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Journal of Guangxi Academy of Sciences

Time-Dependent Wigner Function of the Photo-added Coherent Light Interacting with a Two-level Atom

Qingyi Yang

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

By using the dynamical wave function,the evolution of the system of the photo-added coherent light and a two-level atom in the interaction picture are described.The time-dependent Wigner function can be obtained from these technologies by reducing-density operator and the expansion in Fock states.The properties of wigner function changed by the time and the amplitude of the light field are analyzed by the numerical simulation.And the results show that the negative of the Wigner function varying with the time takes on certain periodicities in the two-photon process,but not in the one-photon process.Meanwhile,the negative value of the Wigner function is gradually decreased when the amplitudes of light field increase,which means the non-classical characteristic tends to be the classical one.

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By using the dynamical wave function,the evolution of the system of the photo-added coherent light and a two-level atom in the interaction picture are described.The time-dependent Wigner function can be obtained from these technologies by reducing-density operator and the expansion in Fock states.The properties of wigner function changed by the time and the amplitude of the light field are analyzed by the numerical simulation.And the results show that the negative of the Wigner function varying with the time takes on certain periodicities in the two-photon process,but not in the one-photon process.Meanwhile,the negative value of the Wigner function is gradually decreased when the amplitudes of light field increase,which means the non-classical characteristic tends to be the classical one.
The Wigner quasi-probability distribution function is an important tool for estimating the quantumness of quantum states. The Wigner distribution function (WDF) is related monotonically to the coherent field state density operator and their probability distributions. In this paper, we analyze the time-dependent resonator coherent field states produced by a flux qubit’s interaction with a resonator through a two-photon coupling. The WDF dynamics of the coherent field states is investigated under the effects of the qubit-resonator detuning and the intrinsic decoherence. The WDF non-classicality associated with the mixedness resonator entropy dynamics can be controlled by varying the qubit-resonator interaction, detuning as well as the decoherence. The intrinsic decoherence clearly affects the WDF non-classicality, identified by the negative values of the WDF. Finally, by fixing one or both of the complex phase space components, we are able to explore the dynamics of the Wigner-distribution functions.
The Wigner functions of the Fock states and their superposition states have negative value clearly. We focus on discussing the time evolution of the Fock states and their superposition states by the Wigner function under the coherent drive (pumping laser) and dissipation channels (cavity radiation). The results show that the negative region of their Wigner function gradually diminishes as the time kt or the gain coefficient g increasing. In addition, the disappearing time is related to the value of g - k. The loss of non-classical features becomes slower when g increases with the k > g; there is the "frozen zone" when k = g; then the loss of non-classical features becomes faster when g increases with k < g.
The presence of negative values in the Wigner quasiprobability distribution is deemed one of the hallmarks of nonclassical phenomena in quantum systems. Here we demonstrate a classical model of squeezed light that, when combined with post-selection on amplitude threshold-crossing detection events, is capable of reproducing observed behavior of single-photon added coherent states. In particular, a classical model of balanced homodyne detection and standard tomographic techniques are used to infer the density matrix in the Fock basis. The resulting Wigner functions exhibit negatively for photon-added vacuum and weak coherent states.
In this paper, the decoherence of the quantum excitation (the photon-added case) of even/odd coherent states, in a photon-loss channel is studied via the evaluation of the negative part of the Wigner quasi-distribution function in terms of the rescaled time ( ). We first obtain the explicit form of the time-dependent Wigner functions of the states considered, for arbitrary values of the photon excitations. To achieve this purpose, an equivalent Fokker–Planck-like equation which describes the time evolution of the Wigner function in the framework of the standard master equation of the density matrix is used. Then, by analyzing the time variation of the corresponding Wigner functions, the loss of the nonclassicality behavior and, hence, the decay of the negative part of the Wigner functions as a result of decoherence are clearly shown. In particular, we derive the threshold value of the rescaled time for single-photon-added even and odd coherent states; through this it is observed that the associated Wigner functions become positive whenever the rescaled time exceeds that value, i.e., the decoherence has become complete. By virtue of numerical calculations, it is also illustrated that the negative volume of the corresponding Wigner functions decreases with increasing time. In addition, the states with larger values of the excitation number m generally (but not absolutely always) possess smaller values of the rescaled threshold time.
The state function of the two-mode SU(1,1) coherent states field interacting with a four-level atom is derived by means of quantum theory.It is studied that the two-mode intensity correlation function,the Cauchy-Schwartz inequality and the second-order coherence properties for each mode of the light field in the system of the two-mode SU(1,1) coherent states field interacting with four-level atom.It is discussed that the influence of the coupling coefficient between the light field and atom and the initial intensity of the light field on file quantum dynamics of the light field.The results of the studies indicate that the statistic properties of the photon depend on the initial state of the system,the correlation of the two-mode of light is both positive and non-classical,the photon anti-bunching of the first mode appear at all time,and the photon bunching and anti-bunching of the second mode appear alternately.
The photon statistical evolution in the process of two coupling two-level atoms interacting with the squeezed coherent state light field is investigated by means of the interacting picture and the quantum theory. Meanwhile, the influence of the squeezed light field factor γ, the coherent vibration amplitude |α|2 of the field-atom, the coupling constant g of two atoms and the coupling constant λ of atom-field on the mean photon number n(t) of stimulated field are also discussed. The relations of them are revealed.