Abstract

We discuss two possible processes that may lead to unidirectional momentum transfer to atoms from a near-resonant standing-wave light field. The first is Bragg scattering of the matter waves from the tilted light grating—this process leaves the atoms unexcited. The second is a multiphoton (Doppleron) process in which the atom, by sequential absorption/emission of photons from/into the two traveling-wave components of the standing wave (which appear at different frequencies owingto the motion of the atom in the field), can complete the energy resonance condition for excitation to its excited state. Detailed consideration of the inteferring process of spontaneous emission and experimental factors such as the interplay among interaction length, angular collimation of the standing wave, and transit-time frequency broadening of the light frequency show that the two processes are both potentially observable but under considerably different experimental conditions.

© 1985 Optical Society of America

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References

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  1. A. Einstein, Phys. Z. 18, 121 (1917); translated in D. ter Haar, The Old Quantum Theory (Pergamon, New York, 1967), pp. 167–183.
  2. L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).
  3. L. Mandel, J. Opt. (Paris) 10, 51 (1979).
    [CrossRef]
  4. A. F. Bernhardt, B. W. Shore, Phys. Rev. A 23, 1290 (1981).
    [CrossRef]
  5. A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, JETP Lett. 31, 509 (1980).
  6. C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
    [CrossRef]
  7. J. Dalibard, C. Cohen-Tannoudji, J. Phys. B. 18, 1661 (1984).
    [CrossRef]
  8. P. E. Moskowitz, “Diffraction of an atomic beam by standing wave radiation,” thesis (Massachusetts Institute of Technology, Cambridge, Mass., 1984) (unpublished).
  9. V. A. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
    [CrossRef]
  10. 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).
  11. E. Arimondo, H. Lew, T. Oka, Phys. Rev. Lett. 43, 753 (1979).
    [CrossRef]
  12. P. E. Moskowitz, P. L. Gould, S. R. Atlas, D. E. Pritchard, Phys. Rev. Lett. 51, 370 (1983).
    [CrossRef]
  13. R. J. Cook, A. F. Bernhardt, Phys. Rev. A 18, 2533 (1978).
    [CrossRef]
  14. E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
    [CrossRef]
  15. C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
    [CrossRef]
  16. R. J. Cook, Phys. Rev. A 22, 1078 (1980).
    [CrossRef]
  17. P. L. Kapitza, P. A. M. Dirac, Proc. Camb. Philos. Soc. 29, 297 (1933).
    [CrossRef]
  18. J. Reid, T. Oka, Phys. Rev. Lett. 38, 67 (1977).
    [CrossRef]
  19. T. Oka, in Frontiers of Laser Spectroscopy, R. Balian, S. Harouche, S. Lieberman, eds. (North-Holland, New York, 1977), Vol. 2, p. 529.
  20. E. Kyrola, S. Stenholm, Opt. Commun. 22, 123 (1977).
    [CrossRef]
  21. V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
    [CrossRef]
  22. W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
    [CrossRef] [PubMed]

1985 (1)

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

1984 (3)

J. Dalibard, C. Cohen-Tannoudji, J. Phys. B. 18, 1661 (1984).
[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).

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

1983 (2)

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

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[CrossRef]

1981 (3)

E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
[CrossRef]

V. A. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

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

1980 (2)

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

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

1979 (3)

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

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

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

1978 (1)

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

1977 (2)

J. Reid, T. Oka, Phys. Rev. Lett. 38, 67 (1977).
[CrossRef]

E. Kyrola, S. Stenholm, Opt. Commun. 22, 123 (1977).
[CrossRef]

1933 (1)

P. L. Kapitza, P. A. M. Dirac, Proc. Camb. Philos. Soc. 29, 297 (1933).
[CrossRef]

1917 (1)

A. Einstein, Phys. Z. 18, 121 (1917); translated in D. ter Haar, The Old Quantum Theory (Pergamon, New York, 1967), pp. 167–183.

Allen, L.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Arimondo, E.

E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
[CrossRef]

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

Atlas, S. R.

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

Bambini, A.

E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
[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]

Blatt, R.

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

J. Dalibard, C. Cohen-Tannoudji, J. Phys. B. 18, 1661 (1984).
[CrossRef]

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[CrossRef]

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]

Dalibard, J.

J. Dalibard, C. Cohen-Tannoudji, J. Phys. B. 18, 1661 (1984).
[CrossRef]

Dirac, P. A. M.

P. L. Kapitza, P. A. M. Dirac, Proc. Camb. Philos. Soc. 29, 297 (1933).
[CrossRef]

Eberly, J. H.

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

Einstein, A.

A. Einstein, Phys. Z. 18, 121 (1917); translated in D. ter Haar, The Old Quantum Theory (Pergamon, New York, 1967), pp. 167–183.

Ertmer, W.

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

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).

GrinchukE, V. A.

V. A. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

Hall, J. L.

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

Kapitza, P. L.

P. L. Kapitza, P. A. M. Dirac, Proc. Camb. Philos. Soc. 29, 297 (1933).
[CrossRef]

Kazantsev, A. P.

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. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

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

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).

Kuzin, F.

V. A. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

Kyrola, E.

E. Kyrola, S. Stenholm, Opt. Commun. 22, 123 (1977).
[CrossRef]

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]

Matsuoka, M.

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[CrossRef]

Minogin, V. G.

