Abstract

A review is presented of some of the principal techniques of laser cooling and trapping that have been developed during the past 20 years. Its approach is primarily experimental, but its quantitative descriptions are consistent in notation with most of the theoretical literature. It begins with a simplified introduction to optical forces on atoms, including both cooling and trapping. Then its three main sections discuss its three selected features, (1) quantization of atomic motion, (2) effects of the multilevel structure of atoms, and (3) the effects of polychromatic light. Each of these features is an expansion in a different direction from the simplest model of a classical, two-level atom moving in a monochromatic laser field.

© 2003 Optical Society of America

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2003 (1)

2002 (3)

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416, 238–246 (2002).
[CrossRef] [PubMed]

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf, “Coherent exchange of momentum between atoms and light,” J. Opt. B 4, 75–79 (2002).
[CrossRef]

2001 (2)

M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

M. Cashen and H. Metcalf, “Bichromatic force on helium,” Phys. Rev. A 63, 025406 (2001).
[CrossRef]

2000 (2)

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Bichromatic force measurements using atomic beam deflections,” Phys. Rev. A 61, 023408 (2000).
[CrossRef]

J. Hack, L. Liu, M. Olshanii, and H. Metcalf, “Velocity-selective coherent population trapping of two-level atoms,” Phys. Rev. A 62, 013405 (2000).
[CrossRef]

1999 (1)

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Measurement of the bichromatic optical force on Rb atoms,” Phys. Rev. A 60, R1763–R1766 (1999).
[CrossRef]

1998 (3)

1997 (5)

N. Simpson, K. Dholakia, L. Allen, and M. Padgett, “The mechanical equivalence of spin and orbital angular momentum of light: an optical spanner,” Opt. Lett. 22, 52–54 (1997).
[CrossRef] [PubMed]

P. A. Molenaar, P. van der Straten, H. G. M. Heideman, and H. Metcalf, “Diagnostic technique for Zeeman-compensated atomic-beam slowing—technique and results,” Phys. Rev. A 55, 605–614 (1997).
[CrossRef]

A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schütze, R. Wynands, and D. Meschede, “Stimulated focusing and deflection of an atomic beam using picosecond laser pulses,” Phys. Rev. A 56, R3354–R3357 (1997).
[CrossRef]

Yu. B. Ovchinnikov, I. Manek, and R. Grimm, “Surface trap for Cs atoms based on evanescent-wave cooling,” Phys. Rev. Lett. 79, 2225–2228 (1997).
[CrossRef]

J. Söding, R. Grimm, Yu. B. Ovchinnikov, P. Bouyer, and C. Salomon, “Short-distance atomic-beam deceleration with a stimulated light force,” Phys. Rev. Lett. 78, 1420–1423 (1997).
[CrossRef]

1996 (4)

W. Ketterle and N. J. Vandruten, “Evaporative cooling of trapped atoms,” Adv. Atom. Mol. Opt. Phys. 37, 181–236 (1996).
[CrossRef]

G. Morigi, B. Zambon, N. Leinfellner, and E. Arimondo, “Scaling laws in velocity-selective coherent-population-trapping laser cooling,” Phys. Rev. A 53, 2616–2626 (1996).
[CrossRef] [PubMed]

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[CrossRef] [PubMed]

T. Takekoshi and R. J. Knize, “CO2-laser trap for cesium atoms,” Opt. Lett. 21, 77–79 (1996).
[CrossRef] [PubMed]

1995 (3)

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75, 2823–2826 (1995).
[CrossRef] [PubMed]

C. S. Adams, H. J. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef] [PubMed]

N. Davidson, H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Long atomic coherence times in an optical dipole trap,” Phys. Rev. Lett. 74, 1311–1314 (1995).
[CrossRef] [PubMed]

1994 (3)

1993 (6)

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[CrossRef] [PubMed]

R. Gupta, C. Xie, S. Padua, H. Batelaan, and H. Metcalf, “Bichromatic laser cooling in a 3-level system,” Phys. Rev. Lett. 71, 3087–3090 (1993).
[CrossRef] [PubMed]

C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
[CrossRef] [PubMed]

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef] [PubMed]

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtois, and C. Salomon, “Quantized motion of cold cesium atoms in 2-dimensional and 3-dimensional optical potentials,” Phys. Rev. Lett. 70, 2249–2252 (1993).
[CrossRef] [PubMed]

B. Lounis, P. Verkerk, J. Y. Courtois, C. Salomon, and G. Grynberg, “Quantized atomic motion in 1D cesium molasses with magnetic field,” Europhys. Lett. 21, 13–17 (1993).
[CrossRef]

1992 (8)

R. Gupta, S. Padua, C. Xie, H. Batelaan, T. Bergeman, and H. Metcalf, “Motional quantization of laser cooled atoms,” Bull. Am. Phys. Soc. 37, 1139 (1992).

P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J. Y. Courtois, and G. Grynberg, “Dynamics and spatial order of cold cesium atoms in a periodic optical potential,” Phys. Rev. Lett. 68, 3861–3864 (1992).
[CrossRef] [PubMed]

P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69, 49–52 (1992).
[CrossRef] [PubMed]

T. Hodapp, C. Gerz, C. Westbrook, C. Furtlehner, and W. Phillips, “Diffusion in optical molasses,” Bull. Am. Phys. Soc. 37, 1139 (1992).

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with 3-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

A. M. Steane, M. Chowdhury, and C. J. Foot, “Radiation force in the magnetooptical trap,” J. Opt. Soc. Am. B 9, 2142–2158 (1992).
[CrossRef]

K. E. Gibble, S. Kasapi, and S. Chu, “Improved magnetooptic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
[CrossRef] [PubMed]

1991 (6)

D. W. Sesko, T. G. Walker, and C. E. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
[CrossRef]

V. Voitsekovich, M. Danileiko, A. Negriiko, V. Romanenko, and L. Yatsenko, “Pressure of light on atoms in the field of frequency-modulated waves,” Ukr. Fiz. Zh. (Russ. Ed.) 36, 192–197 (1991).

