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Physical Review A

Quantum collapses and revivals in a nonlinear Jaynes-Cummings model

David A. Cardimona, Vassilios I. Kovanis, M. P. Sharma, A. Gavrielides

Published Apr 1, 1991• 72 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.43.3710

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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 investigate the atomic inversion dynamics that occur when an atom interacts with a two-mode quantized radiation field. Our work uses Schrodinger theory with the rotating wave approximation. We adiabatically eliminate all but two of the atomic states in order to obtain analytical and numerical results. By varying the width and average photon number of the field statistics, we have uncovered secondary revivals that arise because of the complicated double sum over the two field modes in the population inversion. The diagonal part of the sum (the part that contains commensurate frequencies) is closely related to the degenerate-mode work of Buck and Sukumar.1 The breaking of the exact periodicity with secondary revivals and eventual erratic behavior result from the off-diagonal terms. Use of Poisson statistics allows exact analytic results to be obtained and also allows comparisons with previous work to be made. However, because the width and mean are intimately related for Poisson statistics, we also use Gaussian statistics so that their effects may be separated. To investigate various possible initial field conditions, we use squeezed states (oscillatory in photon number), displaced number states, and generalized states. The latter interpolate between number states, coherent states, and thermal states.
We investigate the effect of the Stark shifts on the atomic-inversion dynamics when a multilevel atom interacts with a two-mode quantized radiation field. We utilize Hamiltonians obtained by adiabatically eliminating all but two of the atomic levels and including terms that give rise to the Stark shifts for a Raman-type process as well as for equal- and unequal-frequency two-photon absorption. We find that the Stark effect is relatively unimportant for Raman scattering but should not be ignored in equal- or unequal-frequency absorption. In equal-frequency absorption, the atomic dynamics can be made exactly periodic through an appropriate choice of detuning.
The two-photon absorption process is studied by considering the interaction of a quantized single-mode field with an effective two-level atom through intermediate states. The equations of motion of the coupled atom–field probability amplitudes for the effective two-level atom are obtained after adiabatically eliminating the intermediate states. These equations are then solved in the rotating-wave approximation. The time constants associated with the Rabi oscillation, collapse, and revival of the atomic inversion are derived, and the photon statistics are discussed with special reference to photon antibunching.
In this paper we study the interaction between two-level atom and quantized single-mode field, namely, Jaynes-Cummings model (JCM). The field and the atom are initially prepared in the binomial state and the excited atomic state, respectively. For this system we prove that the revival-collapse phenomenon exhibited in the atomic inversion of the standard JCM can be numerically (naturally) manifested in the evolution of the squeezing factor of the three-photon (standard) JCM provided that the initial photon-number distribution of the radiation has a smooth envelope.
In this paper we consider a system consisting of a two-level atom in an excited state interacting with two modes of a radiation field prepared initially in l -photon coherent states. This system is described by a two-mode multiphoton (i.e., k 1 , k 2 ) Jaynes–Cummings model (JCM). For this system we investigate the occurrence of the revival–collapse phenomenon (RCP) in the evolution of the single-mode, two-mode, sum and difference quadrature squeezing. We show that there is a class of states for which all these types of squeezing exhibit RCP similar to that involved in the corresponding atomic inversion. Also we show numerically that the single-mode squeezing of the first mode for ( k 1 , k 2 ) = (3,1) provides RCP similar to that of the atomic inversion of the case ( k 1 , k 2 ) = (1,1); however, sum and difference squeezing give partial information on that case. Moreover, we show that single-mode, two-mode and sum squeezing for the case ( k 1 , k 2 ) = (2,2) provides information on the atomic inversion of the single-mode two-photon JCM. We derive the rescaled squeezing factors giving accurate information on the atomic inversion for all cases. The consequences of these results are that the homodyne and heterodyne detectors can be used to detect the RCP for the two-mode JCM.