Quantum coherence and phase-space nonclassicality in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si72.svg" display="inline" id="d1e605"><mml:mi>k</mml:mi></mml:math>-photon thermal-noisy nonlinear JCM with atomic motion

In this paper, we study the quantum interaction between a moving two-level atom and a single-mode quantized field in an optical cavity with degenerate multi-photon transition, in the presence of intensity-dependent coupling and thermal effect. We introduce the appropriate Hamiltonian of the system, and we adopt the initial condition of subsystems, in which the atom is prepared in an arbitrary superposition of ground and excited states, and the field is considered in a thermal state. Consequently, we determine the density matrix of the entire system at any given time. We further assess some of the most important quantum properties, such as quantum coherence, sub-Poissonian statistics, and phase-space nonclassicality by means of negativity of the Wigner quasiprobability distribution function. We then investigate the impact of intensity-dependent nonlinearity, thermal noise, atomic motion, and multi-photon transition on these quantum properties. The numerical results show that the nonclassicality criteria can be significantly influenced and controlled by the effects discussed above. Interestingly, increasing the mean thermal photon number, which highlights the thermal effect, can, in some cases, enhance the nonclassicality features of the system. • The nonlinear JCM with moving atom is described with thermal noise and k -photon transition. • Nonclassicality of the system is studied through coherence, photon statistics, and Wigner function. • The effects of thermal noise, atomic motion, and intensity-dependent function are discussed. • The nonclassicality can, in some cases, be enhanced in the presence of thermal noise.