E. A. Cornell, C. Monroe, and C. E. Wieman, “Multiply loaded, ac magnetic trap for neutral atoms,” Phys. Rev. Lett. 67, 2439–2442 (1991).
[CrossRef] [PubMed]

A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magnetooptical trap,” Europhys. Lett. 14, 231–236 (1991).
[CrossRef]

T. E. Barrett, S. W. Dapore-Schwartz, M. D. Ray, and G. P. Lafyatis, “Slowing atoms with (σ)-polarized light,” Phys. Rev. Lett. 67, 3483–3487 (1991).
[CrossRef] [PubMed]

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

1990 (8)

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

B. Sheehy, S. Q. Shang, P. van der Straten, and H. Metcalf, “Collimation of a rubidium beam below the Doppler limit,” Chem. Phys. 145, 317–325 (1990).
[CrossRef]

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

R. Grimm, Yu. B. Ovchinnikov, A. I. Sidorov, and V. S. Letokhov, “Observation of a strong rectified dipole force in a bichromatic standing light wave,” Phys. Rev. Lett. 65, 1415–1418 (1990).
[CrossRef] [PubMed]

C. Cohen-Tannoudji and W. D. Phillips, “New mechanisms for laser cooling,” Phys. Today 43(10), 33–40 (1990).
[CrossRef]

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
[CrossRef]

B. Sheehy, S. Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, “Magnetic-field-induced laser cooling below the Doppler limit,” Phys. Rev. Lett. 64, 858–861 (1990).
[CrossRef] [PubMed]

M. A. Kasevich, D. S. Weiss, and S. Chu, “Normal-incidence reflection of slow atoms from an optical evanescent wave,” Opt. Lett. 15, 607–609 (1990).
[CrossRef] [PubMed]

1989 (5)

1988 (2)

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

P. Lett, R. Watts, C. Westbrook, W. Phillips, P. Gould, and H. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

1987 (4)

V. Bagnato, G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. Pritchard, “Continuous stopping and trapping of neutral atoms,” Phys. Rev. Lett. 58, 2194–2197 (1987).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

1986 (3)

H. Metcalf and W. Phillips, “Electromagnetic trapping of neutral atoms,” Metrologia 22, 271–278 (1986).
[CrossRef]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

R. Watts and C. Wieman, “Manipulating atomic velocities using diode lasers,” Opt. Lett. 11, 291–293 (1986).
[CrossRef] [PubMed]

1985 (4)

J. Dalibard and W. Phillips, “Stability and damping of radiation pressure traps,” Bull. Am. Phys. Soc. 30, 748 (1985).

S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, “Laser manipulation of atomic beam velocities: demonstration of stopped atoms and velocity reversal,” Phys. Rev. Lett. 54, 996–999 (1985).
[CrossRef] [PubMed]

1984 (1)

J. Prodan and W. Phillips, “Chirping the light fantastic?—recent NBS atom cooling experiments,” Prog. Quantum Electron. 8, 231–235 (1984).
[CrossRef]

1982 (2)

W. Phillips and H. Metcalf, “Laser deceleration of an atomic beam,” Phys. Rev. Lett. 48, 596–599 (1982).
[CrossRef]

J. Prodan, W. Phillips, and H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

1980 (1)

A. Ashkin, “Application of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

1977 (1)

E. Kyrola and S. Stenholm, “Velocity tuned resonances as multi-Doppleron processes,” Opt. Commun. 22, 123–126 (1977).
[CrossRef]

1974 (1)

I. Nebenzahl and A. Szoke, “Deflection of atomic beams by resonance radiation using stimulated emission,” Appl. Phys. Lett. 25, 327–329 (1974).
[CrossRef]

1970 (1)

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

1968 (1)

V. S. Letokhov, “Narrowing of the Doppler width in a standing light wave,” JETP Lett. 7, 272 (1968).

1957 (1)

R. Feynman, F. Vernon, and R. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. App. Phys. 28, 49–52 (1957).
[CrossRef]

Adams, C. S.

C. S. Adams, H. J. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef] [PubMed]

N. Davidson, H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Long atomic coherence times in an optical dipole trap,” Phys. Rev. Lett. 74, 1311–1314 (1995).
[CrossRef] [PubMed]

Ahmad-Bitar, R.

V. Bagnato, G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. Pritchard, “Continuous stopping and trapping of neutral atoms,” Phys. Rev. Lett. 58, 2194–2197 (1987).
[CrossRef] [PubMed]

Allen, L.

Aminoff, C. G.

C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
[CrossRef] [PubMed]

Anderson, B. P.

B. P. Anderson and M. A. Kasevich, “Macroscopic quantum interference from atomic tunnel arrays,” Nature 282, 1686–1689 (1998).

Arimondo, E.

G. Morigi, B. Zambon, N. Leinfellner, and E. Arimondo, “Scaling laws in velocity-selective coherent-population-trapping laser cooling,” Phys. Rev. A 53, 2616–2626 (1996).
[CrossRef] [PubMed]

A. Aspect, C. Cohen-Tannoudji, E. Arimondo, N. Vansteenkiste, and R. Kaiser, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping—theoretical analysis,” J. Opt. Soc. Am. B 6, 2112–2124 (1989).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

Ashkin, A.

A. Ashkin and J. M. Dziedzic, “Optical trapping and manipulation of viruses and bacteria,” Science 235, 1517–1520 (1987).
[CrossRef] [PubMed]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

A. Ashkin and J. M. Dziedzic, “Observation of radiation-pressure trapping of particles by alternating light beams,” Phys. Rev. Lett. 54, 1245–1248 (1985).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

A. Ashkin, “Application of laser radiation pressure,” Science 210, 1081–1088 (1980).
[CrossRef] [PubMed]

A. Ashkin, “Acceleration and trapping of particles by radiation pressure,” Phys. Rev. Lett. 24, 156–159 (1970).
[CrossRef]

Aspect, A.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, “Subrecoil laser cooling and Levy flights,” Phys. Rev. Lett. 72, 203–206 (1994).
[CrossRef] [PubMed]

A. Aspect, C. Cohen-Tannoudji, E. Arimondo, N. Vansteenkiste, and R. Kaiser, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping—theoretical analysis,” J. Opt. Soc. Am. B 6, 2112–2124 (1989).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Bagnato, V.

