Abstract

The application of counterpropagating, short, chirped laser pulses for the deflection and splitting of an atomic beam is investigated. A simple model is proposed to describe the case in which the pulses induce population transfer in the adiabatic-passage regime and in which the effects of spontaneous emission are negligible during the action of a single laser pulse. Spontaneous emission between the pulses is not neglected, however, and it is shown that it has a significant effect on the evolution of the average transversal velocity of the atoms, as well as the dispersion of the transversal velocity.

© 1998 Optical Society of America

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  1. V. S. Letokhov and V. G. Minogin, Phys. Rep. 73, 1 (1981).
    [CrossRef]
  2. A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
    [CrossRef]
  3. C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
    [CrossRef]
  4. H. Metcalf and P. van der Straten, Phys. Rep. 244, 203 (1994).
    [CrossRef]
  5. H. Wallis, Phys. Rep. 255, 203 (1995).
    [CrossRef]
  6. I. Nebenzahl and A. Szöke, Appl. Phys. Lett. 25, 327 (1974).
    [CrossRef]
  7. V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).
  8. K. Mølmer, Phys. Rev. Lett. 66, 2301 (1991).
    [CrossRef]
  9. T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
    [CrossRef]
  10. T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
    [CrossRef] [PubMed]
  11. P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
    [CrossRef] [PubMed]
  12. J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
    [CrossRef] [PubMed]
  13. J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
    [CrossRef] [PubMed]
  14. G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
    [CrossRef]
  15. B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
    [CrossRef]
  16. G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
    [CrossRef]
  17. R. J. Cook, Phys. Rev. A 20, 224 (1979).
    [CrossRef]
  18. J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
    [CrossRef]
  19. J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
    [CrossRef]
  20. R. Grimm, J. Söding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
    [CrossRef] [PubMed]

1997 (2)

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

1996 (4)

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
[CrossRef]

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

1995 (1)

H. Wallis, Phys. Rep. 255, 203 (1995).
[CrossRef]

1994 (5)

C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
[CrossRef]

H. Metcalf and P. van der Straten, Phys. Rep. 244, 203 (1994).
[CrossRef]

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

R. Grimm, J. Söding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
[CrossRef] [PubMed]

1993 (1)

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

1991 (2)

P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
[CrossRef] [PubMed]

K. Mølmer, Phys. Rev. Lett. 66, 2301 (1991).
[CrossRef]

1985 (2)

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 2, 1707 (1985).
[CrossRef]

1981 (1)

V. S. Letokhov and V. G. Minogin, Phys. Rep. 73, 1 (1981).
[CrossRef]

1979 (1)

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

1974 (1)

I. Nebenzahl and A. Szöke, Appl. Phys. Lett. 25, 327 (1974).
[CrossRef]

Adams, C. S.

C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
[CrossRef]

Andrä, H. J.

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

Bakos, J. S.

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
[CrossRef]

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

Bouyer, Ph.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

Cohen-Tannoudji, C.

Cook, R. J.

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

Dalibard, J.

Demeter, G.

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
[CrossRef]

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

Djotyan, G. P.

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
[CrossRef]

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

Grimm, R.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

R. Grimm, J. Söding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
[CrossRef] [PubMed]

Grinchuk, V. A.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

Grishina, I. A.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

Hall, J. L.

P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
[CrossRef] [PubMed]

Kazantsev, A. P.

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

Kuzin, E. F.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

Lawall, J.

J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

Lenz, G.

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

Letokhov, V. S.

V. S. Letokhov and V. G. Minogin, Phys. Rep. 73, 1 (1981).
[CrossRef]

Marte, P.

P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
[CrossRef] [PubMed]

Metcalf, H.

H. Metcalf and P. van der Straten, Phys. Rep. 244, 203 (1994).
[CrossRef]

Meystre, P.

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

Minogin, V. G.

V. S. Letokhov and V. G. Minogin, Phys. Rep. 73, 1 (1981).
[CrossRef]

Mlynek, J.

C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
[CrossRef]

Mølmer, K.

K. Mølmer, Phys. Rev. Lett. 66, 2301 (1991).
[CrossRef]

Nagaeva, M. L.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

Nebenzahl, I.

I. Nebenzahl and A. Szöke, Appl. Phys. Lett. 25, 327 (1974).
[CrossRef]

Nölle, B.