V. G. Minogin, O. T. Serimaa, Opt. Commun. 30, 373 (1979).
[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. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

Oka, T.

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

J. Reid, T. Oka, Phys. Rev. Lett. 38, 67 (1977).
[CrossRef]

T. Oka, in Frontiers of Laser Spectroscopy, R. Balian, S. Harouche, S. Lieberman, eds. (North-Holland, New York, 1977), Vol. 2, p. 529.

Pritchard, D. E.

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

Reid, J.

J. Reid, T. Oka, Phys. Rev. Lett. 38, 67 (1977).
[CrossRef]

Reynaud, S.

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[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. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

Serimaa, O. T.

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

Shore, B. W.

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

Stenholm, S.

E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
[CrossRef]

E. Kyrola, S. Stenholm, Opt. Commun. 22, 123 (1977).
[CrossRef]

Surdutovich, G. I.

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. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

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, 4623 (1984).
[CrossRef]

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[CrossRef]

Yakovlev, V. P.

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. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

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

Zhu, M.

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

J. Opt. (Paris) (1)

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

J. Phys. B (1)

C. Tanguy, S. Reynaud, C. Cohen-Tannoudji, J. Phys. B 17, 4623 (1984).
[CrossRef]

J. Phys. B. (1)

J. Dalibard, C. Cohen-Tannoudji, J. Phys. B. 18, 1661 (1984).
[CrossRef]

JETP Lett. (1)

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

Opt. Commun. (3)

C. Tanguy, S. Reynaud, M. Matsuoka, C. Cohen-Tannoudji, Opt. Commun. 44, 249 (1983).
[CrossRef]

E. Kyrola, S. Stenholm, Opt. Commun. 22, 123 (1977).
[CrossRef]

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

Phys. Lett. 86(A) (1)

V. A. GrinchukE, F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, A. P. Kazantsev, G. I. Surdutovich, V. P. Yakovlev, Phys. Lett. 86(A), 136 (1981).
[CrossRef]

Phys. Rev. A (4)

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

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

E. Arimondo, A. Bambini, S. Stenholm, Phys. Rev. A 24, 898 (1981).
[CrossRef]

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

Phys. Rev. Lett. (4)

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

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

W. Ertmer, R. Blatt, J. L. Hall, M. Zhu, Phys. Rev. Lett. 54, 996 (1985).
[CrossRef] [PubMed]

J. Reid, T. Oka, Phys. Rev. Lett. 38, 67 (1977).
[CrossRef]

Phys. Z. (1)

A. Einstein, Phys. Z. 18, 121 (1917); translated in D. ter Haar, The Old Quantum Theory (Pergamon, New York, 1967), pp. 167–183.

Proc. Camb. Philos. Soc. (1)

P. L. Kapitza, P. A. M. Dirac, Proc. Camb. Philos. Soc. 29, 297 (1933).
[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).

Other (3)

L. Allen, J. H. Eberly, Optical Resonance and Two-Level Atoms (Wiley, New York, 1975).

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

T. Oka, in Frontiers of Laser Spectroscopy, R. Balian, S. Harouche, S. Lieberman, eds. (North-Holland, New York, 1977), Vol. 2, p. 529.

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Figures (3)

Fig. 1
Fig. 1

Schematic view of spatially limited radiation field. Photons of angular spread Δθ are focused to form an interaction region of length L ~ ƛ/Δθ.

Fig. 2
Fig. 2

First-order Bragg scattering can occur when q0 =−1; it takes the system from the initial state to q = 2 via the intermediate excited state with q = 1. For odd values of q the atom is in its excited state, and its energy is uncertain by ħΓ open circles are used for these states in order to suggest their finite linewidth.

Fig. 3
Fig. 3

First-order (i.e., three-photon) Doppleron process shown for q0= 10. In contrast with Bragg scattering, the atom is left in the excited state.

Equations (21)

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ω R = μ / ,
Δ ω = k v Δ θ = k v ƛ / L = T - 1 ,
( x ) = 0 exp ( - x 2 / w 2 ) ,
d = ( 2 Δ ) 1 / 2 π w 2 / λ = ( 2 Δ ) 1 / 2 b ,
q = Δ p z / k ,
q 0 = p z 0 / k .
E = p z 2 - p z 0 2 2 M + ω e g ,
b = 2 k 2 / 2 M ,
E q = ( 2 q q 0 + q 2 ) b + [ 1 - ( - 1 ) q ] ω e g / 2.
sin θ = n λ 2 d ,
p 1 = h / d = 2 k .
P + 2 = sin 2 ( ω R 2 T / 2 ) ,
ω R 2 = ω R 2 / 2 δ ,
R ± 1 = ( ω R / 2 ) 2 δ 2 + ω R 2 / 2 + Γ 2 / 4 Γ = ( ω R 2 δ ) 2 Γ ,
P c d = ( R + 1 + R - 1 ) T = 2 ( ω R / 2 δ ) 2 Γ T .
T ω R 2 / 2 δ = 2
T Γ ω R 2 / 2 δ 2 = 0.2 ,
ω R 3 = ( ω R 2 δ ) 2 ω R ,
R 3 = ω R 3 2 2 ω R 3 2 + Γ 2 Γ ~ ω R 2 Γ 2 ( ω R 2 δ ) 4 Γ .
ω s ± k v ± 2 l ( k v ) = ω e g .
ξ ω s ± k v ± 2 l ( k v ) - ξ ω t = 0 ,

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