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Classical and Quantum Gravity

Jaynes–Cummings model in a weak gravitational wave background

Francesco Sorge

Published Dec 7, 2023• 3 citations
Publisher

Abstract

Abstract Working in the framework of the linearized theory, we analyze the influence of a weak gravitational wave on the dynamics of the Jaynes–Cummings model, describing the interaction between a two-level quantum system and the electromagnetic field in a cavity. We show that the gravitational wave induces a small, time-dependent modulation in the generalized Rabi frequency Ω of the system. Such a modulation has the same frequency as the incoming gravitational wave. We also find that the atomic inversion acquires a similar time-dependent modulation. After a π / 2 − pulse of the electromagnetic driving field in the cavity, an atomic population N 0, previously prepared in its excited state, ends showing a small unbalance Δ N = N e − N g between the excited and the de-excited atoms. The unbalance amplitude is proportional to HN 0, with H being the gravitational strain. We briefly comment about possible astrophysical implications.

DOI
10.1088/1361-6382/ad134f

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Abstract Working in the framework of the linearized theory, we analyze the influence of a weak gravitational wave on the dynamics of the Jaynes–Cummings model, describing the interaction between a two-level quantum system and the electromagnetic field in a cavity. We show that the gravitational wave induces a small, time-dependent modulation in the generalized Rabi frequency Ω of the system. Such a modulation has the same frequency as the incoming gravitational wave. We also find that the atomic inversion acquires a similar time-dependent modulation. After a π / 2 − pulse of the electromagnetic driving field in the cavity, an atomic population N 0, previously prepared in its excited state, ends showing a small unbalance Δ N = N e − N g between the excited and the de-excited atoms. The unbalance amplitude is proportional to HN 0, with H being the gravitational strain. We briefly comment about possible astrophysical implications.
The temporal evolution of quantum statistical properties of an interacting atom–radiation field system in the presence of a classical homogeneous gravitational field is investigated within the framework of the Jaynes–Cummings model. To analyse the dynamical evolution of the atom–radiation system a quantum treatment of the internal and external dynamics of the atom is presented based on an alternative su(2) dynamical algebraic structure. By solving 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 behaviour of the atom–radiation system is explored. Assuming that initially the radiation 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 collapses and revivals of the atomic population inversion, atomic dipole squeezing, atomic momentum diffusion, photon counting statistics and quadrature squeezing of the radiation field is studied.
One of the proposed platforms in which both quantum and general relativistic effects can become observable is an atom interacting with the electromagnetic field in a gravitational-wave background. The periodic modulation of field modes induced by variations of the spacetime metric modifies the atomic emission spectrum. Notably, the temporal modulation of the mode-frequency induced by a plane gravitational wave can be simulated through modulated boundary conditions, such as moving cavity mirrors. We analyze the impact of this modulation on atom-field interactions in the strong atom-cavity coupling regime, where Rabi oscillations occur. We show analytically that the modulation is resonantly enhanced, leading to measurable imprints in the atomic transition probability. This establishes a realistic and experimentally accessible platform for probing analogue general relativistic effects in quantum optical systems.
In this paper, the non-Markovian dissipative dynamics of the phase-damped Jaynes-Cummings model in the presence of a classical homogeneous gravitational field will be analyzed. The model consists of a moving two-level atom simultaneously exposed to the gravitational field and a single-mode traveling radiation field in the presence of a non-Markovian phase damping mechanism. First, the non-Markovian master equation for the reduced density operator of the system in terms of a Hamiltonian describing the atom-field interaction in the presence of a homogeneous gravitational field will be presented. Then, the superoperator technique will be generalized and an exact solution of the non-Markovian master equation will be obtained. Assuming that initially the radiation field is prepared in a Glauber coherent state and the two-level atom is in the excited state, the influence of gravity on the temporal evolution of collapses and revivals of the atomic population inversion, atomic dipole squeezing, and photon counting statistics of the radiation field in the presence of the non-Markovian phase damped will be investigated.
The effective mass that approximately describes the effect of a classical homogeneous gravitational field on an interacting atom-radiation field system is determined within the framework of the Jaynes-Cummings model. By 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. By solving exactly the Schrodinger equation in the interaction picture, the evolving state of the system is found. Influence of a classical homogeneous gravitational field on the energy eigenvalues, the effective mass of atom-radiation field system and the Wigner distribution of the radiation field are studied, when initially the radiation field is prepared in a coherent state and the two-level atom is in a coherent superposition of the excited and ground states.
We present a theoretical scheme based on su(2) algebra to investigate the influence of homogeneous gravitational field on the quantum nondemolition measurement of atomic momentum in dispersive Jaynes-Cummings model. In the dispersive Jaynes-Cummings model, when detuning is large and the atomic motion is in a propagating light wave, we consider a two-level atom with quantized cavity-field in the presence of a homogeneous gravitational field. We derive an effective Hamiltonian describing the dispersive atom-field interaction in the presence of gravitational field. We can see gravitational influence both on the momentum filter and momentum distribution. Moreover, gravitational field decreases both tooth spacing of momentum and the width of teeth of momentum.
We study the interaction between a one-mode electromagnetic field and a two-photon Jaynes-Cummings model in the presence of the classical homogenous gravitational field with an added Kerr-like medium when the atom is prepared initially in the momentum eigenstate. The wave function is calculated by using the Schrodinger equation for a coherent electromagnetic field and an atom in the excited state. The influence of the Kerr-like medium and the classical homogenous gravitational field on the properties of the entropy of the field is examined. Keywords: two-level atom; Kerr-like medium; gravitational field; entropy .