V. Bagnato, G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. Pritchard, “Continuous stopping and trapping of neutral atoms,” Phys. Rev. Lett. 58, 2194–2197 (1987).
[CrossRef] [PubMed]

Bakos, J.

Bardou, F.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, “Subrecoil laser cooling and Levy flights,” Phys. Rev. Lett. 72, 203–206 (1994).
[CrossRef] [PubMed]

Barrett, T. E.

T. E. Barrett, S. W. Dapore-Schwartz, M. D. Ray, and G. P. Lafyatis, “Slowing atoms with (σ)-polarized light,” Phys. Rev. Lett. 67, 3483–3487 (1991).
[CrossRef] [PubMed]

Batelaan, H.

R. Gupta, S. Padua, C. Xie, H. Batelaan, and H. Metcalf, “Simplest atomic system for sub-Doppler laser cooling,” J. Opt. Soc. Am. B 11, 537–541 (1994).
[CrossRef]

R. Gupta, C. Xie, S. Padua, H. Batelaan, and H. Metcalf, “Bichromatic laser cooling in a 3-level system,” Phys. Rev. Lett. 71, 3087–3090 (1993).
[CrossRef] [PubMed]

R. Gupta, S. Padua, C. Xie, H. Batelaan, T. Bergeman, and H. Metcalf, “Motional quantization of laser cooled atoms,” Bull. Am. Phys. Soc. 37, 1139 (1992).

Ben Dahan, M.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[CrossRef] [PubMed]

Bergeman, T.

R. Gupta, S. Padua, C. Xie, H. Batelaan, T. Bergeman, and H. Metcalf, “Motional quantization of laser cooled atoms,” Bull. Am. Phys. Soc. 37, 1139 (1992).

Birkl, G.

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75, 2823–2826 (1995).
[CrossRef] [PubMed]

Bjorkholm, J.

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Blatt, R.

W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, “Laser manipulation of atomic beam velocities: demonstration of stopped atoms and velocity reversal,” Phys. Rev. Lett. 54, 996–999 (1985).
[CrossRef] [PubMed]

Bloch, I.

M. Greiner, O. Mandel, T. Esslinger, T. W. Hänsch, and I. Bloch, “Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms,” Nature 415, 39–44 (2002).
[CrossRef] [PubMed]

A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schütze, R. Wynands, and D. Meschede, “Stimulated focusing and deflection of an atomic beam using picosecond laser pulses,” Phys. Rev. A 56, R3354–R3357 (1997).
[CrossRef]

Bouchaud, J. P.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, “Subrecoil laser cooling and Levy flights,” Phys. Rev. Lett. 72, 203–206 (1994).
[CrossRef] [PubMed]

Bouyer, P.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, P. Bouyer, and C. Salomon, “Short-distance atomic-beam deceleration with a stimulated light force,” Phys. Rev. Lett. 78, 1420–1423 (1997).
[CrossRef]

C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
[CrossRef] [PubMed]

Cable, A.

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Cashen, M.

M. Cashen and H. Metcalf, “Optical forces on atoms in nonmonochromatic light,” J. Opt. Soc. Am. B 20, 915–924 (2003).
[CrossRef]

M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf, “Coherent exchange of momentum between atoms and light,” J. Opt. B 4, 75–79 (2002).
[CrossRef]

M. Cashen and H. Metcalf, “Bichromatic force on helium,” Phys. Rev. A 63, 025406 (2001).
[CrossRef]

M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Bichromatic force measurements using atomic beam deflections,” Phys. Rev. A 61, 023408 (2000).
[CrossRef]

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Measurement of the bichromatic optical force on Rb atoms,” Phys. Rev. A 60, R1763–R1766 (1999).
[CrossRef]

Castin, Y.

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[CrossRef] [PubMed]

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

Chi, F.

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Bichromatic force measurements using atomic beam deflections,” Phys. Rev. A 61, 023408 (2000).
[CrossRef]

M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Measurement of the bichromatic optical force on Rb atoms,” Phys. Rev. A 60, R1763–R1766 (1999).
[CrossRef]

Chowdhury, M.

Chu, S.

N. Davidson, H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Long atomic coherence times in an optical dipole trap,” Phys. Rev. Lett. 74, 1311–1314 (1995).
[CrossRef] [PubMed]

C. S. Adams, H. J. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef] [PubMed]

M. Kasevich and S. Chu, “Laser cooling below a photon recoil with 3-level atoms,” Phys. Rev. Lett. 69, 1741–1744 (1992).
[CrossRef] [PubMed]

K. E. Gibble, S. Kasapi, and S. Chu, “Improved magnetooptic trapping in a vapor cell,” Opt. Lett. 17, 526–528 (1992).
[CrossRef] [PubMed]

M. A. Kasevich, D. S. Weiss, and S. Chu, “Normal-incidence reflection of slow atoms from an optical evanescent wave,” Opt. Lett. 15, 607–609 (1990).
[CrossRef] [PubMed]

P. J. Ungar, D. S. Weiss, S. Chu, and E. Riis, “Optical molasses and multilevel atoms—theory,” J. Opt. Soc. Am. B 6, 2058–2071 (1989).
[CrossRef]

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

S. Chu, J. Bjorkholm, A. Ashkin, and A. Cable, “Experimental observation of optically trapped atoms,” Phys. Rev. Lett. 57, 314–317 (1986).
[CrossRef] [PubMed]

S. Chu, L. Hollberg, J. Bjorkholm, A. Cable, and A. Ashkin, “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pressure,” Phys. Rev. Lett. 55, 48–51 (1985).
[CrossRef] [PubMed]

Clairon, A.

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
[CrossRef]

Cline, R. A.

J. D. Miller, R. A. Cline, and D. J. Heinzen, “Far-off-resonance optical trapping of atoms,” Phys. Rev. A 47, R4567–R4570 (1993).
[CrossRef] [PubMed]

Cohen-Tannoudji, C.

