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Acta Sinica Quantum Optica

The Wehrl′s Entropy and Shannon′s Entropy for the Non-classical Optical Fields with Negative P Representation

Hong Mā

Published Jan 1, 2007• 0 citations
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Abstract

The Wehrl′s Entropy and Shannon′s entropy for the non-classical optical fields with negative P representation are studied in this paper. The results show that the Wehrl′s entropy of the states decreases along with the growth of the state parameter and the average photon numbers and tend to be constant. While the Shannon′s entropy increases along with the increase of state parameter and the average photon numbers. It is also found that the Wehrl′s entropy of the non-classical optical fields with negative P representation decreases while the total noise increases and the Shannon′s entropy decreases along with the decrease of observable fluctuation.

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The Wehrl′s Entropy and Shannon′s entropy for the non-classical optical fields with negative P representation are studied in this paper. The results show that the Wehrl′s entropy of the states decreases along with the growth of the state parameter and the average photon numbers and tend to be constant. While the Shannon′s entropy increases along with the increase of state parameter and the average photon numbers. It is also found that the Wehrl′s entropy of the non-classical optical fields with negative P representation decreases while the total noise increases and the Shannon′s entropy decreases along with the decrease of observable fluctuation.
In this framework, the effect of a Kerr-like medium and the coupling function dependent on the number of photons operator on the interaction between a two-level atom and a non-linear field is studied. A relation between the Kerr-like medium parameter and the field-atom coupling parameter is used to obtain a simplified formula for Rabi frequency. The wave function of the proposed model is obtained, followed by the derivation of the phase distribution and from which the wehrl entropy formula is calculated. The effect of the initial state and the non-linear func?tion dependent on the number of photons operator and the Kerr-like medium on entanglement is calculated through the Wehrl entropy formula, wehrl distribution and the behaviour of photons by studying the correlation function. The entangle?ment decreases when the function dependent on the number of photons operator is taken into account, while the entanglement gradually improves when the squeezed state is considered, and the entanglement decreases significantly when considering the Kerr medium. An oscillatory distribution is formed between the classical and non-classical in the coherent state. The non-classical distribution disappears when considering the squeezed state and the Kerr-like medium.
The Wehrl’s entropy of the Schrödinger-cat states has been calculated numerically in this paper. In particular, we show the dependence of the Wehrl’s entropy on the two parameters of the Schrödinger-cat states, which act as, respectively, the photon number parameter and the phase difference . The Wehrl’s entropy has been found to be in the range , and its changes with respect to are not homogenized. Furthermore, we obtain both the dependence of the Wehrl’s entropy on the average photon number and the relation between the Wehrl’s entropy and the statistical entropy.
Objective: The study was conducted to estimate the nonlocal correlation between a single qubit and radiation field initially considered in the excited and nonlinear binomial distribution. Material and method: Explicit forms of the excited and nonlinear binomial states are presented. We investigate the dynamical properties of Wehrl entropy as an indicator of the statistical properties of the radiation field during the time evolution. The non-classicality of the field based on the evolution of Mandel parameter also discussed Results: Results of our study show that the Wehrl entropy, qubit-field entanglement and Mandel parameter at the periodic time are an opposite monotonic behavior. Also, a high amount of the entanglement is reached for a high value of deformation parameter. Finally the statistical properties of the field is Poissonian or sub-Poissonian photon distribution. Conclusion: It is concluded from the study that the Wehrl entropy and Mandel parameter were a good indications of the statistical and dynamical properties of the field during the interaction time.