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arXiv:quant-ph/0612140 · Journal of Physics A Mathematical and Theoretical

Quantum statistical properties of the Jaynes–Cummings model in the presence of a classical homogeneous gravitational field

M Mohammadi, M. H. Naderi, M. Soltanolkotabi

Published Jan 23, 2007• 16 citations
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Abstract

The temporal evolution of quantum statistical properties of an interacting atom–radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes–Cummings model. To analyse the dynamical evolution of the atom–radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving the Schrödinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behaviour of the atom–radiation system is explored. Assuming that initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.

DOI
10.1088/1751-8113/40/6/014

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The temporal evolution of quantum statistical properties of an interacting atom–radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes–Cummings model. To analyse the dynamical evolution of the atom–radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving the Schrödinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behaviour of the atom–radiation system is explored. Assuming that initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.
In this paper, we investigate the effects of a classical gravitational field on the dynamical behaviour of the nonlinear atom–field interaction within the framework of the f-deformed Jaynes–Cummings model. For this purpose, we first introduce a set of new atomic operators obeying an f-deformed su(2) algebraic structure to derive an effective Hamiltonian for the system under consideration. Then by solving the Schrodinger equation in the interaction picture and considering certain initial quantum states for the atomic and radiation subsystems, we analyse the influence of gravity on the temporal evolution of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and deformed quadrature squeezing of the radiation field.
The effective mass that approximately describes the effect of a classical homogeneous gravitational field on an interacting atom-radiation field system is determined within the framework of the Jaynes-Cummings model. By taking into account both the atomic motion and gravitational field, a full quantum treatment of the internal and external dynamics of the atom is presented. By solving exactly the Schrodinger equation in the interaction picture, the evolving state of the system is found. Influence of a classical homogeneous gravitational field on the energy eigenvalues, the effective mass of atom-radiation field system and the Wigner distribution of the radiation field are studied, when initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states.
In this paper, the non-Markovian dissipative dynamics of the phase-damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field will be analyzed. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a non-Markovian phase damping mechanism. First, the non-Markovian master equation for the reduced density operator of the system in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field will be presented. Then, the superoperator technique will be generalized and an exact solution of the non-Markovian master equation will be obtained. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, and photon counting statistics of the radiation field in the presence of the non-Markovian phase damped will be investigated.
In this paper, we investigate the effects of a classical gravitational field on the dynamical behaviour of nonlinear atom-field interaction within the framework of the f-deformed Jaynes-Cummings model. For this purpose, we first introduce a set of new atomic operators obeying an f-deformed su(2) algebraic structure to derive an effective Hamiltonian for the system under consideration. Then by solving the Schrodinger equation in the interaction picture and considering certain initial quantum states for the atomic and radiation subsystems, we analyze the influence of gravity on the temporal evolution of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics, and deformed quadrature squeezing of the radiation field.
The eigenvalues and eigenstates of the effective Hamiltonian in the interaction of the atom with both classical gravity and quantum radiation within the framework of the Jaynes–Cummings model are obtained. By taking into account both the atomic motion and gravitational field a full quantum treatment of the internal and external dynamics of the atom is presented. By solving exactly the Schrodinger equation in the interaction picture, the evolving state of the system is found by which the the eigenvalues of the atom–field system are obtained. Also, the influence of gravity on atomic dipole squeezing is investigated.
The system of a two-level atom interacting with a quantized radiation field in a gravitational field is studied by making use of a dynamical algebraic method. A full quantum treatment of the internal and external dynamics of the atom is given and an exact expression for the time evolution operator of the system is obtained. The influence of the gravitational field on the collapses and revivals of the atomic population, sub-Poissonian statistics, radiation force, atomic momentum diffusion, and squeezing of the radiation field is also investigated.