The time evolution of the Wehrl entropy and Wehrl phase distribution for the multiphoton Jaynes Cummings model, where the dynamics is described by the phase-damped terms, is studied. Analytical and numerical results under certain parametric conditions are obtained by means of which we analyze the influence of dissipation on the dynamics of Husimi Q-function, Wehrl entropy and Wehrl phase distribution for different values of the Stark shift parameter. Our results show that information about the dynamical properties of the system can be obtained through the Wehrl entropy and Wehrl phase distribution from the point of view of phase-space information. An interesting relation between the correlation, Stark shift and decoherence effect is observed.
In this paper, we consider a unified approach to study the degree of entanglement of two-level systems interacting with a quantized electromagnetic field. We investigate a range of parameters in a generalized Jaynes–Cummings model (JC-model) with intensity-dependent, field nonlinearity and nonresonant coupling. In terms of the density matrix and without the diagonal approximation we derive an explicit expression for the entanglement degree using a function analogous to mutual entropy. This notion is inspired by the fact that the quantum state may be interpreted as a measure of information. With the aid of the quasiprobability distribution function, the statistical properties of the field are analyzed. It is shown that when the atom is initially in its upper-level and the one-photon at resonance, the Q-function splits into two peaks and counter rotate in phase space.
A density of the information-theoretic Wehrl entropy in terms of the Hu- simi
Q -function is defined.The entropic density is then applied to describe the quantum properties of some optical fields including Fock states, cohe- rent and squeezed states, superposition of chaotic and coherent states, and Schr\"odinger cat and cat-like states.The entropic density is compared with both the conventional Wehrl entropy and the Husimi phase distribution.It is shown that the entropic density is a good measure of the phase-space uncertainty (noise), and the phase locking or phase bifurcation effects.The advantages of the entropic description of the superposition principle are presented.It is also demonstrated that the entropic density properly de- scribes phase randomization processes, thus can be used as a measure of decoherence.I. INTRODUCTION Quantum entropy is one of the most fundamental concepts of quantum physics [1], parti- cularly useful in quantum information [2].Quantum entropy has been applied, e.g., as a measure of quantum entanglement, qualltum decoherence, photocount statistics, quantum 数理解析研究所講究録 1142 巻 2000 年 1-22 1 optical correlations, purity of states, quantum noise or accessible information in quantum measurement (capacity of quantum channel).Quantum entropy, as a natural generalization of classical Boltzmann entropy, was propo- sed by von Neumann [3].A classical-like entropy associated with quantum fields was intro- duced by Wehrl [4] in terms of the Glauber coherent states and the Husimi
Q -function [5].A rigorous proof that the von Neumann entropy tends to the Wehrl entropy in the clas- sical limit $\hslasharrow 0$ was given by Beretta [6].The quantum von Neumann entropy can be expanded in power series of classical entropies.As was shown explicitly by Pe\v{r}inov\'a et al. [7], the first term of this expansion is the Wehrl entropy.Bu\v{z}ek et al. [8] related the von Neumann entropy with the sampling entropies based on operational approach to a phase-space measurement.They also identified the Wehrl entropy as a particular example of the sampling entropy, when the quantum ruler is represented by coherent states.Other aspects of the relation between classical and quantum-mechanical entropies have also been extensively studied (see, e.g., excellent surveys by Wehrl [9], and Ohya and Petz [1] with references included therein).The Wehrl entropy has been successfully applied in a description of different properties of quantum optical fields.In particular, it has been shown explicitly that the Wehrl entropy is a useful measure of phase-space uncertainty (quantum noise, phase-space localization, wave-packet spreading) [8,10-14], quantum interference [10], decoherence [11,15,16], ioni- zation [14], squeezing [16-18], Schr\"odinger cat formation
[13,19] or, in general, splitting of
Q -function [15].The von Neumann entropy becomes zero for all pure states, thus cannot be used in discriminating them.Paradoxically, the classical Wehrl entropy is more sensitive in di- stinguishing states than the quantum von Neumann entropy, since it is dependent on the choice of pure states.However, there are properties of quantum fields (including phase decoherence or unique description of superposition states), which are not enough precisely described by the conventional Wehrl entropy.Therefore, we propose a new entropic me-