Abstract

We have observed momentum transfer from a standing-wave light field to an atomic beam. The atomic beam is split symmetrically into two peaks whose separation increases with field strength. The short interaction time ensures that this deflection is due to induced forces; these are described using a semiclassical dressed-atom treatment, which gives good agreement with the data. In addition to the splitting, we have observed diffraction of the atomic beam due to the exchange of even numbers of photons with the field.

© 1985 Optical Society of America

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  1. A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
    [CrossRef]
  2. A. P. Kazantsev, Sov. Phys. Usp. 21, 58 (1978).
    [CrossRef]
  3. R. J. Cook, Phys. Rev. A 22, 1078 (1980).
    [CrossRef]
  4. C. Cohen-Tannoudji, in Cargese Lectures in Physics 2, M. Levy, ed. (Gordon and Breach, New York, 1968), p. 347.
  5. P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
    [CrossRef]
  6. E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
    [CrossRef]
  7. V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
  8. V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).
  9. J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
    [CrossRef]
  10. P. L. Knight, P. W. Milonni, Phys. Rep. 66, 21 (1980).
    [CrossRef]
  11. C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10, 345 (1977).
    [CrossRef]
  12. A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).
  13. R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
    [CrossRef]
  14. A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
    [CrossRef]
  15. A. P. Kazantsev, A. P. Surdutovich, JETP Lett. 21, 158 (1975).
  16. A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
    [CrossRef]
  17. C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
    [CrossRef]
  18. P. E. Moskowitz, “Diffraction of an atomic beam by standing wave radiation,” thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1984) (unpublished).
  19. D. Steel, R. A. McFarlane, Opt. Lett. 8, 33 (1983).
    [CrossRef] [PubMed]
  20. N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1956).
  21. L. Mandel, J. Opt. (Paris) 10, 51 (1979).
    [CrossRef]
  22. A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
    [CrossRef]

1985 (1)

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

1984 (2)

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
[CrossRef]

1983 (2)

D. Steel, R. A. McFarlane, Opt. Lett. 8, 33 (1983).
[CrossRef] [PubMed]

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

1982 (1)

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
[CrossRef]

1981 (2)

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
[CrossRef]

1980 (3)

R. J. Cook, Phys. Rev. A 22, 1078 (1980).
[CrossRef]

P. L. Knight, P. W. Milonni, Phys. Rep. 66, 21 (1980).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).

1979 (2)

L. Mandel, J. Opt. (Paris) 10, 51 (1979).
[CrossRef]

E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

1978 (3)

A. P. Kazantsev, Sov. Phys. Usp. 21, 58 (1978).
[CrossRef]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

1977 (1)

C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10, 345 (1977).
[CrossRef]

1975 (1)

A. P. Kazantsev, A. P. Surdutovich, JETP Lett. 21, 158 (1975).

1970 (1)

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

Arimondo, E.

E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Ashkin, A.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

Atlas, S. R.

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Bernhardt, A. F.

A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
[CrossRef]

R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

Bjorkholm, J. E.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

Chudesnikov, D. O.

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

Cohen-Tannoudji, C.

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
[CrossRef]

C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10, 345 (1977).
[CrossRef]

C. Cohen-Tannoudji, in Cargese Lectures in Physics 2, M. Levy, ed. (Gordon and Breach, New York, 1968), p. 347.

Cook, R. J.

R. J. Cook, Phys. Rev. A 22, 1078 (1980).
[CrossRef]

R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

Freeman, R. R.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

Gould, P. L.

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Grinchuk, V. A.

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

Kazantsev, A. P.

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
[CrossRef]

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).

A. P. Kazantsev, Sov. Phys. Usp. 21, 58 (1978).
[CrossRef]

A. P. Kazantsev, A. P. Surdutovich, JETP Lett. 21, 158 (1975).

Knight, P. L.

P. L. Knight, P. W. Milonni, Phys. Rep. 66, 21 (1980).
[CrossRef]

Kuzin, E. F.

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

Lew, H.

E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Mandel, L.

L. Mandel, J. Opt. (Paris) 10, 51 (1979).
[CrossRef]

McFarlane, R. A.

Milonni, P. W.

P. L. Knight, P. W. Milonni, Phys. Rep. 66, 21 (1980).
[CrossRef]

Moskowitz, P. E.

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

P. E. Moskowitz, “Diffraction of an atomic beam by standing wave radiation,” thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1984) (unpublished).

Nagaeva, M. L.

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

Oka, T.

E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

Pearson, D. B.

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

Pritchard, D. E.

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

Ramsey, N. F.

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1956).

Reynaud, S.

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
[CrossRef]

C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10, 345 (1977).
[CrossRef]

Ryabenko, G. A.

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

Shore, B. W.

A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
[CrossRef]

Steel, D.

Surdutovich, A. P.

A. P. Kazantsev, A. P. Surdutovich, JETP Lett. 21, 158 (1975).

Surdutovich, G. I.

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
[CrossRef]

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).

Tanguy, C.

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
[CrossRef]

Yakovlev, V. P.

