opt. Lett. 38(6), 974–976 (2013).
[Crossref] [PubMed]

F. Le Kien, P. Schneeweiss, and A. Rauschenbeutel, “Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium,” Eur. Phys. J. D 67(5), 92 (2013).
[Crossref]

2012 (2)

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

2011 (1)

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

2010 (2)

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

2008 (1)

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

2007 (1)

S. J. Seltzer, P. J. Meares, and M. V. Romalis, “Synchronous optical pumping of quantum revival beats for atomic magnetometry,” Phys. Rev. A 75, 051407 (2007).
[Crossref]

2006 (4)

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

J. M. Higbie, E. Corsini, and D. Budker, “Robust, high-speed, all-optical atomic magnetometer,” Rev. Sci. Instrum. 77(11), 113106 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

2005 (1)

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

2003 (1)

A. Podvyaznyi, A. Sakantsev, and V. Semenov, “About the Zeeman light-induced frequency shift of the radio-optical resonance in optically oriented isotopes of alkali metals,” Russ. Phys. J. 46, 933 (2003).
[Crossref]

2002 (1)

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

1998 (1)

1995 (1)

1991 (1)

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

1983 (1)

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[Crossref]

1981 (1)

A. Brillet, “Evaluation of the light shifts in an optically pumped cesium beam frequency standard,” Metrologia 17(4), 147–150 (1981).
[Crossref]

1975 (1)

M. Arditi and J. L. Picque, “Precision measurements of light shifts induced by a narrow-band GaAs laser in the 0-0 133 Cs hyperfine transition,” J. Phys. B 8(14), L331 (1975).
[Crossref]

1972 (1)

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968–984 (1972).
[Crossref]

1971 (1)

B. Bulos, A. Marshall, and W. Happer, “Light shifts due to real transitions in optically pumped alkali atoms,” Phys. Rev. A 4(1), 51–59 (1971).
[Crossref]

1968 (1)

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

1961 (1)

M. Arditi and T. R. Carver, “Pressure, light, and temperature shifts in optical detection of 0-0 hyperfine resonance of alkali metals,” Phys. Rev. 124, 800–809 (1961).
[Crossref]

1957 (1)

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

Acosta, V.

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Anielski, P.

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

Arditi, M.

M. Arditi and J. L. Picque, “Precision measurements of light shifts induced by a narrow-band GaAs laser in the 0-0 133 Cs hyperfine transition,” J. Phys. B 8(14), L331 (1975).
[Crossref]

M. Arditi and T. R. Carver, “Pressure, light, and temperature shifts in optical detection of 0-0 hyperfine resonance of alkali metals,” Phys. Rev. 124, 800–809 (1961).
[Crossref]

Balabas, M. V.

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

Bell, W. E.

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

Bison, G.

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

Bloom, A. L.

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

Breschi, E.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Brillet, A.

A. Brillet, “Evaluation of the light shifts in an optically pumped cesium beam frequency standard,” Metrologia 17(4), 147–150 (1981).
[Crossref]

Budker, D.

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

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

J. M. Higbie, E. Corsini, and D. Budker, “Robust, high-speed, all-optical atomic magnetometer,” Rev. Sci. Instrum. 77(11), 113106 (2006).
[Crossref]

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

D. Budker, D. Kimball, and D. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2008).

Bulos, B.

B. Bulos, A. Marshall, and W. Happer, “Light shifts due to real transitions in optically pumped alkali atoms,” Phys. Rev. A 4(1), 51–59 (1971).
[Crossref]

Camparo, J. C.

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[Crossref]

Carver, T. R.

M. Arditi and T. R. Carver, “Pressure, light, and temperature shifts in optical detection of 0-0 hyperfine resonance of alkali metals,” Phys. Rev. 124, 800–809 (1961).
[Crossref]

Chalupczak, W.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[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, 968–984 (1972).
[Crossref]

Corsini, E.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

J. M. Higbie, E. Corsini, and D. Budker, “Robust, high-speed, all-optical atomic magnetometer,” Rev. Sci. Instrum. 77(11), 113106 (2006).
[Crossref]

Corwin, K. L.

DeMille, D.

D. Budker, D. Kimball, and D. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2008).

Di Domenico, G.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Dupont-Roc, J.

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968–984 (1972).
[Crossref]

Epstein, R. J.

Frueholz, R. P.

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[Crossref]

Gao, W.

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

Gawlik, W.

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Godun, R. M.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

Goka, S.

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

Gring, M.

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

Groeger, S.

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

Gruji, Z.

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

Hand, C. F.

