Abstract
This paper is devoted to the study of a new atomic cavity consisting of a single horizontal concave mirror placed in the earth gravitational field. Gravity, by bending the atomic trajectories, plays the role of a second mirror closing the cavity. We first discuss the stability criterion for this cavity, assuming that the mirror has a parabolic shape. We then derive the quantum mechanical modes of such a configuration, with particular emphasis on the paraxial (i.e., close to vertical) motion. Finally, we discuss the possibility of populating those modes from an initial cold atomic cloud dropped above the mirror.
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For a recent overview see, e.g.: Laser Cooling and Trapping of Atoms, ed. by S. Chu, C. Wieman (Special Issue, J. Opt. Soc. Am. B6, 1989)
M.A. Kasevich, E. Riis, S. Chu, R. DeVoe: Phys. Rev. Lett. 63, 612 (1990)
A. Clairon, C. Salomon, S. Guellati, W. Phillips: Europhys. Lett. 16, 165 (1991)
Th. Walker, D. Sesko, C. Wieman: Phys. Rev. Lett. 64, 408 (1990)
T.J. Greytak, D. Kleppner: In New Trends in Atomic Physics, ed. by G. Grynberg, R. Stora (North-Holland, Amsterdam 1984) p. 1125
J.T.M. Walraven: In Fundamental Systems in Quantum Optics (1990), ed. by J. Dalibard, J.M. Raimond, J. Zinn-Justin (North-Holland), Amsterdam, to appear in 1992)
V.I. Balykin, V.S. Letokov: Appl. Phys. B 43, 258 (1982)
V.I. Balykin, V.S. Letokhov, Yu.B. Ovchinnikov, A.I. Sidorov: Phys. Rev. Lett. 60, 2137 (1988)
J.J. Berkhout, O.J. Luiten, I.D. Setija, T.W. Hijmans, T. Mizusaki, J.T.M. Walraven: Phys. Rev. Lett. 63, 1689 (1989)
M.A. Kasevich, D.S. Weiss, S. Chu: Opt. Letters 15, 607 (1990). In this reference the authors also mention an unpublished theoretical analysis of a gravitational cavity
For a general propagator approach to the motion of non-relativistic particles in gravitational or inertial fields, see: C. Bordé: In Fundamental Systems in Quantum Optics, ed. by J. Dalibard, J.M. Raimond, J. Zinn-Justin (North-Holland, Amsterdam, to appear in 1992)
M.A. Abramowitz, I.A. Stegun: Handbook of Mathematical Functions (Dover, New York 1972)
H. Kogelnik, T. Li: Appl. Opt. 5, 1550 (1966)
L.D. Landau, E.M. Lifshitz: Mechanics (Pergamon, Oxford 1976)
H.J. Korsch, J. Lang: J. Phys. A 24, 45 (1991)
P. Lett, W. Phillips, S. Rolston, C. Tanner, R. Watts, C. Westbrook: J. Opt. Soc. Am. B6, 2084 (1989)
D.S. Weiss, E. Riis, Y. Shevy, P.J. Ungar, S. Chu: J. Opt. Soc. Am. B6, 2072 (1989)
C. Salomon, J. Dalibard, W. Phillips, A. Clairon, S. Guellati: Europhys. Lett. 12, 683 (1990)
E. Schrödinger: Ann. d. Phys. 80, 437 (1926)
R.E. Langer: Phys. Rev. 51, 669 (1937)
M.V. Berry, K.E. Mount: Rep. Prog. Phys. 35, 315 (1972)
C. Foot, A. Steane: Europhys. Lett. 14, 231 (1990)
C. Salomon: E.N.S. (private communication)
M.A. Kasevich, D.S. Weiss, E. Riis, K. Moler, S. Kasapi, S. Chu: Phys. Rev. Lett. 66, 2297 (1991)
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Laboratoire associé au CNRS et à l'Université Pierre et Marie Curie
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Wallis, H., Dalibard, J. & Cohen-Tannoudji, C. Trapping atoms in a gravitational cavity. Appl. Phys. B 54, 407–419 (1992). https://doi.org/10.1007/BF00325387
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DOI: https://doi.org/10.1007/BF00325387