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Communications in Theoretical Physics

Quantum Statistical Properties of Binomial Field Interacting with Two Entangled Atoms

Jiao Zhi-Yong, Jun-Mao Ma, Shang Yong-tao, Li Ning, Fu Xia

Published Oct 1, 2008• 2 citations
Publisher

Abstract

Quantum statistical properties of the binomial field interacting with the two entangled atoms are investigated for the different initial conditions. It is found that the sub-Poissonian distribution and the antibunching effect can be presented for the certain ranges of the involved parameters.
DOI
10.1088/0253-6102/50/4/36

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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.
In this article, the quantum properties of light field of the two identical two-level entangled atoms interacting with the binomial optical field were studied by means of time evolution operator and numerical calculations. The results show that the time evolution of the squeezing and coherence properties of the light field depends on the entanglement degree of the initial two identical two-level entangled atoms and the parameters of the binomial optical field. The optical field fluctuation can be completely squeezed via choosing appropriate parameters.
The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.
Quantum statistical properties such as first-order coherence, antibunching, sub-Poisson distribution and the probability distribution of photon number are studied by considering the non-resonant interaction of two radiation fields with a ' Lambda ' structure three-level atom. It is found that the different detunings and the different ratios of average photon number of two radiation fields as well as the time regime have a remarkable influence on quantum statistical properties of the two radiation fields. The author also emphasises that the initial atomic state plays an important role in the non-resonant interaction and tries to explore the connections among these non-classical effects.
Antibunching effect and squeezing property of the binomial state field interact- ing with a cascade three-level atom are studied by using quantum theory and calculation method,and the influences of initial field parameters on the quantum properties of the field are discussed.The results are that,firstly,when the field is initially in a coherent state,its antibunching effect can be displayed discontinuously and squeezing effect can be exhibited in a short time;Secondly,when the initial field is in a middle state between the coherent state and number state,the field shows antibunching effect continuously and the deep degree and sustained time of its squeezing effect increase;Finally,while when the initial field transmits to a fock state,the field reveals continuously antibunching effect but its squeezing effect weak- ens to disappear.Our results show that binomial state field displays remarkable no-classical properties when it interacts with a cascade three-level atom.