Happer, W.

B. Bulos, A. Marshall, and W. Happer, “Light shifts due to real transitions in optically pumped alkali atoms,” Phys. Rev. A 4(1), 51–59 (1971).
[Crossref]

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

Higbie, J. M.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

J. M. Higbie, E. Corsini, and D. Budker, “Robust, high-speed, all-optical atomic magnetometer,” Rev. Sci. Instrum. 77(11), 113106 (2006).
[Crossref]

Hollberg, L.

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

Hovde, D. C.

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

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Ikegami, T.

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

Iwata, G. Z.

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

Jackson Kimball, D. F.

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Kajita, M.

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

Karaulanov, T.

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

Kauer, M.

Kazakov, G.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Kimball, D.

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

D. Budker, D. Kimball, and D. DeMille, Atomic Physics: An Exploration through Problems and Solutions (Oxford University, 2008).

Kimball, D. F.

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

Kitching, J.

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

Knappe, S.

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

Koga, Y.

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

Koss, P.

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

Kotyrba, M.

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

Lang, S.

Le Kien, F.

F. Le Kien, P. Schneeweiss, and A. Rauschenbeutel, “Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium,” Eur. Phys. J. D 67(5), 92 (2013).
[Crossref]

Ledbetter, M. P.

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Lee, C.

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

Litvinov, A.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Lu, Z.-T.

Lucivero, V. G.

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

Marshall, A.

B. Bulos, A. Marshall, and W. Happer, “Light shifts due to real transitions in optically pumped alkali atoms,” Phys. Rev. A 4(1), 51–59 (1971).
[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]

Matisov, B.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Meares, P. J.

S. J. Seltzer, P. J. Meares, and M. V. Romalis, “Synchronous optical pumping of quantum revival beats for atomic magnetometry,” Phys. Rev. A 75, 051407 (2007).
[Crossref]

Mileti, G.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Mitchell, M. W.

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

Nakadan, Y.

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

Ohshima, S.

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

Patton, B.

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

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

Picque, J. L.

M. Arditi and J. L. Picque, “Precision measurements of light shifts induced by a narrow-band GaAs laser in the 0-0 133 Cs hyperfine transition,” J. Phys. B 8(14), L331 (1975).
[Crossref]

Podvyaznyi, A.

A. Podvyaznyi, A. Sakantsev, and V. Semenov, “About the Zeeman light-induced frequency shift of the radio-optical resonance in optically oriented isotopes of alkali metals,” Russ. Phys. J. 46, 933 (2003).
[Crossref]

Pustelny, S.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

Rauschenbeutel, A.

F. Le Kien, P. Schneeweiss, and A. Rauschenbeutel, “Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium,” Eur. Phys. J. D 67(5), 92 (2013).
[Crossref]

Rochester, S.

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Rochester, S. M.

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Romalis, M. V.

S. J. Seltzer, P. J. Meares, and M. V. Romalis, “Synchronous optical pumping of quantum revival beats for atomic magnetometry,” Phys. Rev. A 75, 051407 (2007).
[Crossref]

Sakantsev, A.

A. Podvyaznyi, A. Sakantsev, and V. Semenov, “About the Zeeman light-induced frequency shift of the radio-optical resonance in optically oriented isotopes of alkali metals,” Russ. Phys. J. 46, 933 (2003).
[Crossref]

Schenker, J.-L.

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

Schneeweiss, P.

F. Le Kien, P. Schneeweiss, and A. Rauschenbeutel, “Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium,” Eur. Phys. J. D 67(5), 92 (2013).
[Crossref]

Schori, C.

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

Seltzer, S. J.

S. J. Seltzer, P. J. Meares, and M. V. Romalis, “Synchronous optical pumping of quantum revival beats for atomic magnetometry,” Phys. Rev. A 75, 051407 (2007).
[Crossref]

Semenov, V.

A. Podvyaznyi, A. Sakantsev, and V. Semenov, “About the Zeeman light-induced frequency shift of the radio-optical resonance in optically oriented isotopes of alkali metals,” Russ. Phys. J. 46, 933 (2003).
[Crossref]

Skalla, J.

Smetana, G. S.

Sulai, I. A.

Tang, H.

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

Versolato, O. O.

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

Volk, C. H.

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[Crossref]

Wackerle, G.

Wakai, R. T.

Walker, T. G.

Weis, A.

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Wieman, C. E.

Wojciechowski, A.

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

Wyllie, R.

Wynands, R.

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

Yano, Y.

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

Yashchuk, V.

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Yashchuk, V. V.