F. Bardou, J. P. Bouchaud, O. Emile, A. Aspect, and C. Cohen-Tannoudji, “Subrecoil laser cooling and Levy flights,” Phys. Rev. Lett. 72, 203–206 (1994).
[CrossRef] [PubMed]

C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
[CrossRef] [PubMed]

P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J. Y. Courtois, and G. Grynberg, “Dynamics and spatial order of cold cesium atoms in a periodic optical potential,” Phys. Rev. Lett. 68, 3861–3864 (1992).
[CrossRef] [PubMed]

C. Cohen-Tannoudji and W. D. Phillips, “New mechanisms for laser cooling,” Phys. Today 43(10), 33–40 (1990).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients—simple theoretical models,” J. Opt. Soc. Am. B 6, 2023–2045 (1989).
[CrossRef]

A. Aspect, C. Cohen-Tannoudji, E. Arimondo, N. Vansteenkiste, and R. Kaiser, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping—theoretical analysis,” J. Opt. Soc. Am. B 6, 2112–2124 (1989).
[CrossRef]

A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Cornell, E. A.

E. A. Cornell, C. Monroe, and C. E. Wieman, “Multiply loaded, ac magnetic trap for neutral atoms,” Phys. Rev. Lett. 67, 2439–2442 (1991).
[CrossRef] [PubMed]

Courtois, J. Y.

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtois, and C. Salomon, “Quantized motion of cold cesium atoms in 2-dimensional and 3-dimensional optical potentials,” Phys. Rev. Lett. 70, 2249–2252 (1993).
[CrossRef] [PubMed]

B. Lounis, P. Verkerk, J. Y. Courtois, C. Salomon, and G. Grynberg, “Quantized atomic motion in 1D cesium molasses with magnetic field,” Europhys. Lett. 21, 13–17 (1993).
[CrossRef]

P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J. Y. Courtois, and G. Grynberg, “Dynamics and spatial order of cold cesium atoms in a periodic optical potential,” Phys. Rev. Lett. 68, 3861–3864 (1992).
[CrossRef] [PubMed]

Dalibard, J.

C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
[CrossRef] [PubMed]

Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
[CrossRef]

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
[CrossRef]

J. Dalibard and C. Cohen-Tannoudji, “Laser cooling below the Doppler limit by polarization gradients—simple theoretical models,” J. Opt. Soc. Am. B 6, 2023–2045 (1989).
[CrossRef]

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

J. Dalibard and W. Phillips, “Stability and damping of radiation pressure traps,” Bull. Am. Phys. Soc. 30, 748 (1985).

Danileiko, M.

V. Voitsekovich, M. Danileiko, A. Negriiko, V. Romanenko, and L. Yatsenko, “Pressure of light on atoms in the field of frequency-modulated waves,” Ukr. Fiz. Zh. (Russ. Ed.) 36, 192–197 (1991).

Dapore-Schwartz, S. W.

T. E. Barrett, S. W. Dapore-Schwartz, M. D. Ray, and G. P. Lafyatis, “Slowing atoms with (σ)-polarized light,” Phys. Rev. Lett. 67, 3483–3487 (1991).
[CrossRef] [PubMed]

Davidson, N.

C. S. Adams, H. J. Lee, N. Davidson, M. Kasevich, and S. Chu, “Evaporative cooling in a crossed dipole trap,” Phys. Rev. Lett. 74, 3577–3580 (1995).
[CrossRef] [PubMed]

N. Davidson, H. J. Lee, C. S. Adams, M. Kasevich, and S. Chu, “Long atomic coherence times in an optical dipole trap,” Phys. Rev. Lett. 74, 1311–1314 (1995).
[CrossRef] [PubMed]

Davis, K. B.

W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[CrossRef] [PubMed]

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P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69, 49–52 (1992).
[CrossRef] [PubMed]

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
[CrossRef]

C. Cohen-Tannoudji and W. D. Phillips, “New mechanisms for laser cooling,” Phys. Today 43(10), 33–40 (1990).
[CrossRef]

P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

Prentiss, M.

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

Pritchard, D.

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

V. Bagnato, G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. Pritchard, “Continuous stopping and trapping of neutral atoms,” Phys. Rev. Lett. 58, 2194–2197 (1987).
[CrossRef] [PubMed]

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W. Ketterle, K. B. Davis, M. A. Joffe, A. Martin, and D. E. Pritchard, “High densities of cold atoms in a dark spontaneous-force optical trap,” Phys. Rev. Lett. 70, 2253–2256 (1993).
[CrossRef] [PubMed]

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J. Prodan and W. Phillips, “Chirping the light fantastic?—recent NBS atom cooling experiments,” Prog. Quantum Electron. 8, 231–235 (1984).
[CrossRef]

J. Prodan, W. Phillips, and H. Metcalf, “Laser production of a very slow monoenergetic atomic beam,” Phys. Rev. Lett. 49, 1149–1153 (1982).
[CrossRef]

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V. Bagnato, G. Lafyatis, A. Martin, E. Raab, R. Ahmad-Bitar, and D. Pritchard, “Continuous stopping and trapping of neutral atoms,” Phys. Rev. Lett. 58, 2194–2197 (1987).
[CrossRef] [PubMed]

E. Raab, M. Prentiss, A. Cable, S. Chu, and D. Pritchard, “Trapping of neutral-sodium atoms with radiation pressure,” Phys. Rev. Lett. 59, 2631–2634 (1987).
[CrossRef] [PubMed]

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T. E. Barrett, S. W. Dapore-Schwartz, M. D. Ray, and G. P. Lafyatis, “Slowing atoms with (σ)-polarized light,” Phys. Rev. Lett. 67, 3483–3487 (1991).
[CrossRef] [PubMed]

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M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[CrossRef] [PubMed]

Riis, E.

Rivoire, O.

M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf, “Coherent exchange of momentum between atoms and light,” J. Opt. B 4, 75–79 (2002).
[CrossRef]

M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

Rolston, S. L.

G. Birkl, M. Gatzke, I. H. Deutsch, S. L. Rolston, and W. D. Phillips, “Bragg scattering from atoms in optical lattices,” Phys. Rev. Lett. 75, 2823–2826 (1995).
[CrossRef] [PubMed]

P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69, 49–52 (1992).
[CrossRef] [PubMed]

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

Romanenko, V.

M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

V. Voitsekovich, M. Danileiko, A. Negriiko, V. Romanenko, and L. Yatsenko, “Pressure of light on atoms in the field of frequency-modulated waves,” Ukr. Fiz. Zh. (Russ. Ed.) 36, 192–197 (1991).

