Quantum statistical properties of the Jaynes–Cummings model in the presence of a classical homogeneous gravitational field

Abstract

The temporal evolution of quantum statistical properties of an interacting atom-field system in the presence of a homogeneous gravitational field is investigated within the framework of the Jaynes-Cummings model. Taking into account both the atomic motion and gravitational field a full quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving analytically the Schrödinger equation in the interaction picture, the evolving state of the system is found by which the influence of the gravitational field on the dynamical behavior of the atom-field system is explored. Assuming that initially the field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states, the influence of gravity on the atomic dipole moment, collapses and revivals of the atomic motion, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.

Dynamical behaviours of the nonlinear atom–field interaction in the presence of classical gravity:f-deformation approach

“…The work here extends previous studies in this context [20,39]. To analyze the dynamical evolution of the atom-radiation system, we presented a quantum treatment of the internal and external dynamics of the atom based on an alternative f -deformed su(2) dynamical algebraic structure.…”

“…(30]. It has been shown [39] that these continuous changes in oscillation frequencies influence the collapse and revival times such that subsequent revivals overlap and ultimately a chaotic-like behaviour of time evolution of population inversion occurs. In addition, with the increasing value of the parameter k. g the atomic inversion oscillates around a negative nonzero value, i.e., due to the gravitational field more energy is stored in the cavity-field.…”

“…However, the semi-classical treatment prevent us from studying the pure quantum effects occurring in the course of atom-field interaction. In a series of recently published papers [39,[44][45][46] various aspects of the influence of a classical homogeneous gravitational field on quantum dynamics of the JC model have been analyzed. In Ref.…”

“…The effects of the gravitational field on quantum statistical properties of the lossless as well as the phase-damped JC models have been studied in Refs. [39] and [45], respectively. Also, the effects of gravity on the dynamical evolution of the cavity-field entropy and the creation of the Schrödinger-cat state in the Jaynes-Cummings model have been examined in Ref.…”

Jaynes–Cummings model in a weak gravitational wave background

“…The time evolution of a two-level atom simultaneously exposed to the field of a running laser wave and a homogeneous gravitational field has been studied by Lämmerzahl and Bordé [11] and by Marzlin and Audretsch [12], while the dynamics of a two-level system interacting with a quantized radiation field in a cavity has been investigated by Mohammadi et al [13] in the framework of the Jaynes-Cummings (JC) model [14,15]. Scully et al [16] have considered the radiation from a two-level atom freely falling into a Schwarzschild black hole.…”