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

Zachorowski, J.

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

Zhivun, E.

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

Appl. Opt. (1)

Appl. Phys. Lett. (1)

B. Patton, O. O. Versolato, D. C. Hovde, E. Corsini, J. M. Higbie, and D. Budker, “A remotely interrogated all-optical 87Rb magnetometer,” Appl. Phys. Lett. 101(8), 083502 (2012).
[Crossref]

Eur. Phys. J. D (3)

S. Groeger, G. Bison, J.-L. Schenker, R. Wynands, and A. Weis, “A high-sensitivity laser-pumped Mx magnetometer,” Eur. Phys. J. D 38(2), 239–247 (2006).
[Crossref]

Z. Gruji, P. Koss, G. Bison, and A. Weis, “A sensitive and accurate atomic magnetometer based on free spin precession,” Eur. Phys. J. D 69(5), 135 (2015).
[Crossref]

F. Le Kien, P. Schneeweiss, and A. Rauschenbeutel, “Dynamical polarizability of atoms in arbitrary light fields: general theory and application to cesium,” Eur. Phys. J. D 67(5), 92 (2013).
[Crossref]

IEEE Trans. Instrum. Meas. (1)

S. Ohshima, Y. Nakadan, T. Ikegami, and Y. Koga, “Light shifts in an optically pumped Cs beam frequency standard,” IEEE Trans. Instrum. Meas. 40(6), 1003–1007 (1991).
[Crossref]

J. Appl. Phys. (1)

S. Pustelny, A. Wojciechowski, M. Gring, M. Kotyrba, J. Zachorowski, and W. Gawlik, “Magnetometry based on nonlinear magneto-optical rotation with amplitude-modulated light,” J. Appl. Phys. 103(6), 063108 (2008).
[Crossref]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

M. Arditi and J. L. Picque, “Precision measurements of light shifts induced by a narrow-band GaAs laser in the 0-0 133 Cs hyperfine transition,” J. Phys. B 8(14), L331 (1975).
[Crossref]

Metrologia (1)

A. Brillet, “Evaluation of the light shifts in an optically pumped cesium beam frequency standard,” Metrologia 17(4), 147–150 (1981).
[Crossref]

Opt. Lett. (1)

Phys. Rev. (3)

M. Arditi and T. R. Carver, “Pressure, light, and temperature shifts in optical detection of 0-0 hyperfine resonance of alkali metals,” Phys. Rev. 124, 800–809 (1961).
[Crossref]

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

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

Phys. Rev. A (10)

V. Acosta, M. P. Ledbetter, S. M. Rochester, D. Budker, D. F. Jackson Kimball, D. C. Hovde, W. Gawlik, S. Pustelny, J. Zachorowski, and V. V. Yashchuk, “Nonlinear magneto-optical rotation with frequency-modulated light in the geophysical field range,” Phys. Rev. A 73, 053404 (2006).
[Crossref]

S. Pustelny, D. F. Jackson Kimball, S. M. Rochester, V. V. Yashchuk, and D. Budker, “Influence of magnetic-field inhomogeneity on nonlinear magneto-optical resonances,” Phys. Rev. A 74, 063406 (2006).
[Crossref]

J. C. Camparo, R. P. Frueholz, and C. H. Volk, “Inhomogeneous light shift in alkali-metal atoms,” Phys. Rev. A 27, 1914–1924 (1983).
[Crossref]

W. Chalupczak, R. M. Godun, P. Anielski, A. Wojciechowski, S. Pustelny, and W. Gawlik, “Enhancement of optically pumped spin orientation via spin-exchange collisions at low vapor density,” Phys. Rev. A 85, 043402 (2012).
[Crossref]

Y. Yano, W. Gao, S. Goka, and M. Kajita, “Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping,” Phys. Rev. A 90, 013826 (2014).
[Crossref]

E. Breschi, G. Kazakov, C. Schori, G. Di Domenico, G. Mileti, A. Litvinov, and B. Matisov, “Light effects in the atomic-motion-induced Ramsey narrowing of dark resonances in wall-coated cells,” Phys. Rev. A 82, 063810 (2010).
[Crossref]

D. Budker, L. Hollberg, D. F. Kimball, J. Kitching, S. Pustelny, and V. V. Yashchuk, “Microwave transitions and nonlinear magneto-optical rotation in anti-relaxation-coated cells,” Phys. Rev. A 71, 012903 (2005).
[Crossref]

B. Bulos, A. Marshall, and W. Happer, “Light shifts due to real transitions in optically pumped alkali atoms,” Phys. Rev. A 4(1), 51–59 (1971).
[Crossref]

