Abstract

In this paper, the Breit–Rabi formula has been verified experimentally by precisely measuring the quadratic Zeeman coefficient of the ground-state clock transition of Rb87. The resonant spectra of the clock transition are obtained by using both microwave and Raman pulses to drive the transition. The line widths are optimized to be 120 Hz for microwave spectra and 300 Hz for Raman spectra so that the resolution of measurement can be increased. In our experiment, the uncertainty of the measured quadratic Zeeman coefficient is better than 1×108HzT2. The coefficient is demonstrated to be (575.09±0.48)×108HzT2 for the microwave spectroscopy and (574.59±0.89)×108HzT2 for the Raman spectroscopy which agrees well with the calculated result of 575.15×108HzT2.

© 2014 Optical Society of America

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    [CrossRef]

2012

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

2011

Y. Ovchinnikov and G. Marra, “Accurate rubidium atomic fountain frequency standard,” Metrologia 48, 87–100 (2011).
[CrossRef]

I. Chan, B. Barrett, and A. Kumarakrishnan, “Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap,” Phys. Rev. A 84, 032509 (2011).
[CrossRef]

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

2010

K. Numazaki, H. Imai, and A. Morinaga, “Measurement of the second-order Zeeman effect on the sodium clock transition in the weak-magnetic-field region using the scalar Aharonov–Bohm phase,” Phys. Rev. A 81, 032124 (2010).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

2009

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

2008

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

2006

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

2002

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

2001

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
[CrossRef]

2000

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
[CrossRef]

1992

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

1986

1968

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

1931

G. Breit and I. I. Rabi, “Measurement of nuclear spin,” Phys. Rev. 38, 2082–2083 (1931).
[CrossRef]

Abgrall, M.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Barrett, B.

I. Chan, B. Barrett, and A. Kumarakrishnan, “Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap,” Phys. Rev. A 84, 032509 (2011).
[CrossRef]

Bertoldi, A.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Bize, S.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Borde, C. J.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Breit, G.

G. Breit and I. I. Rabi, “Measurement of nuclear spin,” Phys. Rev. 38, 2082–2083 (1931).
[CrossRef]

Cacciapuoti, L.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Canuel, B.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Chaibi, W.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

Chan, I.

I. Chan, B. Barrett, and A. Kumarakrishnan, “Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap,” Phys. Rev. A 84, 032509 (2011).
[CrossRef]

Cheng, B.

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Chiow, S. W.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

Chu, S.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
[CrossRef]

Chung, K. Y.

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
[CrossRef]

Chupin, B.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Clairon, A.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

de Angelis, M.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Dimarcq, N.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Duan, X. C.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Ezekiel, S.

Fattori, M.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Fils, J.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Fixler, J. B.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

Foster, G. T.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

Gauguet, A.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Gerginov, V.

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

Gertsvolf, M.

L. Marmet and M. Gertsvolf, “Evaluation of NRC-FCs1: mapping the C-field using the Larmor frequency,” in Proceedings of the 2010 IEEE International Frequency Control Symposium (IEEE, 2010), pp. 312–317.

Gibble, K.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

Guena, J.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Hayne, G. S.

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

Hemmer, P. R.

Herrmann, S.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

Holleville, D.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Hu, Z. K.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Huang, M. M.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

Hughes, W. M.

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

Imai, H.

K. Numazaki, H. Imai, and A. Morinaga, “Measurement of the second-order Zeeman effect on the sodium clock transition in the weak-magnetic-field region using the scalar Aharonov–Bohm phase,” Phys. Rev. A 81, 032124 (2010).
[CrossRef]

Kasevich, M.

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

Kasevich, M. A.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
[CrossRef]

Kumarakrishnan, A.

I. Chan, B. Barrett, and A. Kumarakrishnan, “Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap,” Phys. Rev. A 84, 032509 (2011).
[CrossRef]

Lamporesi, G.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Landragin, A.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Laurent, P.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Leduc, F.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Lévèque, T.

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

Li, R.

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

Li, R. B.

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

Li, T.

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Lin, Q.

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Long, Q.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

Lours, M.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Luo, J.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Lv, D. S.

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Marmet, L.

L. Marmet and M. Gertsvolf, “Evaluation of NRC-FCs1: mapping the C-field using the Larmor frequency,” in Proceedings of the 2010 IEEE International Frequency Control Symposium (IEEE, 2010), pp. 312–317.

Marra, G.

Y. Ovchinnikov and G. Marra, “Accurate rubidium atomic fountain frequency standard,” Metrologia 48, 87–100 (2011).
[CrossRef]

McGuirk, J. M.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
[CrossRef]

Moler, K.

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

Morinaga, A.

