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Modern Physics Letters B

Jaynes–Cummings Model with Intensity Independent Interaction and Initial Field in the Binomial State

B. Baseia, Gil C. Marques, S. B. Duarte, A. L. De Brito

Published Jan 10, 1997• 0 citations
Publisher

Abstract

Recently, we introduced a new version of the Jaynes–Cummings model in which the interaction Hamiltonian is independent of the excitation number, or field intensity. Exact solution for this model was found allowing the study of nonclassical effects exhibited by the atom and the field, the latter initially in a coherent state. Here, we extend this study to the case of a field initially in the binomial state to investigate those nonclassical effects, as population trapping and sub-Poissonian statistics as function of the interpolating parameters of this state. The previous results are obtained from the present treatment, in the limit of a coherent state allowed by the binomial state.

DOI
10.1142/s0217984997000050

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Recently, we introduced a new version of the Jaynes–Cummings model in which the interaction Hamiltonian is independent of the excitation number, or field intensity. Exact solution for this model was found allowing the study of nonclassical effects exhibited by the atom and the field, the latter initially in a coherent state. Here, we extend this study to the case of a field initially in the binomial state to investigate those nonclassical effects, as population trapping and sub-Poissonian statistics as function of the interpolating parameters of this state. The previous results are obtained from the present treatment, in the limit of a coherent state allowed by the binomial state.
We introduce a new version of the JC-Model using the (non-Hermitian) phase operators [Formula: see text] in the interaction Hamiltonian, which becomes independent of the excitation number or the field intensity, thus being able to describe properties of the atom in the saturation regime. We employ the “dressed-states” formalism to find an exact solution for our system. As applications we investigate the occurrence of nonclassical effects in the field (squeezing and sub-Poissonian statistics) and in the atom (collapses and revivals of Rabi oscillations and population trapping).
An electromagnetic field state is found which maintains the population inversion of the atom stationary during the interaction with the field through a Jaynes-Cummings model (JCM) with a Kerr type nonlinearity in the cavity. The condition of stationarity of the population inversion includes the phase coupling of atomic dipole with the field. We have shown that the Kerr nonlinearity in the cavity field significantly modifies the photon statistics of the trapped field state through an intensity dependent detuning in the field compared to the normal JCM trapping state. We have also demonstrated the novel features of sub-Poissonian character and the squeezing of the trapped field state. The dynamics of the initial trapped field is studied in terms of squeezing and the Q-function.
We have shown that the Jaynes-Cummings model (JCM) with an environment-induced pure decoherence is an exactly solvable problem. Rabi oscillation of atomic population inversion and oscillation in the field population get trapped due to decoherence. But the decay of the coherence properties of the atom as well as of the field is comparatively slower than that of the population terms. It is also shown that although the fast oscillation in nonclassical properties are suppressed due to decoherence but an initial Poissonian field acquires a sub-Poissonian character in the steady state. So unlike the ordinary spontaneous emission all the nonclassical properties of the system are not erased.
The Jaynes-Cummings model describes the interaction between a two-level atom and a single mode of the radiation field. This system has a conservation law which restricts its dynamics. On the basis of this conservation law alone one can make useful statements about the photon statistics of the fields which arise in the model. Two cases are considered. In the first the field is initially in a coherent state. Here it is found that the field statistics become less sub-Poissonian as the amplitude of the initial state increases. The case of an initial thermal state is also considered. In that situation, if the average number of photons present in the initial state is greater than 2.55, then the field statistics can never become sub-Poissonian.