Salomon, C.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, P. Bouyer, and C. Salomon, “Short-distance atomic-beam deceleration with a stimulated light force,” Phys. Rev. Lett. 78, 1420–1423 (1997).
[CrossRef]

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, “Bloch oscillations of atoms in an optical potential,” Phys. Rev. Lett. 76, 4508–4511 (1996).
[CrossRef] [PubMed]

G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtois, and C. Salomon, “Quantized motion of cold cesium atoms in 2-dimensional and 3-dimensional optical potentials,” Phys. Rev. Lett. 70, 2249–2252 (1993).
[CrossRef] [PubMed]

B. Lounis, P. Verkerk, J. Y. Courtois, C. Salomon, and G. Grynberg, “Quantized atomic motion in 1D cesium molasses with magnetic field,” Europhys. Lett. 21, 13–17 (1993).
[CrossRef]

P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J. Y. Courtois, and G. Grynberg, “Dynamics and spatial order of cold cesium atoms in a periodic optical potential,” Phys. Rev. Lett. 68, 3861–3864 (1992).
[CrossRef] [PubMed]

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
[CrossRef]

C. Salomon, J. Dalibard, A. Aspect, H. Metcalf, and C. Cohen-Tannoudji, “Channeling atoms in a laser standing wave,” Phys. Rev. Lett. 59, 1659–1662 (1987).
[CrossRef] [PubMed]

Schütze, R.

A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schütze, R. Wynands, and D. Meschede, “Stimulated focusing and deflection of an atomic beam using picosecond laser pulses,” Phys. Rev. A 56, R3354–R3357 (1997).
[CrossRef]

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T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

Sesko, D. W.

Shang, S. Q.

B. Sheehy, S. Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, “Magnetic-field-induced laser cooling below the Doppler limit,” Phys. Rev. Lett. 64, 858–861 (1990).
[CrossRef] [PubMed]

B. Sheehy, S. Q. Shang, P. van der Straten, and H. Metcalf, “Collimation of a rubidium beam below the Doppler limit,” Chem. Phys. 145, 317–325 (1990).
[CrossRef]

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B. Sheehy, S. Q. Shang, P. van der Straten, and H. Metcalf, “Collimation of a rubidium beam below the Doppler limit,” Chem. Phys. 145, 317–325 (1990).
[CrossRef]

B. Sheehy, S. Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, “Magnetic-field-induced laser cooling below the Doppler limit,” Phys. Rev. Lett. 64, 858–861 (1990).
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R. Grimm, Yu. B. Ovchinnikov, A. I. Sidorov, and V. S. Letokhov, “Observation of a strong rectified dipole force in a bichromatic standing light wave,” Phys. Rev. Lett. 65, 1415–1418 (1990).
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Söding, J.

J. Söding, R. Grimm, Yu. B. Ovchinnikov, P. Bouyer, and C. Salomon, “Short-distance atomic-beam deceleration with a stimulated light force,” Phys. Rev. Lett. 78, 1420–1423 (1997).
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R. Grimm, J. Söding, and Yu. B. Ovchinnikov, “Coherent beam splitter for atoms based on a bichromatic standing light wave,” Opt. Lett. 19, 658–660 (1994).
[CrossRef] [PubMed]

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P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69, 49–52 (1992).
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C. G. Aminoff, A. M. Steane, P. Bouyer, P. Desbiolles, J. Dalibard, and C. Cohen-Tannoudji, “Cesium atoms bouncing in a stable gravitational cavity,” Phys. Rev. Lett. 71, 3083–3086 (1993).
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A. M. Steane, M. Chowdhury, and C. J. Foot, “Radiation force in the magnetooptical trap,” J. Opt. Soc. Am. B 9, 2142–2158 (1992).
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A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magnetooptical trap,” Europhys. Lett. 14, 231–236 (1991).
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E. Kyrola and S. Stenholm, “Velocity tuned resonances as multi-Doppleron processes,” Opt. Commun. 22, 123–126 (1977).
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K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

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I. Nebenzahl and A. Szoke, “Deflection of atomic beams by resonance radiation using stimulated emission,” Appl. Phys. Lett. 25, 327–329 (1974).
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Tanner, C. E.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

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van der Straten, P.

P. A. Molenaar, P. van der Straten, H. G. M. Heideman, and H. Metcalf, “Diagnostic technique for Zeeman-compensated atomic-beam slowing—technique and results,” Phys. Rev. A 55, 605–614 (1997).
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B. Sheehy, S. Q. Shang, P. van der Straten, and H. Metcalf, “Collimation of a rubidium beam below the Doppler limit,” Chem. Phys. 145, 317–325 (1990).
[CrossRef]

B. Sheehy, S. Q. Shang, P. van der Straten, S. Hatamian, and H. Metcalf, “Magnetic-field-induced laser cooling below the Doppler limit,” Phys. Rev. Lett. 64, 858–861 (1990).
[CrossRef] [PubMed]

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W. Ketterle and N. J. Vandruten, “Evaporative cooling of trapped atoms,” Adv. Atom. Mol. Opt. Phys. 37, 181–236 (1996).
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A. Aspect, C. Cohen-Tannoudji, E. Arimondo, N. Vansteenkiste, and R. Kaiser, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping—theoretical analysis,” J. Opt. Soc. Am. B 6, 2112–2124 (1989).
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A. Aspect, E. Arimondo, R. Kaiser, N. Vansteenkiste, and C. Cohen-Tannoudji, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping,” Phys. Rev. Lett. 61, 826–829 (1988).
[CrossRef] [PubMed]

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G. Grynberg, B. Lounis, P. Verkerk, J. Y. Courtois, and C. Salomon, “Quantized motion of cold cesium atoms in 2-dimensional and 3-dimensional optical potentials,” Phys. Rev. Lett. 70, 2249–2252 (1993).
[CrossRef] [PubMed]

B. Lounis, P. Verkerk, J. Y. Courtois, C. Salomon, and G. Grynberg, “Quantized atomic motion in 1D cesium molasses with magnetic field,” Europhys. Lett. 21, 13–17 (1993).
[CrossRef]

P. Verkerk, B. Lounis, C. Salomon, C. Cohen-Tannoudji, J. Y. Courtois, and G. Grynberg, “Dynamics and spatial order of cold cesium atoms in a periodic optical potential,” Phys. Rev. Lett. 68, 3861–3864 (1992).
[CrossRef] [PubMed]

Vernon, F.

