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International Journal of Quantum Chemistry

Theoretical study on quantum dynamics of bose system interacting with photon field

Hidemi Nagao, Masayoshi Nakano, Kiyoshi Nishikawa, Kizashi Yamaguchi

Published Jan 1, 2001• 1 citation
Publisher

Abstract

Abstract We investigate the quantum dynamics of two‐boson and two‐level systems interacting with a one‐mode photon field. The time evolution of the population for each state is calculated in terms of the Jaynes–Cummings model. We find the collapses and revivals of the order parameter for the Bose–Einstein condensation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 401–408, 2001

DOI
10.1002/qua.1090

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Abstract We investigate the quantum dynamics of two‐boson and two‐level systems interacting with a one‐mode photon field. The time evolution of the population for each state is calculated in terms of the Jaynes–Cummings model. We find the collapses and revivals of the order parameter for the Bose–Einstein condensation. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 401–408, 2001
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 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.
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.
In this paper, we study the interaction between the time-dependent field and a two-level atom with one mode electromagnetic field. We consider that the field of photons is assumed to be coupled with modulated coupling parameter which depends explicitly on time. It is shown that the considered model can be reduced to a well-known form of the time-dependent generalized Jaynes–Cummings model. Under special initial conditions, in which the atom and the field are prepared in the excited and the coherent states, respectively, the explicit time evolution of the wave function of the entire system is analytically obtained. Our proposal has many advantages over the previous optical schemes and can be realized in several multiple experiments, such as trapped ions and quantum electrodynamics cavity. The influence of the time-dependent field parameter on the collapses-revivals, the normal squeezing of the radiation, the anti-bunching of photons and the entanglement phenomena for the considered atomic system is examined. The linear entropy, the von Neumann entropy are used to quantify entanglement in the quantum systems. We noticed that these phenomena are affected by the existence of both the time-dependent coupling field and detuning parameters.
Abstract In this paper we present a general theoretical model for the interaction between a number of two-level atoms constituting Bose-Einstein condensate (BEC) and a single-mode quantized field. In addition to the usual interacting terms, we take into account interatom as well as higher-order atom-field interactions. To simplify the Hamiltonian of system, after using the Bogoliubov approximation we proceed to calculate the transformed operators of atoms and field. Then, to quantify the spontaneous emission, we get analytical expressions for the expectation value of J ^ z as the atomic population inversion (API), in the cases of number and coherent states for the atomic subsystem. Our results show that the above-mentioned model interaction leads to the appearance of collapse-revival phenomenon in API. In more detail, the revival time may be tuned by adjusting the interatom interaction constant. Also, the damping process lowers the amplitude of API, but does not change the CR times for weak damping. Moreover, increasing the damping may decrease the number of CRs in a given interval of time such that no revival occurs. Briefly, it may be concluded that in the resonant case the revival times are insensitive to the change of the higher-order atom-field interaction constant and are affected only by the interatom interactions. Finally, we express that, how we can find a practical procedure to measure the quantum states of atoms in BEC .