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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) 0 0 0 2 Abstract n u J The semiclassical approximation of coherent state path integrals is employed 5 1 to study the dynamics of the Jaynes-Cummings model. Decomposing the Hilbert space into subspaces of given excitation quanta above the ground 1 v state, the semiclassical propagator is shown to describe the exact quantum 2 dynamics of the model. We also present a semiclassical approximation that 7 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- 0 0 tribution of the dominant semiclassical paths and the relevant fluctuations 0 about them are evaluated. This theory leads to an accurate description of / h spontaneous emission going beyond the usual classical field approximation. p - 03.65.Sq, 42.50-p, 32.80-t t n a u q : v i X r a Typeset using REVT X E 1 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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