Quantum mean-field treatment of the dynamics of a two-level atom in a simple cubic lattice

TL;DR

This paper uses mean-field approximation to analyze the dynamics of a two-level atom in a ferromagnetic lattice near the Curie temperature, revealing effects of magnetic field direction and temperature on dephasing, occupation probability, and entanglement.

Contribution

It introduces a quantum mean-field approach to study atom-lattice dynamics, deriving self-consistency equations and analyzing entanglement behavior near phase transition.

Findings

Magnetic field direction influences dephasing and excited state occupation.

Thermal fluctuations reduce excited state occupation probability.

Entanglement exhibits sudden death and revival near critical temperature.

Abstract

The mean field approximation is used to investigate the general features of the dynamics of a two-level atom in a ferromagnetic lattice close to the Curie temperature. Various analytical and numerical results are obtained. We first linearize the lattice Hamiltonian, and we derive the self-consistency equation for the order parameter of the phase transition for arbitrary direction of the magnetic field. The reduced dynamics is deduced by tracing out the degrees of freedom of the lattice, which results in the reduction of the dynamics to that of an atom in an effective spin bath whose size is equal to the size of a unit cell of the lattice. It is found that the dephasing and the excited state occupation probability may be enhanced by applying the magnetic field along some specific directions. The dependence on the change of the temperature and the magnitude of spin is also investigated. It turns out that the increase of thermal fluctuations may reduce the occupation probability of the excited state. The entanglement of two such atoms that occupy non-adjacent cells is studied and its variation in time is found to be not much sensitive to the direction of the magnetic field. Entanglement sudden death and revival is shown to occur close to the critical temperature.