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Physical Review A

Dynamics of a two-level model with fine structure

Chun-rong Fu, Aly A. Shaban, Chang-De Gong

Published Jun 1, 1996• 2 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.53.4500

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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.
The Jaynes–Cummings interaction of a two-level atom with the radiation field is studied when the radiation is initially in a strongly squeezed coherent state. The dynamic response of the atomic inversion shows echoes after each revival when the squeezed coherent state exhibits an oscillatory photon-counting distribution due to the phase-space interference effect. The sensitivity of the dynamic behavior to approximations used in computing the atomic inversion is discussed. Comparison is made with the intensity-dependent interaction model of Buck and Sukumar [ Phys. Lett.81A, 132 ( 1981)]; this model does not exhibit echoes. The mean, variance, and entropy for the photon-number distribution are calculated and found to show behavior similar to that of the atomic inversion.
The dynamics of the Jaynes-Cummings interaction of a two-level atom interacting with a single mode of the radiation field is investigated, as the state of the field is gradually changed from a coherent state to a squeezed coherent state. The effect of mild squeezing on the coherent light is shown to be striking: the photon number distribution gets localized and it peaks maximally for a particular value of squeezing. The atomic inversion retains its structure for a longer time. The mean linear entropy shows that the atom has a tendency to get disentangled from field within the collapse region and also in the revival region, for mild squeezing. These properties are absent for the case of a coherent state or for an excessively squeezed coherent state. We also elucidate a connection between these properties and the photon statistics of the mildly squeezed coherent state; these states have the minimum variance and are also maximally sub-Poissonian.
We investigate some of the fundamental features of the interaction of squeezed light with two-level atoms in the framework of the Jaynes-Cummings model. We start our analysis by calculating the collapses and revivals of the atomic inversion. We discuss the degree of purity of the field (given by the entropy) and its disentanglement from the atomic source. The connection with the evolution of the Q-function is also made. We notice that contrary to the coherent state case, the field turns into a nearly pure (squeezed) state at the revival time as if the field was prepared in a coherent state. The field also becomes a superposition of squeezed states at half of the revival time, and this is confirmed by investigating the photon number distribution. The phase properties of the field are discussed using the Pegg-Barnett formalism.
With the help of a two-photon Jaynes-Cummings model, which is an exactly solvable model, we have dealt analytically with the dynamical behavior of the atom and the field for a two-photon process in squeezed and coherent fields under the appropriate approximation. The features of collapses and revivals of Rabi oscillations for the atom and the field in a two-photon process represent strict periodicity. The phase jump and the large and negative frequency for the combination Rabi oscillation are exhibited in the case of a squeezed field. The results show that squeezing in a field strikingly affects the evolution behavior of the atom and the field.
With the concept of negative photon and the -photon J C model, we investigate analytically the effect of virtual photon field on the collapse revival effect of atomic inversion and squeezing of atom, we find that there is a significant effect of virtual photon field on atomic inversion and squeezing of atom; with the one-photon model as an example, we find that the squeezing of atom occurs periodically, the time and times of squeezing are only related to the resonance frequency and the amplitude of squeezing related to coupling constant of atom field, mean photon number and resonance frequency; also we show that the effect of squeezing of atom does not exist within rotating wave approximation if . Taking the approach of nearest-neighboring spectrum in the quantum chaos field, we investigate the properties of energy spectrum in one-photon JC model and show that the integrable region, non-integrable region and transition region of this system can be illustrated by a phase diagram;also we discuss the influence of interaction of atoms on spectrum and statistics of adjacent energy levels, we find that the influence of interaction is little obvious in strong field but takes great important role in weak field.