Entanglement of a two-atom system driven by the quantum vacuum in arbitrary cavity size

TL;DR

This paper investigates how two atoms become entangled over time when interacting with a quantum field inside a spherical cavity of arbitrary size, revealing complex fluctuation patterns and conditions for entanglement revival.

Contribution

It provides an exact analysis of entanglement dynamics for two atoms in a cavity of any size, including numerical results showing fluctuation patterns and entanglement revival phenomena.

Findings

Concurrence exhibits quasi-random fluctuations with periodic-like behavior.

Maximally entangled states can become disentangled and vice versa after time 2R.

Long-term concurrence can be predicted with good accuracy.

Abstract

We study the dynamical entanglement of two identical atoms interacting with a quantum field. As a simplified model for this physical system we consider two harmonic oscillators linearly coupled to a massless scalar field in the dressed coordinates and states approach and enclose the whole system inside a spherical cavity of radius R. Through a quantity called concurrence, the entanglement evolution for the two-atom system will be discussed, for a range of initial states composed of a superposition of atomic states. Our results reveals how the concurrence of the two atoms behaves through the time evolution, for arbitrary cavity size and for arbitrary coupling constant, weak, intermediate or strong. All our computations are exact and only the final step is numerical. These numerical solutions give us fascinating results for the concurrence, such as quasi-random fluctuations, with a resemblance of periodicity. Another interesting result we found is when the system is initially maximally entangled (disentangled), after the time t = 2R, the system becomes again strongly entangled (disentangled) particularly during the first oscillations, later this phenomenon could be wrecked depending on the initial condition. We also show the concurrence after a too long time elapsed with a good precision.