Abstract

We show that the characteristic Rabi frequency and nonlinear susceptibility of atoms in a dilute Bose gas remain unchanged by the process of condensation. We neglect the effects of atomic dipole –dipole interactions and spontaneous emission.

© 1996 Optical Society of America

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References

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  1. M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
    [CrossRef] [PubMed]
  2. C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
    [CrossRef] [PubMed]
  3. T. Hiroshima, Y. Yamamoto, “Nonlinear optical response of cold atoms,”submitted toPhys. Rev. A.
  4. L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
    [CrossRef] [PubMed]
  5. O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
    [CrossRef] [PubMed]
  6. H. Politzer, Phys. Rev. A 43, 6444 (1991).
    [CrossRef] [PubMed]
  7. J. Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
    [CrossRef] [PubMed]
  8. L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
    [CrossRef] [PubMed]
  9. Analytic solutions to Eq. (3) appear in F. Hioe, J. Opt. Soc. Am. B 4, 1327 (1987).
    [CrossRef]

1995 (4)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
[CrossRef] [PubMed]

O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
[CrossRef] [PubMed]

1994 (2)

J. Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
[CrossRef] [PubMed]

1991 (1)

H. Politzer, Phys. Rev. A 43, 6444 (1991).
[CrossRef] [PubMed]

1987 (1)

Anderson, M. H.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Bradley, C. C.

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

Castin, Y.

O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
[CrossRef] [PubMed]

Cooper, J.

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
[CrossRef] [PubMed]

Cornell, E. A.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Dalibard, J.

O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
[CrossRef] [PubMed]

Ensher, J. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Hioe, F.

Hiroshima, T.

T. Hiroshima, Y. Yamamoto, “Nonlinear optical response of cold atoms,”submitted toPhys. Rev. A.

Hulet, R. G.

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

Javanainen, J.

J. Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
[CrossRef] [PubMed]

Lewenstein, M.

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
[CrossRef] [PubMed]

Matthews, M. R.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Morice, O.

O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
[CrossRef] [PubMed]

Politzer, H.

H. Politzer, Phys. Rev. A 43, 6444 (1991).
[CrossRef] [PubMed]

Sackett, C. A.

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

Tollett, J. J.

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

Wieman, C. E.

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Yamamoto, Y.

T. Hiroshima, Y. Yamamoto, “Nonlinear optical response of cold atoms,”submitted toPhys. Rev. A.

You, L.

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
[CrossRef] [PubMed]

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

Phys. Rev. A (4)

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 51, 4712 (1995).
[CrossRef] [PubMed]

O. Morice, Y. Castin, J. Dalibard, Phys. Rev. A 51, 3896 (1995).
[CrossRef] [PubMed]

H. Politzer, Phys. Rev. A 43, 6444 (1991).
[CrossRef] [PubMed]

L. You, M. Lewenstein, J. Cooper, Phys. Rev. A 50, R3565 (1994).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

C. C. Bradley, C. A. Sackett, J. J. Tollett, R. G. Hulet, Phys. Rev. Lett. 75, 1687 (1995).
[CrossRef] [PubMed]

J. Javanainen, Phys. Rev. Lett. 72, 2375 (1994).
[CrossRef] [PubMed]

Science (1)

M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, E. A. Cornell, Science 269, 198 (1995).
[CrossRef] [PubMed]

Other (1)

T. Hiroshima, Y. Yamamoto, “Nonlinear optical response of cold atoms,”submitted toPhys. Rev. A.

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Figures (3)

Fig. 1
Fig. 1

(a) For a total of N atoms, in the basis of bare, independent atoms there are 2N possible basis states; (b) in the symmetrized Bose basis there are (N + 1) states. The qth state is that where q atoms are excited.

Fig. 2
Fig. 2

Numerical integration of the coupled equations [Eq. (3)] for N = 100 atoms: (a) population in state |0〉, (b) mean number of excited atoms 〈q〉.

Fig. 3
Fig. 3

Perturbation paths for calculation of χ(3): (a) path a, (b) path b.

Equations (8)

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H 0 q = q ( ω 0 + 2 k 2 2 m ) q ,
q V q + 1 = - Ω 2 ( q + 1 ) 1 / 2 ( N - q ) 1 / 2 exp ( j ω t ) + c . c . ,
a q t + i q Δ ω a q = j Ω * 2 ξ q - 1 a q - 1 + j Ω 2 ξ q a q + 1 ( 0 q N ) ,
P ( R ) = e i r i δ ( R - R i ) .
q P ( R ) q + 1 = ξ q V μ a b exp ( j k · R ) ,
ψ ( t ) P ( R ) ψ ( t ) = 1 V μ a b exp [ j ( ω t - k · R ) ] × q = 0 N - 1 ξ q a q a q + 1 * + c . c.
P ( 3 ) ( R ) = - 1 V μ a b Ω 2 Ω 4 Δ ω 3 exp [ j ( ω t - k · R ) ] × ( ξ 0 4 - ξ 0 2 ξ 1 2 / 2 ) + c . c .
- N V μ a b Ω 2 Ω 4 Δ ω 3 exp [ j ( ω t - k · R ) ] + c . c .

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