R. Feynman, F. Vernon, and R. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. App. Phys. 28, 49–52 (1957).
[CrossRef]

Voitsekovich, V.

V. Voitsekovich, M. Danileiko, A. Negriiko, V. Romanenko, and L. Yatsenko, “Pressure of light on atoms in the field of frequency-modulated waves,” Ukr. Fiz. Zh. (Russ. Ed.) 36, 192–197 (1991).

Walker, T.

T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

Walker, T. G.

Watts, R.

P. Lett, R. Watts, C. Westbrook, W. Phillips, P. Gould, and H. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
[CrossRef] [PubMed]

R. Watts and C. Wieman, “Manipulating atomic velocities using diode lasers,” Opt. Lett. 11, 291–293 (1986).
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Watts, R. N.

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

Weiss, D. S.

Westbrook, C.

T. Hodapp, C. Gerz, C. Westbrook, C. Furtlehner, and W. Phillips, “Diffusion in optical molasses,” Bull. Am. Phys. Soc. 37, 1139 (1992).

P. Lett, R. Watts, C. Westbrook, W. Phillips, P. Gould, and H. Metcalf, “Observation of atoms laser cooled below the Doppler limit,” Phys. Rev. Lett. 61, 169–172 (1988).
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P. S. Jessen, C. Gerz, P. D. Lett, W. D. Phillips, S. L. Rolston, R. J. C. Spreeuw, and C. I. Westbrook, “Observation of quantized motion of Rb atoms in an optical field,” Phys. Rev. Lett. 69, 49–52 (1992).
[CrossRef] [PubMed]

C. I. Westbrook, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, P. D. Lett, and P. L. Gould, “Localization of atoms in a 3-dimensional standing wave,” Phys. Rev. Lett. 65, 33–36 (1990).
[CrossRef] [PubMed]

P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

Wieman, C.

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
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T. Walker, D. Sesko, and C. Wieman, “Collective behavior of optically trapped neutral atoms,” Phys. Rev. Lett. 64, 408–411 (1990).
[CrossRef] [PubMed]

R. Watts and C. Wieman, “Manipulating atomic velocities using diode lasers,” Opt. Lett. 11, 291–293 (1986).
[CrossRef] [PubMed]

Wieman, C. E.

D. W. Sesko, T. G. Walker, and C. E. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
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E. A. Cornell, C. Monroe, and C. E. Wieman, “Multiply loaded, ac magnetic trap for neutral atoms,” Phys. Rev. Lett. 67, 2439–2442 (1991).
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M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Bichromatic force measurements using atomic beam deflections,” Phys. Rev. A 61, 023408 (2000).
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M. Williams, F. Chi, M. Cashen, and H. Metcalf, “Measurement of the bichromatic optical force on Rb atoms,” Phys. Rev. A 60, R1763–R1766 (1999).
[CrossRef]

Wynands, R.

A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schütze, R. Wynands, and D. Meschede, “Stimulated focusing and deflection of an atomic beam using picosecond laser pulses,” Phys. Rev. A 56, R3354–R3357 (1997).
[CrossRef]

Xie, C.

R. Gupta, S. Padua, C. Xie, H. Batelaan, and H. Metcalf, “Simplest atomic system for sub-Doppler laser cooling,” J. Opt. Soc. Am. B 11, 537–541 (1994).
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R. Gupta, C. Xie, S. Padua, H. Batelaan, and H. Metcalf, “Bichromatic laser cooling in a 3-level system,” Phys. Rev. Lett. 71, 3087–3090 (1993).
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R. Gupta, S. Padua, C. Xie, H. Batelaan, T. Bergeman, and H. Metcalf, “Motional quantization of laser cooled atoms,” Bull. Am. Phys. Soc. 37, 1139 (1992).

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M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf, “Coherent exchange of momentum between atoms and light,” J. Opt. B 4, 75–79 (2002).
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M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

V. Voitsekovich, M. Danileiko, A. Negriiko, V. Romanenko, and L. Yatsenko, “Pressure of light on atoms in the field of frequency-modulated waves,” Ukr. Fiz. Zh. (Russ. Ed.) 36, 192–197 (1991).

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G. Morigi, B. Zambon, N. Leinfellner, and E. Arimondo, “Scaling laws in velocity-selective coherent-population-trapping laser cooling,” Phys. Rev. A 53, 2616–2626 (1996).
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W. Ertmer, R. Blatt, J. L. Hall, and M. Zhu, “Laser manipulation of atomic beam velocities: demonstration of stopped atoms and velocity reversal,” Phys. Rev. Lett. 54, 996–999 (1985).
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Adv. Atom. Mol. Opt. Phys. (1)

W. Ketterle and N. J. Vandruten, “Evaporative cooling of trapped atoms,” Adv. Atom. Mol. Opt. Phys. 37, 181–236 (1996).
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Appl. Opt. (1)

Appl. Phys. Lett. (1)

I. Nebenzahl and A. Szoke, “Deflection of atomic beams by resonance radiation using stimulated emission,” Appl. Phys. Lett. 25, 327–329 (1974).
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Bull. Am. Phys. Soc. (3)

R. Gupta, S. Padua, C. Xie, H. Batelaan, T. Bergeman, and H. Metcalf, “Motional quantization of laser cooled atoms,” Bull. Am. Phys. Soc. 37, 1139 (1992).

J. Dalibard and W. Phillips, “Stability and damping of radiation pressure traps,” Bull. Am. Phys. Soc. 30, 748 (1985).

T. Hodapp, C. Gerz, C. Westbrook, C. Furtlehner, and W. Phillips, “Diffusion in optical molasses,” Bull. Am. Phys. Soc. 37, 1139 (1992).