K. Numazaki, H. Imai, and A. Morinaga, “Measurement of the second-order Zeeman effect on the sodium clock transition in the weak-magnetic-field region using the scalar Aharonov–Bohm phase,” Phys. Rev. A 81, 032124 (2010).
[CrossRef]

Müller, H.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

Nemitz, N.

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

Numazaki, K.

K. Numazaki, H. Imai, and A. Morinaga, “Measurement of the second-order Zeeman effect on the sodium clock transition in the weak-magnetic-field region using the scalar Aharonov–Bohm phase,” Phys. Rev. A 81, 032124 (2010).
[CrossRef]

Ontai, G. P.

Ovchinnikov, Y.

Y. Ovchinnikov and G. Marra, “Accurate rubidium atomic fountain frequency standard,” Metrologia 48, 87–100 (2011).
[CrossRef]

Petelski, T.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Peters, A.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
[CrossRef]

Prevedelli, M.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Rabi, I. I.

G. Breit and I. I. Rabi, “Measurement of nuclear spin,” Phys. Rev. 38, 2082–2083 (1931).
[CrossRef]

Robinson, H. G.

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

Rosenbusch, P.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Rovera, D.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Ruoxin, L.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Santarelli, G.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Shi, C. Y.

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Snadden, M. J.

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
[CrossRef]

Steven, C.

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

Stuhler, J.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Sun, B. L.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Tao, T. J.

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Tino, G. M.

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

Tobar, M. E.

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

Virdis, A.

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Wang, J.

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

Wang, X. L.

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

Wang, Y. Z.

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Wang, Z. Y.

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Wei, R.

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Weiss, D. S.

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

Weyers, S.

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

White, C. W.

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

Wu, B.

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

Xu, Y. F.

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Zhan, M. S.

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

Zhao, J. B.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Zhou, L.

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

Zhou, M. K.

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

Zhou, Z. C.

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Chin. Opt. Lett

C. Y. Shi, R. Wei, Z. C. Zhou, D. S. Lv, T. Li, and Y. Z. Wang, “Magnetic field measurement on 87Rb atomic fountain clock,” Chin. Opt. Lett 8, 549–552 (2010).
[CrossRef]

Chin. Phys. B

Z. C. Zhou, R. Wei, C. Y. Shi, T. Li, and Y. Z. Wang, “Magnetic field measurement based on a stimulated two-photon Raman transition,” Chin. Phys. B 20, 034206 (2011).
[CrossRef]

Chin. Phys. Lett

X. L. Wang, B. Cheng, B. Wu, Z. Y. Wang, and Q. Lin, “A simplified cold atom source for 3-D MOT loading,” Chin. Phys. Lett 28, 053701 (2011).
[CrossRef]

X. L. Wang, T. J. Tao, B. Cheng, B. Wu, Y. F. Xu, Z. Y. Wang, and Q. Lin, “A digital phase lock loop for an external cavity diode laser,” Chin. Phys. Lett 28, 084214 (2011).
[CrossRef]

Eur. Phys. J. D

A. Bertoldi, G. Lamporesi, L. Cacciapuoti, M. de Angelis, M. Fattori, T. Petelski, A. Peters, M. Prevedelli, J. Stuhler, and G. M. Tino, “Atom interferometry gravity-gradiometer for the determination of the Newtonian gravitational constant G,” Eur. Phys. J. D 40, 271–279 (2006).
[CrossRef]

IEEE Trans. Ultrason. Ferroelectr. Freq. Control

J. Guena, M. Abgrall, D. Rovera, P. Laurent, B. Chupin, M. Lours, G. Santarelli, P. Rosenbusch, M. E. Tobar, L. Ruoxin, K. Gibble, A. Clairon, and S. Bize, “Progress in atomic fountains at LNE-SYRTE,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 59, 391–409 (2012).
[CrossRef]

J. Opt. Soc. Am. B

Metrologia

A. Peters, K. Y. Chung, and S. Chu, “High-precision gravity measurements using atom interferometry,” Metrologia 38, 25–61 (2001).
[CrossRef]

Y. Ovchinnikov and G. Marra, “Accurate rubidium atomic fountain frequency standard,” Metrologia 48, 87–100 (2011).
[CrossRef]

S. Weyers, V. Gerginov, N. Nemitz, R. Li, and K. Gibble, “Distributed cavity phase frequency shifts of the caesium fountain PTB-CSF2,” Metrologia 49, 82–87 (2012).
[CrossRef]

Opt. Commun.

R. B. Li, L. Zhou, J. Wang, and M. S. Zhan, “Measurement of the quadratic Zeeman shift of 85Rb hyperfine sublevels using stimulated Raman transitions,” Opt. Commun. 282, 1340–1344 (2009).
[CrossRef]

Phys. Rev.