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
[CrossRef]

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).

J. Opt. (Paris) (1)

L. Mandel, J. Opt. (Paris) 10, 51 (1979).
[CrossRef]

J. Phys. B (2)

C. Cohen-Tannoudji, S. Reynaud, J. Phys. B 10, 345 (1977).
[CrossRef]

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4632 (1984).
[CrossRef]

JETP Lett. (2)

A. P. Kazantsev, A. P. Surdutovich, JETP Lett. 21, 158 (1975).

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).

Opt. Commun. (2)

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, D. O. Chudesnikov, Opt. Commun. 52, 311 (1985).
[CrossRef]

A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Opt. Commun. 43, 180 (1982).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. (1)

V. A. Grinchuk, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).

Phys. Rep. (1)

P. L. Knight, P. W. Milonni, Phys. Rep. 66, 21 (1980).
[CrossRef]

Phys. Rev. A (3)

R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
[CrossRef]

A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
[CrossRef]

R. J. Cook, Phys. Rev. A 22, 1078 (1980).
[CrossRef]

Phys. Rev. Lett. (4)

A. Ashkin, Phys. Rev. Lett. 25, 1321 (1970).
[CrossRef]

P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
[CrossRef]

E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
[CrossRef]

J. E. Bjorkholm, R. R. Freeman, A. Ashkin, D. B. Pearson, Phys. Rev. Lett. 41, 1361 (1978).
[CrossRef]

Sov. Phys. JETP (1)

V. A. Grinchuk, A. P. Kazantsev, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, G. I. Surdutovich, V. P. Yakovlev, Sov. Phys. JETP 59, 56 (1984).

Sov. Phys. Usp. (1)

A. P. Kazantsev, Sov. Phys. Usp. 21, 58 (1978).
[CrossRef]

Other (3)

C. Cohen-Tannoudji, in Cargese Lectures in Physics 2, M. Levy, ed. (Gordon and Breach, New York, 1968), p. 347.

P. E. Moskowitz, “Diffraction of an atomic beam by standing wave radiation,” thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1984) (unpublished).

N. F. Ramsey, Molecular Beams (Oxford U. Press, London, 1956).

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Figures (6)

Fig. 1
Fig. 1

Transition from the atomic basis (|g>, |e>) to the dressed basis (|w>, |s>). The case shown is for Δ <0.

Fig. 2
Fig. 2

The differential cross section dσ/dp is plotted as a function of p for the case Δ = 0. Note the divergence at ±pm, the maximum (classically) allowed momentum transfer.

Fig. 3
Fig. 3

Experimental apparatus.

Fig. 4
Fig. 4

Atomic-beam profiles for the following laser powers: (A) 0, (B) 5, (C) 10, and (D) 20 mW. Vertical bars under the data are the result of the numerical convolution described in the text (Subsection 4.B).

Fig. 5
Fig. 5

Rms momentum transferred versus square root of laser power. The three data points correspond to scans (B), (C), and (D) of Fig. 4. The lower curve is the result of the classical calculation (accounting for all allowed hyperfine transitions) described in the text (Subsection 4.A.1). The upper curve (straight line) obtains for the case of exact resonance with a two-state system.

Fig. 6
Fig. 6

Rms momentum transferred versus laser detuning. The laser power is fixed at 7.2 mW (in each traveling wave) for all points. The solid curve is the result of the model described in Subsection 4.A.1. The parameters of the fit are described in Subsection 4.A.2.

Equations (19)

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

H = H atom - μ · E .
ω R ± 2 = ± 2 ( Ω R 2 cos 2 k z + Δ 2 ) 1 / 2 ,
E = 2 ^ E 0 cos k z cos ω t ,
Ω R = 2 E 0 ( μ · ^ ) ,
Δ = ω - ω 0 ,
F w , s = - ω R ± ( z ) 2 ,
p ( z ) = p ( z ) z ^ = F ( z ) T .
Γ 0 d z = Γ 0 d σ d p d p .
d σ d p = 1 k p 0 { ( 1 - ζ 2 ) 2 + [ ( 1 - ζ 2 ) 2 4 - δ 2 ζ 2 ] 1 / 2 + δ 2 } 1 / 2 [ ( 1 - ζ 2 ) 2 - 4 δ 2 ζ 2 ] 1 / 2 ,
ζ = p / p 0 , δ = Δ / Ω R , p 0 = Ω R k 2 T .
p m = k 2 [ ( Ω R 2 + Δ 2 ) 1 / 2 - Δ ]
p 2 = p m 2 2 .
d σ d p = 1 k p 0 × 1 ( 1 - ζ 2 ) 1 / 2
p 2 = p 0 2 2 .
ψ ( z , t ) = a s exp + i ω R - t / 2 S + a w exp + i ω R + t / 2 W ,
P ( p , T ) = P n ( T ) = J n 2 ( Ω R T 2 ) ,
n = p / k .
E ˙ E Δ
P n ( T ) = J n / 2 2 ( Ω R 2 T 8 Δ )

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