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Lecture notes in physics. M, Monographs

Weak Quantum Chaos in a System of N Atoms in a Resonant Cavity Interacting with an External Resonant Field

Published Oct 3, 2008• 0 citations
Publisher
DOI
10.1007/978-3-540-48415-8_14

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With the help of Lyapunov exponents different routes to quantum chaos are demonstrated numerically in two semiclassical models of the interaction of N two-level atoms with their own radiation field in a resonant cavity. The usual transition to chaos is observed when varying the external control parameter b which describes the interaction of the atomic ensemble with the field. After reaching its critical value b approximately equal to 1 the system becomes more and more chaotic as b increases. As the second control parameter a (the dimensionless individual Rabi frequency) increases the system undergoes transitions to chaos by a completely different way. We observe a complex sequence of order-to-chaos transitions that resembles those for the classical Lorenz attractor.
Nonlinear dynamics in the fundamental interaction between a two-level atom with recoil and a quantized radiation field in a high-quality cavity is studied. We consider the strongly coupled atom-field system as a quantum-classical hybrid with dynamically coupled quantum and classical degrees of freedom. It is shown that at given initial conditions the regime of atomic motion is governed mainly by the detuning of the atom-field resonance /spl delta/. We show that, even in the absence of any other interaction with environment, the interaction of a purely quantum atom-field system with the external atomic degree of freedom provides the emergence of classical dynamical chaos from quantum electrodynamics (QED). It manifest itself in the classical degree of freedom as a random walking of an atom inside the cavity and in the quantum degrees of freedom as a sensitive dependence of atomic inversion on small variations in initial conditions. It is shown that dependence of variance of entanglement on /spl delta/, correlates strongly with the dependence of maximum Lyapunov exponent on /spl delta/. This result provides a quantum-classical correspondence in a closed physical system.