Chem. Phys. (1)

B. Sheehy, S. Q. Shang, P. van der Straten, and H. Metcalf, “Collimation of a rubidium beam below the Doppler limit,” Chem. Phys. 145, 317–325 (1990).
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Europhys. Lett. (4)

C. Salomon, J. Dalibard, W. D. Phillips, A. Clairon, and S. Guellati, “Laser cooling of cesium atoms below 3 μK,” Europhys. Lett. 12, 683–688 (1990).
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Y. Castin and J. Dalibard, “Quantization of atomic motion in optical molasses,” Europhys. Lett. 14, 761–766 (1991).
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B. Lounis, P. Verkerk, J. Y. Courtois, C. Salomon, and G. Grynberg, “Quantized atomic motion in 1D cesium molasses with magnetic field,” Europhys. Lett. 21, 13–17 (1993).
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A. M. Steane and C. J. Foot, “Laser cooling below the Doppler limit in a magnetooptical trap,” Europhys. Lett. 14, 231–236 (1991).
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J. App. Phys. (1)

R. Feynman, F. Vernon, and R. Hellwarth, “Geometrical representation of the Schrödinger equation for solving maser problems,” J. App. Phys. 28, 49–52 (1957).
[CrossRef]

J. Opt. B (1)

M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf, “Coherent exchange of momentum between atoms and light,” J. Opt. B 4, 75–79 (2002).
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J. Opt. Soc. Am. B (10)

G. Demeter, G. Djotyan, and J. Bakos, “Deflection and splitting of atomic beams with counterpropagating, short, chirped laser pulses,” J. Opt. Soc. Am. B 15, 16–24 (1998).
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P. D. Lett, R. N. Watts, C. E. Tanner, S. L. Rolston, W. D. Phillips, and C. I. Westbrook, “Optical molasses,” J. Opt. Soc. Am. B 6, 2084–2107 (1989).
[CrossRef]

A. Aspect, C. Cohen-Tannoudji, E. Arimondo, N. Vansteenkiste, and R. Kaiser, “Laser cooling below the one-photon recoil energy by velocity-selective coherent population trapping—theoretical analysis,” J. Opt. Soc. Am. B 6, 2112–2124 (1989).
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H. Metcalf, “Magneto-optical trapping and its application to helium metastables,” J. Opt. Soc. Am. B 6, 2206–2210 (1989).
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D. W. Sesko, T. G. Walker, and C. E. Wieman, “Behavior of neutral atoms in a spontaneous force trap,” J. Opt. Soc. Am. B 8, 946–958 (1991).
[CrossRef]

A. M. Steane, M. Chowdhury, and C. J. Foot, “Radiation force in the magnetooptical trap,” J. Opt. Soc. Am. B 9, 2142–2158 (1992).
[CrossRef]

R. Gupta, S. Padua, C. Xie, H. Batelaan, and H. Metcalf, “Simplest atomic system for sub-Doppler laser cooling,” J. Opt. Soc. Am. B 11, 537–541 (1994).
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JETP Lett. (1)

V. S. Letokhov, “Narrowing of the Doppler width in a standing light wave,” JETP Lett. 7, 272 (1968).

Metrologia (1)

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Nature (3)

C. Monroe, “Quantum information processing with atoms and photons,” Nature 416, 238–246 (2002).
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B. P. Anderson and M. A. Kasevich, “Macroscopic quantum interference from atomic tunnel arrays,” Nature 282, 1686–1689 (1998).

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Opt. Commun. (1)

E. Kyrola and S. Stenholm, “Velocity tuned resonances as multi-Doppleron processes,” Opt. Commun. 22, 123–126 (1977).
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Opt. Lett. (6)

Phys. Rev. A (10)

A. Goepfert, I. Bloch, D. Haubrich, F. Lison, R. Schütze, R. Wynands, and D. Meschede, “Stimulated focusing and deflection of an atomic beam using picosecond laser pulses,” Phys. Rev. A 56, R3354–R3357 (1997).
[CrossRef]

K. Lindquist, M. Stephens, and C. Wieman, “Experimental and theoretical study of the vapor-cell Zeeman optical trap,” Phys. Rev. A 46, 4082–4090 (1992).
[CrossRef] [PubMed]

M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, and H. Metcalf, “Strong optical forces in frequency-modulated light,” Phys. Rev. A 64, 063411 (2001).
[CrossRef]

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Figures (18)

Fig. 1
Fig. 1

Schematic diagram of apparatus for beam slowing. The tapered magnetic field is produced by layers of varying length on the solenoid.

Fig. 2
Fig. 2

The velocity distribution measured with the TOF method. The experimental width of approximately 16(γ/k) is shown by the dashed vertical lines between the arrows. The Gaussian fit through the data yields a FWHM of 2.97 m/s (from Ref. 9).

Fig. 3
Fig. 3

Velocity dependence of the optical damping forces for 1D OM. The two dotted traces show the force from each beam, and the solid curve is their sum. The straight line shows how this force mimics a pure damping force over a restricted velocity range. These are calculated for s0=2 and δ=-γ, so there is some power broadening evident.

Fig. 4
Fig. 4

Scheme for optical brightening of an atomic beam. First the transverse velocity components of the atoms are damped out by an OM, then the atoms are focused to a spot, and finally the atoms are recollimated in a second OM (from Ref. 12).

Fig. 5
Fig. 5

A single focused laser beam produces the simplest type of optical trap.

Fig. 6
Fig. 6

Light intensity experienced by an atom located in a plane 30 μm above the beam waists of two quasi-focused sheets of light traveling parallel and arranged to form a V-shaped trough. The x and y dimensions are in micrometers (from Ref. 26).

Fig. 7
Fig. 7

Schematic diagram of the transformation of the eigenfunctions from the internal atomic states |g; p to the eigenstates |±〉. The coupling between the two states |g; p and |g; p by Raman transitions mixes them, and since they are degenerate, the eigenstates of ℋ are the nondegenerate states |±〉.

Fig. 8
Fig. 8

Energy levels of atoms moving in the periodic potential of the light shift in a standing wave. There are discrete bound states deep in the wells that broaden at higher energy and become bands separated by forbidden energies above the tops of the wells. Under conditions appropriate to laser cooling, optical pumping among these states favors populating the lowest ones as indicated schematically by the arrows.

