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Chinese Journal of Luminescence

EFFECTS OF HYPERGEOMETRIC STATE ONTHE DYNAMICAL EVOLUTION OFINTENSITY-DEPENDENT JAYNES-CUMMINGS MODEL

Wang Xiao-guan

Published Jan 1, 1999• 0 citations
OpenAlex

Abstract

The hypergeometric state is a one-parameter generalization of the binomial state. Itcan reduce to the binomial state in certain limit. The interaction of the binomial statewith two-level atoms in cavities has been studied in detail in the literature. In this article, we study the interaction of the hypergeometric state with two-level atoms. We usethe intensity-dependent Jaynes-Cummings model and the interaction is of intensity-dependent type. The dynamics of atomic population inversion and second order correlationfunction of the field were studied in detail. The collapse and revival phenomena arefound when the initial field state is the hypergeometric state. The field can show antibunching effects. The anti-bunching effect is better than that of the binomial state.

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Modern Physics Letters B•Jan 10, 1997•0 citations
The hypergeometric state is a one-parameter generalization of the binomial state. Itcan reduce to the binomial state in certain limit. The interaction of the binomial statewith two-level atoms in cavities has been studied in detail in the literature. In this article, we study the interaction of the hypergeometric state with two-level atoms. We usethe intensity-dependent Jaynes-Cummings model and the interaction is of intensity-dependent type. The dynamics of atomic population inversion and second order correlationfunction of the field were studied in detail. The collapse and revival phenomena arefound when the initial field state is the hypergeometric state. The field can show antibunching effects. The anti-bunching effect is better than that of the binomial state.
The dynamical properties of a two-level atom interacting with a single non-decaying mode of an electromagnetic field in a binomial state are studied. The statistical aspects of the field, such as intensity-intensity correlation and squeezing, are also investigated. The binomial state reduces to a pure number state and a pure coherent state in different limits. Hence it enables us to study how the sinusoidal Rabi oscillations in a pure number state develop to give rise to the phenomenon of collapse and revival which has been studied extensively in the coherent-state field. In addition, the binomial state exhibits squeezing for certain values of parameters, but it is not a minimum-uncertainty-product state.
Abstract In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.
The evolution of entanglement of a bipartite spin-1/2 system coupled to a micromaser cavity field in an intensity-dependent Jaynes–Cummings model is studied in this paper. The dynamical process of the entanglement is investigated for different cavity fields. We find that the interactions lead to a phenomenon of periodic entanglement and disentanglement between the qubits. Effects such as the growth of the magnitude of atomic entanglement with the increase of the cavity photon number, arising out of the intensity-dependent atom-cavity coupling lead to interesting dissimilarities from the case of entanglement generated by the standard Jaynes–Cummings interaction.
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.