Semiclassical Dynamics of the JaynesCummings Model.pdf
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Semiclassical Dynamics of the Jaynes-Cummings Model
Adrian Alscher and Hermann Grabert
Fakult¨at f¨ur Physik, Albert-Ludwigs-Universit¨at,
Hermann-Herder-Strasse 3, D-79104 Freiburg, Deutschland
(February 1, 2008)
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2 Abstract
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The semiclassical approximation of coherent state path integrals is employed
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1 to study the dynamics of the Jaynes-Cummings model. Decomposing the
Hilbert space into subspaces of given excitation quanta above the ground
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v state, the semiclassical propagator is shown to describe the exact quantum
2 dynamics of the model. We also present a semiclassical approximation that
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0 does not exploit the special properties of the Jaynes-Cummings Hamiltonian
6 and can be extended to more general situations. In this approach the con-
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0 tribution of the dominant semiclassical paths and the relevant fluctuations
0 about them are evaluated. This theory leads to an accurate description of
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h spontaneous emission going beyond the usual classical field approximation.
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I. INTRODUCTION
Since the sixties of the last century the Jaynes-Cummings model [1] is frequently con-
sidered as a simple model to describe a two-level atomic system interacting with an
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