Abstract

We consider the effects of optical pumping on the conversion of laser-frequency modulation into intensity modulation by an atomic absorption line in a vapor of alkali atoms driven in a Λ-configuration. It is found that, due to optical pumping in combination with the excited-state hyperfine structure, the absorption line shape is distorted substantially as the Fourier frequency of the FM is changed. The most significant effect of the distortion is a shift of the apparent line center, which depends on how the frequency of the modulation compares with the optical pumping rate. This shift has implications for locking lasers to atomic transitions and also for FM–AM noise conversion in atomic vapors.

[Optical Society of America ]

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References

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  1. See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
    [PubMed]
  2. R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
    [PubMed]
  3. A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).
  4. R. Grimm and J. Mlynek, Phys. Rev. Lett. 63, 232 (1989).
    [PubMed]
  5. F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).
  6. W. Happer, Rev. Mod. Phys. 44, 169 (1972).
  7. R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).
  8. F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
    [PubMed]
  9. J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).
  10. J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).
  11. J. C. Camparo and J. G. Coffer, Phys. Rev. A 59, 728 (1999).
  12. G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
    [CrossRef]
  13. M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
    [CrossRef]
  14. D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
    [CrossRef] [PubMed]

2001

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

2000

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

1999

J. C. Camparo and J. G. Coffer, Phys. Rev. A 59, 728 (1999).

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

1998

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

1993

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

1989

R. Grimm and J. Mlynek, Phys. Rev. Lett. 63, 232 (1989).
[PubMed]

1986

A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).

1981

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

1972

W. Happer, Rev. Mod. Phys. 44, 169 (1972).

Abgrall, M.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Affolderbach, C.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

Agarwal, G. S.

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

Allegrini, M.

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

Ananthalakshmi, P.

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

Arimondo, E.

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

Artoni, M.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Beall, J. A.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Bergquist, J. C.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Camparo, J. C.

J. C. Camparo and J. G. Coffer, Phys. Rev. A 59, 728 (1999).

Cancio, P.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Carusotto, I.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Clairon, A.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Coffer, J. G.

J. C. Camparo and J. G. Coffer, Phys. Rev. A 59, 728 (1999).

de Tomasi, F.

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

Deng, J.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

Drullinger, R. E.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

Fleishhauer, A.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Giusfredi, G.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Grimm, R.

R. Grimm and J. Mlynek, Phys. Rev. Lett. 63, 232 (1989).
[PubMed]

Hänsch, T. W.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Happer, W.

W. Happer, Rev. Mod. Phys. 44, 169 (1972).

Hollberg, L.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

Holzwarth, R.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Ingusio, M.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Itano, W. M.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Jennings, D. A.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

Kazantsev, A. P.

A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).

Kemp, W.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

Kitching, J.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

Knapp, S.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

Knappe, S.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

Laurent, P.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Lemonde, P.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Lukin, M. D.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Mair, A.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Mileti, G.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

Minardi, F.

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Mlynek, J.

R. Grimm and J. Mlynek, Phys. Rev. Lett. 63, 232 (1989).
[PubMed]

Niering, M.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Phillips, D. F.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Phillips, W.

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

Pokasov, P.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Pritchard, D. E.

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

Rafac, R. J.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Reichert, J.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Robinson, H. G.

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

Salomon, C.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Santarelli, G.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Silfiedel, A.

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

Stahler, M.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

Sudutovich, G. I.

A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).

Udem, T.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Vukucevic, N.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

Walkup, R.

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

Walls, F. L.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

Walsworth, R. L.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

Weidemann, W.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

Weitz, M.

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

Wineland, D. J.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Wynands, R.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

Yakovlev, V. P.

A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).

Young, B. C.

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Europhys. Lett.

M. Stahler, S. Knappe, C. Affolderbach, W. Kemp, and R. Wynands, Europhys. Lett. 54, 323 (2001).
[CrossRef]

IEEE J. Quantum Electron.

G. Mileti, J. Deng, F. L. Walls, D. A. Jennings, and R. E. Drullinger, IEEE J. Quantum Electron. 34, 233 (1998).
[CrossRef]

IEEE Trans. Instrum. Meas.

J. Kitching, S. Knapp, N. Vukucevic, R. Wynands, L. Hollberg, and W. Weidemann IEEE Trans. Instrum. Meas. 49, 1313 (2000).

J. Opt. Soc. Am. B

J. Kitching, H. G. Robinson, L. Hollberg, S. Knapp, and R. Wynands, “Optical-pumping noise in laser-pumped, all-optical microwave frequency standards,” J. Opt. Soc. Am. B (to be published).

JETP Lett.

A. P. Kazantsev, G. I. Sudutovich, and V. P. Yakovlev, JETP Lett. 43, 180 (1986).

Phys. Rev. A

F. Minardi, M. Artoni, P. Cancio, M. Ingusio, G. Giusfredi, and I. Carusotto, Phys. Rev. A 60, 4164 (1999).

Phys. Rev. A

R. Walkup, A. Silfiedel, W. Phillips, and D. E. Pritchard, Phys. Rev. A 23, 1869 (1981).

F. de Tomasi, M. Allegrini, E. Arimondo, G. S. Agarwal, and P. Ananthalakshmi, Phys. Rev. A 48, 3820 (1993).
[PubMed]

J. C. Camparo and J. G. Coffer, Phys. Rev. A 59, 728 (1999).

Phys. Rev. Lett.

D. F. Phillips, A. Fleishhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, Phys. Rev. Lett. 86, 783 (2001).
[CrossRef] [PubMed]

R. Grimm and J. Mlynek, Phys. Rev. Lett. 63, 232 (1989).
[PubMed]

See, for example, M. Niering, R. Holzwarth, J. Reichert, P. Pokasov, T. Udem, M. Weitz, T. W. Hänsch, P. Lemonde, G. Santarelli, M. Abgrall, P. Laurent, C. Salomon, and A. Clairon, Phys. Rev. Lett. 84, 5496 (2000).
[PubMed]

R. J. Rafac, B. C. Young, J. A. Beall, W. M. Itano, D. J. Wineland, and J. C. Bergquist, Phys. Rev. Lett. 85, 2462 (2000).
[PubMed]

Rev. Mod. Phys.

W. Happer, Rev. Mod. Phys. 44, 169 (1972).

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Figures (3)

Fig. 1
Fig. 1

Optical setup laser tunings.

Fig. 2
Fig. 2

(A) dc absorption line and (B) lock-in output for FM at a frequency of 50  kHz as a function of optical detuning for an average optical intensity of 50 μW/cm2 per sideband.

Fig. 3
Fig. 3

Frequency difference between lock-in output zeros for modulation at a fixed frequency of 50  kHz and variable frequency f2. The average intensities in each of the two first-order sidebands were 170 μW/cm2 (circles), 47 μW/cm2 (triangles), and 15 μW/cm2 (squares). The solid curves are fits to Eq.  (1).

Equations (1)

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ωdifff=ωdiffmax1+f2/ϕcIopt2,

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