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Communications in Theoretical Physics

Interaction of Negative Binomial States with Two-Level Atoms

Wang XiaoGuang, Hong‐Chen Fu

Published Jul 30, 2000• 2 citations
Publisher

Abstract

We study the interaction of negative binomial states with two-level atoms. The dynamical evolutions of atomic population inversion, field entropy, Q function, and phase distribution are investigated in detail. The field becomes a superposition of negative binomial states at certain times, and this is confirmed further by its photon number distribution.

DOI
10.1088/0253-6102/34/1/155

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We study the interaction of negative binomial states with two-level atoms. The dynamical evolutions of atomic population inversion, field entropy, Q function, and phase distribution are investigated in detail. The field becomes a superposition of negative binomial states at certain times, and this is confirmed further by its photon number distribution.
In this article, we propose two new quantum field states, displaced binomial state and displaced negative binomial state. Their photon number distributions and sub-Poissonian properties are discussed. The results show that the displaced binomial state is a kind of intermediate quantum state between the coherent state and displaced number state and it may be sub-Poissonian and super-Poissonian at different parameters. The displaced negative binomial state is always super-Poissonian and is an intermediate state between coherent state and displaced Sussking-Glogower phased state. Finally, we study the dynamical evolution of atomic population inversion in the intensity-dependent interaction between these two states and two-level atoms.
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 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.