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Acta Physica Sinica

CHARACTERISTIC OF QUANTUM COLLAPSE AND REVIVAL IN THE MOTION OF A TRAPPED ATOM FOR HIGH DETUNING

Zhongjie Wang, Lu Yi-Qun, Lu Tongxing, (1)安徽师范大学物理系，芜湖 241000; (2)中国科学院安徽光学精密机械研究所，合肥 230031

Published Jan 1, 2000• 1 citation
Publisher

Abstract

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.

DOI
10.7498/aps.49.875

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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 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.
Within certain limits, the dynamics of a single trapped ion oscillating about the node of a standing-wave light field is described by the Jaynes-Cummings model, which is routinely used for cavity-QED experiments. We propose a technique to measure quantum collapse and revival in the population inversion of a single trapped ion, and show that this method is uniquely suited for the measurement of final temperatures of the trapped ion as well as for the analysis of nonclassical states of the ion motion, such as Fock and squeezed states. The results are discussed with particular consideration given to the effects of a finite laser bandwidth.