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Optical Fiber Communication Conference

Correlation between translational and internal motion of a single atom in a hig-finesse cavity

Sergey V. Prants, V. Yu. Sirotkin

Published Jan 1, 2001• 0 citations
Publisher

Abstract

In the strong-coupling regime we study the full correlated dynamics of a cold atom in a standing-wave cavity field with the center-of-mass motion included and show how to create effective periodic optical potentials to drive the motion by varying the atom-field detuning.
DOI
10.1364/icqi.2001.pa34

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We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly-coupled atom-cavity system with atomic center-of-mass motion included in modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigen frequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of external sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low- frequency translational motion is modulated by the high- frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultra cold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, the effect which is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
A new effect of chaotic motion of the center of mass of a cold atom in the coherent field of a standing light wave in a high-finesse Fabry-Pérot cavity is theoretically predicted and numerically implemented in the absence of any random fluctuations due to spontaneous emission. Numerical experiments demonstrate that the Hamiltonian chaos arises near resonance in the range of parameters characteristic of the strong coupling regime that was implemented in recent experiments. The effect is of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.
Strong coupling of the internal and external degrees of freedom of a cold atom to each other and to the spatially periodic field of the standing light wave in a high-finesse cavity is responsible for the dynamic instability of the atomic center-of-mass motion. Due to a weak interaction of the internal nonlinear resonances in the standard model of cavity QED, a stochastic layer appears, whose width in the semiclassical approximation is estimated in terms of the main parameters of the system: atomic recoil frequency, mean number of excitations, and detuning from the resonance. As a result, the atomic motion in the absolutely regular potential has the fractal character, with long Lévy flights alternating with small chaotic oscillations in potential wells.
by Mambwe Mumba We examine a system comprised of a single two-level atom inside a driven optical cavity.We allow for cavity decay and atomic spontaneous emission out the side of the cavity.There is a spatial dependent coupling between the atom and the cavity mode, which we take into account, using explicit trapping potentials for the atom.Previous work has revolved around a harmonic oscillator potential, we also find here a solution for a realistic optical lattice potential when the lattice wavelength is half the driving laser wavelength.Atomic and cavity detunings are included, as well as effective Franck-Condon factors.Analytic results are obtained for various intensity-intensity and field-intensity correlation functions, using quantum trajectory theory in the weak driving field limit.Nonclassical effects are obtained, and we investigate the effect of a nonstationary atom on these effects.These result from violation of inequalities that must be satisfied if there is an underlying classical stochastic field; violations imply that there is no well defined electric field at all times, with some underlying positive definite probability distribution.The center of mass wave function is specified either by a list of probability amplitudes, or these amplitudes are calculated from an explicit wave function(typically a Gaussian).The correlation functions are quite sensitive to the center of mass wave function, and perhaps correlation functions can be used as probes of atomic motion.We also examine a new inequality between intensity-intensity and field intensity correlation functions, that is violated here.
We study the coupled translational and internal dynamics of a two-level atom in a spatially periodic optical potential created by a single-mode field in a high-finesse Fabry-Perot cavity. The strongly coupled atom-cavity system with atomic center-of-mass motion included is modeled by semiclassical nonlinear Heisenberg equations of motion with two degrees of freedom. At exact resonance between the internal atomic transition and the cavity eigenfrequency, the internal and translational degrees of freedom are separated from each other resulting in periodically modulated Rabi oscillations and regular translational motion. Near the atom-field resonance, the coupled dynamics is found to be irregular and even chaotic in the sense of extremal sensitivity to initial conditions. It is manifested as a chaotic motion of an atom in an absolutely regular spatially periodic potential in the absence of any random fluctuations. This effect may be explained as a result of the interaction of nonlinear resonances in the atom-field nonlinear pendulum whose low-frequency translational motion is modulated by the high-frequency Rabi oscillations. The irregular motion is studied in detail in numerical experiments using the arsenal of methods of the dynamical systems theory. The results obtained are compared with recent experiments with ultracold single atoms interacting with single photons in the strong-coupling regime. We estimate the ranges of the system's control parameters, the detuning, the recoil frequency, and the mean number of intracavity photons, in which the interaction of nonlinear resonances may lead, under realistic conditions, to local instability of the center-of-mass motion and some manifestations of dynamical chaos, which is the effect of interest in studying the quantum-classical correspondence and quantum chaos in atomic optics.