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Journal of the Optical Society of America B

Dynamics of a two-mode two-photon Jaynes–Cummings model interacting with correlated SU(1, 1) coherent states

Christopher C. Gerry, Ronald F. Welch

Published Feb 1, 1992• 36 citations
Publisher

Abstract

We study the quantum dynamics of a two-mode two-photon Jaynes–Cummings model of a two-level atom interacting with the correlated two-mode SU(1, 1) coherent states. The collapse and revival patterns in this case are noted to be quite different from those in the case of uncorrelated coherent states and correlated pair-coherent states. As an example of the time evolution of the field statistics we show that violation of the Cauchy–Schwartz inequality by the initial field states may be nullified. We also discuss the evolution of the variance of the two-mode field quadrature operator.

DOI
10.1364/josab.9.000290

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We study the quantum dynamics of a two-mode two-photon Jaynes–Cummings model of a two-level atom interacting with the correlated two-mode SU(1, 1) coherent states. The collapse and revival patterns in this case are noted to be quite different from those in the case of uncorrelated coherent states and correlated pair-coherent states. As an example of the time evolution of the field statistics we show that violation of the Cauchy–Schwartz inequality by the initial field states may be nullified. We also discuss the evolution of the variance of the two-mode field quadrature operator.
The state function of the two-mode SU(1,1) coherent states field interacting with a four-level atom is derived by means of quantum theory.It is studied that the two-mode intensity correlation function,the Cauchy-Schwartz inequality and the second-order coherence properties for each mode of the light field in the system of the two-mode SU(1,1) coherent states field interacting with four-level atom.It is discussed that the influence of the coupling coefficient between the light field and atom and the initial intensity of the light field on file quantum dynamics of the light field.The results of the studies indicate that the statistic properties of the photon depend on the initial state of the system,the correlation of the two-mode of light is both positive and non-classical,the photon anti-bunching of the first mode appear at all time,and the photon bunching and anti-bunching of the second mode appear alternately.
We investigate quantum nonlocality dynamics of a three-level atom and a class of two-mode non-classical states (including the entangled coherent state, the pair coherent state and the two-mode squeezed state) in the non-degenerate two-photon Jaynes-Cummings model. It is shown that the time evolution of the Bell nonlocality for the case of the entangled coherent state is closely related to the average number of photons in the two-mode field. For the cases of the pair coherent state and the two-mode squeezed state, the effect of Bell nonlocality sudden death is demonstrated, and the absolute value of the 〈BCHSH〉 exhibits exact periodic collapses and revivals.
We present a two-mode squeezed Jaynes–Cummings model, built upon the formalism of pair coherent states (PCSs), to investigate the dynamics of a two-level atom interacting with a two-mode quantized field. By solving the time-dependent Schrödinger equation under the rotating-wave approximation, we elucidate the system’s quantum evolution, with particular emphasis on how the squeezing degree and photon number difference modulate atomic population inversion and entanglement. We further quantify the nonclassical traits of the two-mode squeezed PCSs via Mandel’s parameter and the violation of the Cauchy–Schwarz inequality, highlighting their sensitivity to model parameters. These findings illuminate the subtle interplay of squeezing, photon statistics, and entanglement in advanced quantum optical systems.
The collapse and revival of quantum states appear in diverse areas of physics. In quantum optics the occurrence of such a phenomena in the evolution of an atomic state, interacting with a light field initially in a coherent state, was predicted by using the Jaynes-Cummings model (JCM), and subsequently demonstrated experimentally. In this paper we revisit the JCM with the Monte-Carlo wave function approach and investigate the time evolution of the photon emission rate of the atom in a cavity. Analytical and numerical quantum trajectory calculations show that the cavity and the initial field statistics strongly influence the photon emission dynamics. A coherent field indeed gives rise to a collapse and revival behavior that mirrors atomic state evolution. However, there are differences between the two. The emission rate for a field in a Fock number state exhibits a sinusoidal oscillation, and there exists a quiescent period for a thermal field. These properties are quite different from those in free space. It is also shown that the fluctuation in photon emission is much less than that of the atomic population.