Abstract

We consider the velocity-dependent light pressure force on a two-level atom interacting with a two-dimensional nearly resonant standing-wave light field. We show that there can be anisotropic cooling–heating forces that will cool the atoms along one field axis while heating them along the perpendicular axis. The force is identified as a spontaneous vortex force associated with the local traveling-wave character of the two-dimensional field. We provide a simple interpretation of this anomalous force in terms of the interplay between the vortical momentum flow of the light field and a motion-induced population transfer between the ground and excited atomic states.

© 1994 Optical Society of America

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  1. A. P. Kazantsev, I. V. Krasnov, J. Opt. Soc. Am. B 6, 2140 (1989).
    [CrossRef]
  2. A. Hemmerich, T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992); A. Hemmerich, D. Schropp, T. W. Hänsch, Phys. Rev. A 44, 1910 (1991).
    [CrossRef] [PubMed]
  3. V. E. Shapiro, J. Phys. B 23, 2445S (1990).
    [CrossRef]
  4. K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
    [CrossRef]
  5. J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
    [CrossRef]
  6. V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
    [CrossRef]
  7. J. Dalibard, C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
    [CrossRef]
  8. We have completely neglected the effects of diffusion in this theory. We have carried out Monte Carlo studies that indicate that the effects described here will be important even in the presence of the diffusive heating associated with spontaneous emission.
  9. P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
    [CrossRef]

1992

A. Hemmerich, T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992); A. Hemmerich, D. Schropp, T. W. Hänsch, Phys. Rev. A 44, 1910 (1991).
[CrossRef] [PubMed]

1991

K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
[CrossRef]

1990

V. E. Shapiro, J. Phys. B 23, 2445S (1990).
[CrossRef]

1989

1985

1980

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

1979

V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
[CrossRef]

Ashkin, A.

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

Berg-Sorensen, K.

K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
[CrossRef]

Bonderup, E.

K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
[CrossRef]

Cohen-Tannoudji, C.

Dalibard, J.

Gordon, J. P.

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

Hänsch, T. W.

A. Hemmerich, T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992); A. Hemmerich, D. Schropp, T. W. Hänsch, Phys. Rev. A 44, 1910 (1991).
[CrossRef] [PubMed]

Hemmerich, A.

A. Hemmerich, T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992); A. Hemmerich, D. Schropp, T. W. Hänsch, Phys. Rev. A 44, 1910 (1991).
[CrossRef] [PubMed]

Kazantsev, A. P.

Krasnov, I. V.

Lett, P.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

Minogin, V. G.

V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
[CrossRef]

Mølmer, K.

K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
[CrossRef]

Phillips, W. D.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

Rolston, S. L.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

Serimaa, O. T.

V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
[CrossRef]

Shapiro, V. E.

V. E. Shapiro, J. Phys. B 23, 2445S (1990).
[CrossRef]

Tanner, C. E.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

Watts, R. N.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

Westbrook, C. I.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. B

V. E. Shapiro, J. Phys. B 23, 2445S (1990).
[CrossRef]

K. Mølmer, K. Berg-Sorensen, E. Bonderup, J. Phys. B 24, 2327 (1991).
[CrossRef]

Opt. Commun.

V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
[CrossRef]

Phys. Rev. A

J. P. Gordon, A. Ashkin, Phys. Rev. A 21, 1606 (1980).
[CrossRef]

Phys. Rev. Lett.

A. Hemmerich, T. W. Hänsch, Phys. Rev. Lett. 68, 1492 (1992); A. Hemmerich, D. Schropp, T. W. Hänsch, Phys. Rev. A 44, 1910 (1991).
[CrossRef] [PubMed]

Other

We have completely neglected the effects of diffusion in this theory. We have carried out Monte Carlo studies that indicate that the effects described here will be important even in the presence of the diffusive heating associated with spontaneous emission.

P. Lett, W. D. Phillips, S. L. Rolston, C. E. Tanner, R. N. Watts, C. I. Westbrook[J. Opt. Soc. Am. B6, 2084 (1989)]Y. Castin, J. Dalibard, C. Cohen-Tannoudji[inLight Induced Kinetic Effects on Atoms, Ions and Molecules , L. Moi, S. Gozzini, C. Gabbanini, E. Arimondo, F. Sturmia, eds. (ETS Editrice, Pisa (1991)]A. M. Steane, C. J. Foot, Europhys. Lett. 14, 231 (1991)
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

(a) Steady-state population difference ρggρee, (b) vector momentum flux field W(r) in the 2-d laser field. Here g1 = g2 = 0.2β, Δ = 0, and ϕ = π/4. The x and y coordinates are in units of λopt/2.

Fig. 2
Fig. 2

Friction coefficient α versus detuning Δ. Solid curves, αi; dashed curves, αa. (a) g1 = g2 = 0.3β, ϕ = π/4; (b) g1 = g2 = 2β, ϕ = π/4. Δ is in units of β, and α is in units of ħk2.

Fig. 3
Fig. 3

Comparison of anisotropic force calculated from an analytic solution and Floquet numerical solutions. Solid curves, [Fa] versus v; dashed curves, [Fa]ŷ versus vŷ. The straight dashed lines are corresponding results of the low-velocity analytic solution. (a) g1 = g2 = 0.3β, ϕ = π/4; (b) g1 = g2 = 2β, ϕ = π/4. Here v is in units of β/k, and F is in units of ħkβ.

Equations (4)

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F sp = 1 2 k β ( β 2 + Δ 2 ) Π g 1 g 2 sin ϕ [ - cos ( k x ) sin ( k y ) x ^ + sin ( k x ) cos ( k y ) y ^ ] ,
α i = 1 2 β Δ ( β 2 + Δ 2 ) 2 g 0 2 [ - 1 + 3 8 g 0 2 β 2 + Δ 2 + 1 4 ( 2 + cos 2 ϕ ) g 0 2 β 2 + Δ 2 ] ,
α a = 1 8 β 2 g 0 4 ( β 2 + Δ 2 ) 3 sin 2 ϕ .
- R st ( r ) [ 1 - 1 2 g 0 2 β 2 ( sin 2 k x + sin 2 k y ) - g 0 2 β 2 cos ϕ sin k x sin k y ] .

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