Abstract

We demonstrate a new type of high-resolution two-photon frequency modulation (FM) spectroscopy with cold atoms in a magneto-optical trap. Instead of modulating the probe as in ordinary FM spectroscopy, we modulate the trap itself by FM of the trapping beams. We present theoretical as well as experimental results for both absorption and polarization rotation spectroscopy. Finally, we demonstrate two-photon FM spectroscopy, using the intrinsic phase noise of the trapping diode lasers.

© 1998 Optical Society of America

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  1. E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
    [CrossRef] [PubMed]
  2. C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
    [CrossRef] [PubMed]
  3. R. W. Fox, S. L. Gilbert, L. Hollberg, J. H. Marquardt, and H. G. Robinson, Opt. Lett. 18, 1456 (1993).
    [CrossRef] [PubMed]
  4. T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
    [CrossRef]
  5. N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, Opt. Lett. 19, 1474 (1994).
    [CrossRef] [PubMed]
  6. N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
    [CrossRef] [PubMed]
  7. G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
    [CrossRef]
  8. T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
    [CrossRef] [PubMed]
  9. R. G. Devoe and R. Brewer, Phys. Rev. A 26, 705 (1982).
    [CrossRef]
  10. S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).
  11. E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
    [CrossRef]
  12. E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
    [CrossRef] [PubMed]

1997 (1)

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

1996 (1)

C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
[CrossRef] [PubMed]

1995 (1)

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

1992 (1)

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

1991 (1)

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
[CrossRef] [PubMed]

1987 (1)

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

1984 (1)

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

1983 (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

1982 (1)

R. G. Devoe and R. Brewer, Phys. Rev. A 26, 705 (1982).
[CrossRef]

Avila, G.

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

Bjorklund, G. C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Brewer, R.

R. G. Devoe and R. Brewer, Phys. Rev. A 26, 705 (1982).
[CrossRef]

Cable, A.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

Carri, J.

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Cerez, P.

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

Chu, S.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

de Clerq, E.

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

de Labachellerie, M.

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

Devoe, R. G.

R. G. Devoe and R. Brewer, Phys. Rev. A 26, 705 (1982).
[CrossRef]

Edamatsu, E. S.

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

Fox, R. W.

Georgiades, N. Ph.

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef] [PubMed]

Gilbert, S. L.

Grangier, P.

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

Grelu, P.

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

Hall, J. L.

C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
[CrossRef] [PubMed]

Hollberg, L.

Kimble, H. J.

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Lenth, W.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Levenson, M. D.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Marquardt, J. H.

Mitsui, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
[CrossRef] [PubMed]

Oates, C. W.

C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
[CrossRef] [PubMed]

Ortiz, C.

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

Parkins, A. S.

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

Polzik, E. S.

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

N. Ph. Georgiades, E. S. Polzik, and H. J. Kimble, Opt. Lett. 19, 1474 (1994).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Prentiss, M.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

Pritchard, D. E.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

Raab, E. L.

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

Robinson, H. G.

Roch, J.

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

Stenholm, S.

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

Tanaka, U.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
[CrossRef] [PubMed]

Tetu, M.

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

van der Veldt, T.

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

Vogel, K. R.

C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
[CrossRef] [PubMed]

Yabuzaki, T.

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
[CrossRef] [PubMed]

Appl. Phys. B (1)

G. C. Bjorklund, M. D. Levenson, W. Lenth, and C. Ortiz, Appl. Phys. B 32, 145 (1983).
[CrossRef]

J. Phys. (Paris) (1)

E. de Clerq, M. de Labachellerie, G. Avila, P. Cerez, and M. Tetu, J. Phys. (Paris) 45, 239 (1984).
[CrossRef]

Opt. Commun. (1)

T. van der Veldt, J. Roch, P. Grelu, and P. Grangier, Opt. Commun. 137, 420 (1997).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

R. G. Devoe and R. Brewer, Phys. Rev. A 26, 705 (1982).
[CrossRef]

Phys. Rev. Lett. (5)

T. Yabuzaki, T. Mitsui, and U. Tanaka, Phys. Rev. Lett. 67, 2453 (1991); D. H. McIntyre, C. E. Fairchild, J. Cooper, and R. Walser, Opt. Lett. 18, 1816 (1993).
[CrossRef] [PubMed]

N. Ph. Georgiades, E. S. Polzik, E. S. Edamatsu, H. J. Kimble, and A. S. Parkins, Phys. Rev. Lett. 75, 3426 (1995).
[CrossRef] [PubMed]

E. L. Raab, M. Prentiss, A. Cable, S. Chu, and D. E. Pritchard, Phys. Rev. Lett. 59, 2631 (1987); K. E. Gibble, S. Kasapi, and S. Chu, Opt. Lett. 17, 526 (1992).
[CrossRef] [PubMed]

C. W. Oates, K. R. Vogel, and J. L. Hall, Phys. Rev. Lett. 76, 2866 (1996).
[CrossRef] [PubMed]

E. S. Polzik, J. Carri, and H. J. Kimble, Phys. Rev. Lett. 68, 3020 (1992).
[CrossRef] [PubMed]

Other (1)

S. Stenholm, Foundations of Laser Spectroscopy (Wiley, New York, 1984).

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Figures (3)

Fig. 1
Fig. 1

Setup used for modulation spectroscopy of trapped atoms. The current i+ contains the absorption signal, and i- contains the polarization rotation signal. Inset, the relevant energy levels of the Cs atoms.

Fig. 2
Fig. 2

Comparison of (a) the experimentally obtained FM absorption signals, (b) the three-level theory, and (c) the full theory. The coherent signals from F=4F=5F=6 and F=455 are centered at -18 and -46 MHz, respectively. The incoherent signal from 456 is located at 10  MHz, whereas the incoherent signal from 455 is superimposed upon the coherent 456 signal. SA settings for the experiment: resolution bandwidth, 100  kHz; video bandwidth, 100  Hz; sweep time, 500  ms across the trace.

Fig. 3
Fig. 3

(a) Experimentally observed FM polarization rotation signal. The experimental parameters as well as SA settings are the same as in Fig.  2. (b) FM absorption signal obtained from the phase noise of the trapping laser at 3  MHz. SA settings: resolution bandwidth, 100  kHz; video bandwidth, 300  Hz; sweep time, 200  ms across the trace. The pump intensity is somewhat lower than in Fig.  2, giving a smaller ac Stark splitting.

Equations (1)

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χχr+iχiα28α2+γ22+4Δ12×iγ32-Δ2iγ32-Δ2iγ3/2-Δ2-Δ1-α2.

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