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Journal of Anhui Normal University

QUANTUM CHAOS IN THE MOTION OF A TRAPPED ATOM FOR HIGH DETUNING

Zhong Wang

Published Jan 1, 2001• 0 citations
OpenAlex

Abstract

The quantum dynamics of the trapped atoms, which acts with a standing light field and traveling light field, is investigated. This quantum system shows chaotic behavior in the classical limit. Evolution of the quantum mean energy of the atom with time displays the characteristic of collapse-revival when corresponding classical system is integrable. The coherence characteristic of regular collapse-revival will disappear when corresponding classical system is non-integrable.

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The quantum dynamics of the trapped atoms, which acts with a standing light field and traveling light field, is investigated. This quantum system shows chaotic behavior in the classical limit. Evolution of the quantum mean energy of the atom with time displays the characteristic of collapse-revival when corresponding classical system is integrable. The coherence characteristic of regular collapse-revival will disappear when corresponding classical system is non-integrable.
In this paper the quantum dynamics of the trapped atom which acts with a standing light field and a travelling light field is investigated. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse-revival which implies that the vibration states of the system have squeezing effect. The larger the nonlinearity of the system, the higher the frequency of collapse-revival of the system, and the smaller the quantum mean energy of the ion. The higher the intensity of the travelling light field, the higher the degree of squeezing of the vibration states of the system can be observed.
The quantum dynamics of a trapped ion which acts with two standing light fields with different frequency is investigated on the condition of high detuning. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the ion have squeezing effect. The higher the value of the squeezing parameter G 3 . The higher the degree of squeezing of the vibration states of the ion can be observed. If G 3 is greater than a particular value, the degree of squeezing will become smaller.
In this paper the dynamics of the two level trapped ion which acts with standing light field is investigated analytically. Evolution of the quantum mean energy of the ion with time displays the characteristic of collapse revival which implies the vibration states of the system have squeezing effect. The collapse revival of the quantum mean energy of the ion will become irregular because of the higher term in Hamiltonian of the system. The higher term will suppress coherence of the vibration state of the ion.
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.
A single two-level atom, with quantized centre-of-mass motion, is constrained to move in a one-dimensional harmonic potential, while interacting with a single-mode classical travelling light field. When the atom's centre-of-mass motion is in a coherent state, we show that the atomic inversion exhibits collapses and revivals. Whereas in the Jaynes-Cummings model this behaviour occurs due to the discrete nature of the light field, in our case the behaviour is due to the discrete nature of the vibrational trap states. The Q -function for the external motion is also calculated and shown to break into two peaks in the collapse region. Finally the parameter ranges under which the collapses and revivals can be observed are discussed, as well as the possibility of an experiment.