C. Cohen-Tannoudji and J. Dupont-Roc, “Experimental study of Zeeman light shifts in weak magnetic fields,” Phys. Rev. A 5, 968–984 (1972).
[Crossref]

S. J. Seltzer, P. J. Meares, and M. V. Romalis, “Synchronous optical pumping of quantum revival beats for atomic magnetometry,” Phys. Rev. A 75, 051407 (2007).
[Crossref]

Phys. Rev. Lett. (2)

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

M. V. Balabas, T. Karaulanov, M. P. Ledbetter, and D. Budker, “Polarized alkali-metal vapor with minute-long transverse spin-relaxation time,” Phys. Rev. Lett. 105(7), 070801 (2010).
[Crossref] [PubMed]

Rev. Mod. Phys. (1)

D. Budker, W. Gawlik, D. Kimball, S. Rochester, V. Yashchuk, and A. Weis, “Resonant nonlinear magneto-optical effects in atoms,” Rev. Mod. Phys. 74(4), 1153–1201 (2002).
[Crossref]

Rev. Sci. Instrum. (3)

C. Lee, G. Z. Iwata, E. Corsini, J. M. Higbie, S. Knappe, M. P. Ledbetter, and D. Budker, “Small-sized dichroic atomic vapor laser lock,” Rev. Sci. Instrum. 82(4), 043107 (2011).
[Crossref] [PubMed]

V. G. Lucivero, P. Anielski, W. Gawlik, and M. W. Mitchell, “Shot-noise-limited magnetometer with subpicotesla sensitivity at room temperature,” Rev. Sci. Instrum. 85(11), 113108 (2014).
[Crossref] [PubMed]

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[Crossref]

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[Crossref]

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[Crossref]

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Figures (4)

Fig. 1
Fig. 1

a) The experimental setup. The amplitude-modulated, circularly polarized pump beam propagates along (orthogonally to B⃗0 ‖ ŷ). A local oscillator (LO) pulses the pump intensity via an acousto-optical modulator (AOM) and serves as a reference for a lock-in amplifier (LIA), whose analog output is recorded with a data acquisition card (DAQ) and stored on a computer (PC). After transmitting through the cell, the linearly polarized probe beam is analyzed with a balanced polarimeter, consisting of a polarizing beam splitter (PBS) and two photodiodes. The circularly polarized light-shift beam (LS beam) propagates along B⃗0. Its diameter is varied with a computer controlled, motorized iris while its time-averaged power is kept constant with an AOM in a feedback loop. An image of the iris is formed inside the cell and on the beam profiler using a lens system. The optical frequency of the LS beam is measured with a wavemeter and controlled by the PC. For noise reduction, we perform synchronous detection of the VLS signal while harmonically modulating the LS beam power at ωM. b) shows the recorded time series for the LIA Y output for a single light shift measurement with the simultaneous modulation of the LO frequency and the LS power. c) The FFT of the signal in b) shows the calibration peak at ωC/2π and the LS amplitude at ωM/2π.

Fig. 2
Fig. 2

Change of the magnetic resonance center frequency as a function of the light-shift beam area for different LS beam detunings and a constant beam power. The complete data include detunings from −60 GHz to +60 GHz with respect to the 133Cs D1 F = 4 transitions. Just a fraction of the data is displayed here for better visibility of the individual sets. While the beam area x, and therefore the beam intensity, is modified by an order of magnitude, the MR center frequency changes are on average 3% and are of technical origin as explained in the text. Different colors represent distinct optical frequencies of the LS beam, the detuning is indicated by the arrows on the right. The data points are represented by circles, and the lines are linear fits δνLS (x) = aLS + bLS (x − 〈x〉) to the datasets. 〈x〉 is the mean area of the fitted set. The fit parameters are average light shift aLS and light shift change per unit area change bLS.

Fig. 3
Fig. 3

Average vector light shift aLS dependence on the optical frequency as derived from the fits to the data displayed in Fig. 2. The error bars are hidden within the points since the average ratio between data value and error is 140. The red curve shows a fit to the data with ∝ 1/ΔLS.

Fig. 4
Fig. 4

Light-shift change per unit area bLS divided by the average light-shift aLS (bLS/aLS from Fig. 2) as a function of the LS beam detuning. The data were rescaled to express the change of the measured light shift over each dataset to its mean value in percent. The red line is a sinusoidal fit revealing an etalon effect potentially in the cell wall.

Equations (1)

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δ ν β I Δ LS ,

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