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Journal of Experimental and Theoretical Physics Letters

Chaotic Rabi vacuum oscillations in cavity quantum electrodynamics

Leonid E. Kon’kov, Sergei V Prants

Published Jun 1, 1997• 27 citations
Publisher

Abstract

It is shown in numerical simulations with two-level atoms moving through a single-mode high- Q cavity that spontaneous emission of a new type — chaotic Rabi vacuum oscillations — arises in the strong atom-field coupling regime.
DOI
10.1134/1.567433

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We study nonlinear dynamics in the fundamental cavity QED system, consisting of a point-like collection of two-level atoms moving through a single-mode cavity, with a spatially inhomogenous field. In the semiclassical, strong-coupling and rotating-wave approximations, the model is shown to be integrable with atoms moving at exact resonance through a cavity with an arbitrary spatial profile of the mode along the propagation axis. The general exact semiclassical solution is derived in an explicit form, in terms of Jacobian elliptic functions. Numerical simulation confirms that perturbations, which are produced by a modulation of the coupling between moving atoms and a cavity mode, provide, our of resonance, a mechanism responsible for Hamiltonian chaos. Taking into account the interatomic quantum correlations, we go beyond the semiclassical model and derive a dynamical system, which is able to describe vacuum Rabi oscillation with moving atoms. At resonance, this system is again shown to be integrable with a general semiquantum solution found. Out of resonance, it can demonstrate chaotic vacuum Rabi oscillations, which may be considered as a new kind of reversible spontaneous emission.
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It is shown that a type of reversible spontaneous emission, the chaotic vacuum Rabi oscillations, may occur in the interaction of two-level atoms strongly coupled with a single cavity mode under a modulation of the atom-field coupling. Such a modulation arises naturally if the atoms move through a cavity in maserlike experiments. The existence of homoclinic chaos in reversible spontaneous emission is proven analytically. Evidence of intermittency associated with the spatial modulation of the vacuum Rabi frequency is shown numerically for the values of parameters that are achievable in present-day experiments with Rydberg atoms moving through a high-Q microwave cavity in the strong-coupling regime.
Cavity qed is the domain of quantum optics which studies the behaviour of single atoms and photons coupled together in an electromagnetic resonator. During the last ten years, various spectacular effects have been observed on such systems, either on the atom’s or on the field’s properties. The presence of a cavity around an atom can produce an alteration of the atomic radiative rates which has been observed in several experiments. Ideally, cavity qed deals with two-level atoms coupled resonantly or nearly resonantly to a single cavity mode. This is of course a simplification of real situations, in which atoms have many levels and the cavity sustains more than one mode. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect. The amplitudes associated to the upper and lower atomic states oscillate as a function of time, revealing the ‘vacuum Rabi oscillation’ effect.
The spectrum of spontaneously emitted photons from an atom interacting with a single cavity mode depends on the relative sizes of the mode coupling constant and the cavity loss rate. If the coupling constant is not too large, perturbation theory can he used to show that the atomic linewidth is either increased (enhanced spontaneous emission) or decreased (inhibited spontaneous emission) by the presence of the cavity. When the coupling constant is so large that perturbation theory cannot be used, the spontaneous- emission spectrum forms a doublet, with peaks located at the normal-mode frequencies for the coupled-dipole and cavity-mode oscillators (the so-called "vacuum" Rabi splitting).