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Journal of Modern Optics

Effect of Atomic Coherence on the Collapses and Revivals in Some Generalized Jaynes-Cummings Models

Peng Zhou, Zhi Lin Hu, Jin Sheng Peng

Published Jan 1, 1992• 23 citations
Publisher

Abstract

The influence of the atomic coherence on the collapses and revivals of the atomic inversion is some generalized Jaynes-Cummings models is examined. It is shown that the collapse and revival times are independent of the initial state of the atom, while the amplitude of the revivals is sensitive to this coherence and the phase of the field. Under certain conditions, the amplitude of the revivals can be decreased and the revivals can become the doublet structure.

DOI
10.1080/713823345

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The influence of the atomic coherence on the collapses and revivals of the atomic inversion is some generalized Jaynes-Cummings models is examined. It is shown that the collapse and revival times are independent of the initial state of the atom, while the amplitude of the revivals is sensitive to this coherence and the phase of the field. Under certain conditions, the amplitude of the revivals can be decreased and the revivals can become the doublet structure.
In this paper we consider a system consisting of a two-level atom, initially prepared in a coherent superposition of upper and lower levels, interacting with a radiation field prepared in generalized quantum states in the framework of multiphoton Jaynes–Cummings model. For this system, we show that there is a class of states for which the fluctuation factors can exhibit the revival-collapse phenomenon (RCP) similar to that exhibited in the corresponding atomic inversion. This is shown not only for normal fluctuations but also for amplitude-squared fluctuations. Furthermore, apart from this class of states we generally demonstrate that the fluctuation factors associated with three-photon transition can provide the RCP similar to that occurring in the atomic inversion of the one-photon transition. These are novel results and their consequence is that the RCP occurring in the atomic inversion can be measured via a homodyne detector. Furthermore, we discuss the influence of the atomic relative phases on such phenomenon.
We have studied the effects of the fine structure of energy levels on the dynamics of the atom and light field. A significant influence is exhibited in the collapse-revival behavior of atomic inversion, the light squeezing, the phase of the field, and the antibunching of a light beam. When the energy difference between the doublet is large (\ensuremath{\Delta}\ensuremath{\ge}20g, where g is the coupling constant), the dynamics of the atomic inversion becomes identical to that of the usual Jaynes-Cummings model, as expected. However, the fine-structure effects on the phase and the antibunching of the light field exist in a much larger range. In particular, for a strong field, the normally ordered variance of the photon-number operator exhibits complicated collapse and revival patterns and the light displays strong antibunching in each revival envelope. Numerical calculations also show that this model does not produce significant squeezing due to the influence of the fine structure. \textcopyright{} 1996 The American Physical Society.
We study the evolution of the wavefunction in the intensity dependent Jaynes—Cummings model. It is shown that apart from the periodic revivals indicated by the dynamics of inversion, half-time revivals of the wavefunction take place in the limit of [nbar] ≫ 1. The decoupled atomic state is a superposition of the upper and lower levels and is independent of the initial atomic condition. The decoupled field state is an even or odd coherent state with a spiked distribution function, depending on the initial atomic state.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of a radiation field prepared in a Glauber-Lachs state is investigated to study the development of seemingly chaotic oscillations of the atomic inversion from a regular collapse-and-revival phenomenon, as the field statistics is changed from the coherent state to the thermal state. The effect of thermal photons on the coherent light is shown to be striking: Both the photon distribution as well as the atomic inversion are highly sensitive to even a very small addition of thermal photons to an initially coherent radiation field. We also compare the collapse and revival occurring in the micromaser case with the Glauber-Lachs version of the Jaynes-Cummings model.
Collapse and revivals in the Jaynes-Cummings model are studied within the context of the Mollow transformation for a single-mode coherent-state cavity field. The Mollow-transformed Jaynes-Cummings Hamiltonian has two atom-field terms, one corresponding to a classical field and the other to a quantized field driving the atomic transition. As such it maps onto the complementary problem of an atom in an optical cavity, whose field is initially in the vacuum state, driven by an external classical field. Both problems have the same atomic-state dynamics. It is shown that the revivals can be associated with two distinct properties of the quantized field of the transformed Hamiltonian. Revivals occurring at even (odd) multiples of the revival time are correlated with field states that are close to the initial field state and for which the average energy in the field is a minimum (maximum). Using semiclassical dressed states, we are able to map the problem for the field states onto one involving two uncoupled oscillators driven by off-resonant fields, provided effects related to dispersion are neglected. Analytic expressions for the photon number distribution of the transformed cavity field, including dispersion, are obtained for the even revival times.