The work considers a qubit interacting off-resonantly a nonlinear Kerr-like quantum-harmonicoscillator cavity field through nonlinear intensity-dependent and one-photon interactions. The analytical solution for the master equation is obtained when the qubit starts with an excited pure state while the harmonic-oscillator field starts with a coherent state. The dynamics of the phase space Husimi-distribution and its Wehrl-Husimi entropy entanglement/mixedness is explored under the effects of the atom-field detuning, Kerr-like nonlinearity as well as atomic spontaneous-emission dissipation. For resonant case, the Wehrl-Husimi entropy qubit-oscillator entanglement and atomic mixedness are generated (due to the unitary nonlinear intensity-dependent evolution) with a regular oscillatory behavior. For off-resonant case, the quantum coherence is generated partially with a high-frequency irregular oscillatory behavior. The Kerrlike nonlinearity and the atomic spontaneous dissipation lead to enhancing the generated atomic mixedness Wehrl-Husimi entropy enhances and stabilizing the atomic state in a maximally mixed state. The phase space Husimi-distribution information dynamics of the corresponding the generated atomic mixed states confirms the vital link between the formed interference Husimi-distributions and the generated atomic Wehrl-Husimi entropy mixedness. It is found that the dynamics of the Husimi-distribution information and its Wehrl-Husimi entropy is highly sensitive to the qubit-cavity detuning, Kerr-like nonlinearity as well as the dissipation.
INDEX TERMSMaster equation, Husimi-distribution, spontaneous decay.A.-B. A. MOHAMED received the M.S. and Ph.D. degrees in applied mathematics from Assiut University, Egypt. He has been a Professor of mathematics with Prince Sattam bin Abdulaziz University, Saudi Arabia, since 2018, and Assiut University, since 2019. His research interests include applied mathematics and mathematical physics, including different directions in quantum information and computation. A. ALMUTLG received the B.S. degree (Hons.