Fig. 9
Fig. 9

(a) Fluorescence spectrum in a 1D linlin optical molasses. Atoms are first captured and cooled in an MOT; then the MOT light beams are switched off, leaving a pair of linlin beams. Then the measurements are made with δ=-4γ at low intensity. The open symbols are scaled up to emphasize the sidebands by a factor of 20 compared with the original data indicated by the filled symbols. The center peak is due to spontaneous emission of the atoms to the same vibrational state from which they are excited, whereas the sideband on the left (right) is due to spontaneous emission to a vibrational state with one vibrational quantum number lower (higher) (see Fig. 8). The presence of these sidebands is a direct proof of the existence of the band structure. (b) Same as (a) except the 1D molasses is σ+σ-, which has no spatially dependent light shift and hence no vibrational states (from Ref. 47).

Fig. 10
Fig. 10

Egg-crate potential of an optical lattice shown in two dimensions. The potential wells are separated by λ/2.

Fig. 11
Fig. 11

Plot of the measured velocity distribution versus time in the accelerated 1D lattice. (a) Atoms in a 1D lattice are accelerated for a certain time ta, and the momentum of the atoms after the acceleration is measured. The atoms accelerate only to the edge of the Brillouin zone, where the velocity is +vr, and then the velocity distribution appears at -vr. (b) Mean velocity of the atoms as a function of the quasi-momentum, i.e., the force times the acceleration time (from Ref. 56).

Fig. 12
Fig. 12

Polarization gradient field for the linlin configuration.

Fig. 13
Fig. 13

Spatial dependence of the light shifts of the ground-state sublevels of the J=1/23/2 transition for the case of the linlin polarization configuration. The arrows show the path followed by atoms being cooled in this arrangement. Atoms starting at z=0 in the Mg=+1/2 sublevel must climb the potential hill as they approach the z=λ/4 point where the light becomes σ- polarized, and there they are optically pumped to the Mg=-1/2 sublevel. Then they must begin climbing another hill toward the z=λ/2 point, where the light is σ+ polarized and they are optically pumped back to the Mg=+1/2 sublevel. The process repeats until the atomic kinetic energy is too small to climb the next hill. Each optical pumping event results in absorption of light at a lower frequency than emission, thus dissipating energy to the radiation field.

Fig. 14
Fig. 14

Spatial dependence of the light shifts of the ground-state sublevels of the J=1/23/2 transition for the case of a purely σ+ standing wave that has no polarization gradient and is appropriate for magnetically induced laser cooling. The arrows show the path followed by atoms being cooled in this arrangement. Atoms starting at z=0 in the strongly light-shifted Mg=+1/2 sublevel must climb the potential hill as they approach the node at z=λ/4. There they undergo Zeeman mixing in the absence of any light and may emerge in the Mg=-1/2 sublevel. They will then gain less energy as they approach the antinode at z=λ/2 than they lost climbing into the node. Then they are optically pumped back to the Mg=+1/2 sublevel in the strong light of the antinode, and the process repeats until the atomic kinetic energy is too small to climb the next hill. Each optical pumping event results in absorption of light at a lower frequency than emission, thus dissipating energy to the radiation field.

Fig. 15
Fig. 15

Arrangement for a MOT in one dimension. The horizontal dashed line represents the laser frequency seen by an atom at rest in the center of the trap. Because of the Zeeman shifts of the atomic transition frequencies in the inhomogeneous magnetic field, atoms at z=z are closer to resonance with the σ- laser beam than with the σ+ beam and are therefore driven toward the center of the trap.

Fig. 16
Fig. 16

Bichromatic force on moving atoms in two standing waves of frequencies ωa±δ, where δ=20γ, plotted in units of Frad=kγ/2. The Rabi frequency for each component of each standing wave was Ω=22γ, and the spatial phase shift between the two standing waves was ϕ=π/2.

Fig. 17
Fig. 17

He* atoms were produced in a LN2-cooled, dc discharge source with a longitudinal velocity distribution shown by a dashed curve. For these data the detuning δ=184 γ, Ω=225 γ, and χ=π/2, appropriate for slowing. The laser and atomic beams intersect at a few tens of milliradians, and their diameters determine the interaction length to be a few centimeters.

Fig. 18
Fig. 18

At the beginning of the frequency sweep with the atoms in the ground state (south pole), the initial detuning δ0 is much larger than the Rabi frequency Ω. Thus R executes small, rapid orbits near the south pole because the torque vector Ω is nearly polar as shown in part (a). As shown in part (b), δ=0, R executes orbits in a vertical plane because the only remaining component of the torque vector Ω is Ω, and thus Ω is in the equatorial plane. Near the end of the sweep δ is again very large, R orbits near the north pole as shown in part (c), and is finally left at the north pole with the atom in the excited state. Atoms that start at the north pole (excited state) are similarly driven in this coherent way to the south pole.

Tables (2)

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Table 1 Overview of Paper Contents

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Table 2 Parameters of Interest for Slowing Various Atoms a

Equations (21)

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F=dp/dt=kγp,
γp=s0γ/21+s0+[2(δ+ωD)/γ]2,
ωls=(Ω2+δ2-δ)/2.
F(x)=-U(x)=-γ28δIs I(x),
FOM8k2δs0vγ[1+s0+(2δ/γ)2]2-βv,
I(r)=I0exp(-r2/w02),
Fγ24δI0Isrw02exp(-2r2/w02)
H=Hatom+Hrad+Hint+Hkin,
|±(|g;-1±|g;+1)/2.
|e;0|μ|±|2=|e;0|μ|g;-1±e;0|μ|g;+1|2/2.
±(P)|Hkin|(P)=2ωrP,
ΓNC=(γs0/2)[1-1-[P/P0]2],
|±=[|g-1;-1±|g+1;+1]/2,
E=E0xˆ cos(ωlt-kz)+E0yˆ cos(ωlt+kz)=E0[(xˆ+yˆ)cos ωlt cos kz+(xˆ-yˆ)sin ωlt sin kz].
E=E0(xˆ+yˆ)cos ωlt,
E=E0[xˆ sin(ωlt+π/4)-yˆ cos(ωlt+π/4)].
ΔEg=δs0Cge2/21+(2δ/γ)2,
ωZ<kv<γp.
F=-βv-κr,
E±(z, t)=E0εˆ cos[ωctkz+β sin(ωmt±χ/2)],
γβωmβΩδ0.

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