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

Nölle, H.

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

Ovchinnikov, Yu. B.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

R. Grimm, J. Söding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
[CrossRef] [PubMed]

Prentiss, M.

J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

Ryabenko, G. A.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

Salomon, Ch.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

Schmand, J.

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

Sigel, M.

C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
[CrossRef]

Söding, J.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

R. Grimm, J. Söding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
[CrossRef] [PubMed]

Sörlei, Zs.

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Opt. Soc. Am. B 13, 1697 (1996).
[CrossRef]

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

Surdutovich, G. I.

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

Szöke, A.

I. Nebenzahl and A. Szöke, Appl. Phys. Lett. 25, 327 (1974).
[CrossRef]

van der Straten, P.

H. Metcalf and P. van der Straten, Phys. Rep. 244, 203 (1994).
[CrossRef]

Wallis, H.

H. Wallis, Phys. Rep. 255, 203 (1995).
[CrossRef]

Wilkens, M.

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

Yakovlev, V. P.

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

Zaugg, T.

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

Zoller, P.

P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

I. Nebenzahl and A. Szöke, Appl. Phys. Lett. 25, 327 (1974).
[CrossRef]

Europhys. Lett. (1)

B. Nölle, H. Nölle, J. Schmand, and H. J. Andrä, Europhys. Lett. 33, 261 (1996).
[CrossRef]

J. Mod. Opt. (1)

G. P. Djotyan, J. S. Bakos, G. Demeter, and Zs. Sörlei, J. Mod. Opt. 44, 1511 (1997).
[CrossRef]

J. Opt. Soc. Am. B (2)

Laser Phys. (1)

V. A. Grinchuk, I. A. Grishina, E. F. Kuzin, M. L. Nagaeva, G. A. Ryabenko, and V. P. Yakovlev, Laser Phys. 6, 1 (1996).

Opt. Commun. (1)

T. Zaugg, M. Wilkens, P. Meystre, and G. Lenz, Opt. Commun. 97, 189 (1993).
[CrossRef]

Opt. Lett. (1)

Phys. Rep. (5)

V. S. Letokhov and V. G. Minogin, Phys. Rep. 73, 1 (1981).
[CrossRef]

A. P. Kazantsev, G. A. Ryabenko, G. I. Surdutovich, and V. P. Yakovlev, Phys. Rep. 129, 75 (1985).
[CrossRef]

C. S. Adams, M. Sigel, and J. Mlynek, Phys. Rep. 240, 143 (1994).
[CrossRef]

H. Metcalf and P. van der Straten, Phys. Rep. 244, 203 (1994).
[CrossRef]

H. Wallis, Phys. Rep. 255, 203 (1995).
[CrossRef]

Phys. Rev. A (4)

T. Zaugg, P. Meystre, G. Lenz, and M. Wilkens, Phys. Rev. A 49, 3011 (1994).
[CrossRef] [PubMed]

P. Marte, P. Zoller, and J. L. Hall, Phys. Rev. A 44, 4118 (1991).
[CrossRef] [PubMed]

J. S. Bakos, G. P. Djotyan, G. Demeter, and Zs. Sörlei, Phys. Rev. A 53, 2885 (1996).
[CrossRef] [PubMed]

R. J. Cook, Phys. Rev. A 20, 224 (1979).
[CrossRef]

Phys. Rev. Lett. (3)

J. Söding, R. Grimm, Yu. B. Ovchinnikov, Ph. Bouyer, and Ch. Salomon, Phys. Rev. Lett. 78, 1420 (1997).
[CrossRef]

K. Mølmer, Phys. Rev. Lett. 66, 2301 (1991).
[CrossRef]

J. Lawall and M. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Schematic arrangement of the situation considered; a collimated atomic beam crosses a region where it interacts with short, chirped laser pulses from alternating directions.

Fig. 2
Fig. 2

Time sequence of the laser pulses; one elementary cycle lasts from the beginning of one pulse at t1 to the beginning of the third pulse at t3. The arrows on top depict the direction of propagation of the pulses.

Fig. 3
Fig. 3

(a) Stationary-state force fst and (b) diffusion constant Dst as functions of u=τ1+τ2 pulse length and v=(τ2 -τ1)/(τ1+τ2) in the region u[0.01, 0.1]. The unit of momentum is k, and the unit of time is Γ-1.

