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Physical Review A

Collapse and revival phenomenon in the evolution of a resonant field in a Kerr-like medium

G. S. Agarwal, Ravinder Rupchand Puri

Published Mar 1, 1989• 140 citations
Publisher

Abstract

A quantum theory of the propagation of a single-mode resonant field through a Kerr-like medium is given. Numerical studies show the existence of the quantum collapses and revivals in the otherwise periodic exchange of energy between the field and the atomic oscillator. Approximate analytical methods are developed to explain the numerical results for the case of weak nonlinearity of the Kerr medium. For large nonlinearity, the correspondence with the Jaynes-Cummings model is discussed.

DOI
10.1103/physreva.39.2969

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A quantum theory of the propagation of a single-mode resonant field through a Kerr-like medium is given. Numerical studies show the existence of the quantum collapses and revivals in the otherwise periodic exchange of energy between the field and the atomic oscillator. Approximate analytical methods are developed to explain the numerical results for the case of weak nonlinearity of the Kerr medium. For large nonlinearity, the correspondence with the Jaynes-Cummings model is discussed.
The collapse-and-revival phenomenon in the population inversion and the time evolution of the quasiprobability Q function of an atom undergoing a two-photon process are investigated when the cavity is supposed to be filled with a Kerr-like medium. An exact expression for the atomic population inversion has been given for a field initially in the coherent state. The closed form of this expression as well as that of the Q function are obtained under the high-field approximation. Also, the tendency toward inhibited decay of the excited state has been explicitly shown. This study reveals how the simultaneous occurrence of two nonlinear processes affects the atomic dynamics.
We study the non-resonant interaction of a moving four-level N -type atom with cavity fields in the presence of a nonlinear Kerr-like medium. The exact solutions of the considered models are obtained when the atom is initially in an upper state, while the field is in a coherent state. We derive an expression for the occupation numbers of the photon state. Also, the momentum increment of the atomic system is obtained. The influence of the detuning parameters or the Kerr medium on the evolution time of the momentum increment is examined numerically. The existence of the detuning parameters leads to the retraction of the revivals for the three atomic systems. On the other hand, the presence of the Kerr medium is conducive to increasing the regularity and periodicity of the collapse–revival phenomenon for the one- and two-mode systems, while chaotic behaviour occurs for the three-mode system.
We investigate the atomic inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field in a Raman-type process. By utilizing the rotating-wave approximation and adiabatically eliminating all but two of the atomic levels, we derive a nonlinear-interaction Hamiltonian for this system. Working in the Schr\"odinger picture, we obtain numerical results that depend on the width and average photon number of the field statistics. Varying these photon statistics allows us to uncover secondary revivals that arise due to the complicated double sum over the two field modes that appear in the solutions. The origin of this phenomenon is described analytically.
We show that a single mode of an electromagnetic field in the binomial state or in the squeezed coherent state, propagating in a non-absorbing nonlinear medium modelled as an anharmonic oscillator, gives rise to interesting quantum effects such as collapses and revivals in the energy exchange between the field and the medium. Analytic expressions are obtained for the energy exchange variable. We have exploited the characteristics of the binomial state which provides a means of systematic study of the collapses and revivals with variation in the field statistics from Poissonian to sub-Poissonian. Effects of variation in initial squeezing in the field are also included.
The time evolution of atomic population of the system, where the two identical two-level atoms in Bell states interact with two-mode entangled coherent field in a cavity filled with the Kerr medium, was investigated by means of quantum theory and numerical method. The effects of the atomic initial state, mean photon numbers of field, the degree of the entanglement for the entangled coherent field, and the coupling strength between the Kerr medium and field on the atom’s population are discussed via numerical calculations. The results show that the atomic population is time-independent provided that the atoms are in β11〉 state. For the other three Bell states, there will appear the periodical collapse-revival of atomic population if the initial mean photon number reaches some special values. With the increase of the initial mean photon number, the oscillation frequency of the time-evolution of atomic population increases correspondingly, and the amplitude decreases. The degree of the entanglement of the two-mode entangled coherent field has no effect on the frequency of the Rabi oscillation, but has an obvious effect on the amplitude of Rabi oscillation. When the coupling strength between the Kerr medium and field reaches some special values, it has the obvious effects on the cycle of collapse-revival of atomic population, the frequency and the amplitude of Rabi oscillation.