G. Breit and I. I. Rabi, “Measurement of nuclear spin,” Phys. Rev. 38, 2082–2083 (1931).
[CrossRef]

C. W. White, W. M. Hughes, G. S. Hayne, and H. G. Robinson, “Determination of g-factor ratios for free Rb85 and Rb87 atoms,” Phys. Rev. 174, 23–32 (1968).
[CrossRef]

Phys. Rev. A

I. Chan, B. Barrett, and A. Kumarakrishnan, “Precise determination of atomic g-factor ratios from a dual isotope magneto-optical trap,” Phys. Rev. A 84, 032509 (2011).
[CrossRef]

A. Gauguet, B. Canuel, T. Lévèque, W. Chaibi, and A. Landragin, “Characterization and limits of a cold-atom Sagnac interferometer,” Phys. Rev. A 80, 063604 (2009).
[CrossRef]

Z. K. Hu, X. C. Duan, M. K. Zhou, B. L. Sun, J. B. Zhao, M. M. Huang, and J. Luo, “Simultaneous differential measurement of a magnetic-field gradient by atom interferometry using double fountains,” Phys. Rev. A 84, 013620 (2011).
[CrossRef]

M. K. Zhou, Z. K. Hu, X. C. Duan, B. L. Sun, J. B. Zhao, and J. Luo, “Precisely mapping the magnetic field gradient in vacuum with an atom interferometer,” Phys. Rev. A 82, 061602 (2010).
[CrossRef]

J. M. McGuirk, G. T. Foster, J. B. Fixler, M. J. Snadden, and M. A. Kasevich, “Sensitive absolute-gravity gradiometry using atom interferometry,” Phys. Rev. A 65, 033608 (2002).
[CrossRef]

K. Numazaki, H. Imai, and A. Morinaga, “Measurement of the second-order Zeeman effect on the sodium clock transition in the weak-magnetic-field region using the scalar Aharonov–Bohm phase,” Phys. Rev. A 81, 032124 (2010).
[CrossRef]

K. Moler, D. S. Weiss, M. Kasevich, and C. Steven, “Theoretical analysis of velocity-selective Raman transitions,” Phys. Rev. A 45, 342–348 (1992).
[CrossRef]

Phys. Rev. Lett.

H. Müller, S. W. Chiow, Q. Long, S. Herrmann, and S. Chu, “Atom interferometry with up to 24-photon-momentum-transfer beam splitters,” Phys. Rev. Lett. 100, 180405 (2008).
[CrossRef]

J. M. McGuirk, M. J. Snadden, and M. A. Kasevich, “Large area light-pulse atom interferometry,” Phys. Rev. Lett. 85, 4498–4501 (2000).
[CrossRef]

B. Canuel, F. Leduc, D. Holleville, A. Gauguet, J. Fils, A. Virdis, A. Clairon, N. Dimarcq, C. J. Borde, and A. Landragin, “Six-axis inertial sensor using cold-atom interferometry,” Phys. Rev. Lett. 97, 010402 (2006).
[CrossRef]

Other

L. Marmet and M. Gertsvolf, “Evaluation of NRC-FCs1: mapping the C-field using the Larmor frequency,” in Proceedings of the 2010 IEEE International Frequency Control Symposium (IEEE, 2010), pp. 312–317.

D. A. Steck, “Alkali D line data,” Rubidium 87 D Line Data, 2010, http://steck.us/alkalidata .

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Figures (7)

Fig. 1.
Fig. 1.

Experimental apparatus.

Fig. 2.
Fig. 2.

Zeeman splitting as a function of the field’s detuning. The applied magnetic field is about 73 μT for both the microwave and Raman spectrum measurements. The clock transition frequency of the Rb87 ground state corresponds to the point where the detuning is 0.

Fig. 3.
Fig. 3.

Homogeneity of the magnetic field around the interrogation region. The applied current of the bias field is 2 A. The duration of the microwave pulse is 1.2 ms.

Fig. 4.
Fig. 4.

Histogram of the measured magnetic field. The applied magnetic field is about 17.9 μT, and the number of counts is 662.

Fig. 5.
Fig. 5.

Resonant spectra of the ground-state clock transition of Rb87 obtained by scanning the detuning of the microwave and Raman pulse.

Fig. 6.
Fig. 6.

Quadratic Zeeman frequency shift versus the magnetic field strength. The experimental data are plotted as dots and the polynomial fit is shown as solid curves. (a) RS and (b) MWS.

Fig. 7.
Fig. 7.

Statistical distribution of the central frequency of the clock transitions. The applied magnetic field is about 17.9 μT, and the number of counts is 190. The measurement was performed by MWS.

Tables (1)

Tables Icon

Table 1. Summary of the Experimental Results

Equations (2)

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

Δω=(gJgI)2μB2B2/(2hΔEHfs)κB2,
Pb(τ)=Ωeff2Ωeff2+(ωωabδAC)2×sin2(Ωeff2+(ωωabδAC)2τ/2),

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