Fig. 4
Fig. 4

(a) Total momentum I transferred to the atoms during a time 50Γ-1 and (b) width σz of the distribution after this time in the region u[0.01, 0.1], assuming an initial width of σz0 =10.

Fig. 5
Fig. 5

Evolution of the velocity distribution of atoms g(z) for the first 40 cycles of laser pulses. The intervals between the pulses are τ1=0.03, τ2=0.1, the initial Gaussian distribution has been normalized to N=1000, and the initial width is σz =5k. T on the horizontal axis gives time measured by the number of cycles.

Fig. 6
Fig. 6

Evolution of the velocity distribution of atoms g(z) from after the 80th cycle to the 400th cycle. The intervals between the pulses are τ1=0.02, τ2=0.1, the initial Gaussian distribution has been normalized to N=1000, and the initial width is σz=5k. Note that the orientation of this figure is different from that of Fig. 5, for a clear view.

Fig. 7
Fig. 7

Evolution of the velocity distribution of atoms for the first 100 cycles of laser pulses when τ1=τ2=0.02. Initial distribution is the same as for Figs. 5 and 6.

Equations (35)

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

a(t1, z)=b(t1, z+1),
b(t1, z)=a(t1, z-1).
a(t2, z)=a(t1, z)+[1-exp(-Γτ1)]×-1+1f(z)b(t1, z+z)dz,
b(t2, z)=exp(-Γτ1)b(t1, z).
a(t2, z)=b(t2, z-1),
b(t2, z)=a(t2, z+1),
a(t3, z)=a(t2, z)+[1-exp(-Γτ2)]×-1+1f(z)b(t2, z+z)dz,
b(t3, z)=exp(-Γτ2)b(t2, z).
a(t3, z)=P1a(t1, z-2)+(1-P1)(1-P2)a(t1, z)+(1-P2)b(t1, z+2),
b(t3, z)=P2b(t1, z+2)+P2(1-P1)a(t1, z).
g(t3, z)=b(t1, z+2)+a(t1, z)(1-P1)+P1a(t1, z-2).
Pa(t3)=1-P2+P1P2Pa(t1),
Pb(t3)=P2-P1P2Pa(t1).
Past=1-P21-P1P2,
Pbst=P2(1-P1)1-P1P2.
Pa(t3)=Past+[Pa(t1)-Past]P1P2,
Pa(t)=Past+[Pa(t0)-Past]exp(-Γt),
z¯a=za(z)dz,z¯b=zb(z)dz.
z¯a(t3)=z¯a(t1)(1-P2+P1P2)+(1-P2)×[z¯b(t1)-2Pb(t1)]+2P1Pa(t1),
z¯b(t3)=P2[z¯b(t1)-2Pb(t1)]+P2(1-P1)z¯a(t1).
z¯(t3)=z¯a(t3)+z¯b(t3)=z¯(t1)+2[P1Pa(t1)-Pb(t1)],
Δzst=2 P1-P21-P1P2,
σz2(t3)=σz2(t1)+4(P1+1)Q(t1)+W(t1),
Q=Pbz¯a-Paz¯b,
W=4(Pb+P1Pa)-4(P1Pa-Pb)2.
Q(t3)=Qst+P1P2[Q(t1)-Qst],
Qst=2P1P2(1-P1)(1-P22)(1-P1P2)3.
σz2(t3)=σz2(t1)+4(P1+1)Qst+Wst=σz2(t1)+K,
z¯(n)=z¯(0)+i=0n-12[Pa(i)P1-Pb(i)]=z¯(0)+nΔzst+2(P1+1)×[Pa(0)-Past] (1-P1P2)n1-P1P2.
a0(z)=τ2τ1+τ2 g0(z)+(1-P2) τ1τ1+τ2 g0(z+1),
b0(z)=P2 τ1τ1+τ2 g0(z+1),
Pa(0)=1-P2τ1τ1+τ2,
z¯a(0)=(P2-1)τ1τ1+τ2,z¯b(0)=-P2τ1τ1+τ2,
σz2(0)=σz02+τ1τ2(τ1+τ2)2.
Pb=2(1-P1)PastΓ(τ1+τ2),

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