Sudden Freezing and Thawing of Entanglement Sharing in a Shrunken Volume

TL;DR

This paper investigates the dynamic behavior of entanglement sharing in a two-atom cavity system, revealing sudden freezing and thawing phenomena and establishing limits on entanglement sharing.

Contribution

It introduces the concept of sudden entanglement freezing and thawing, providing analytical insights into entanglement dynamics in a simplified quantum system.

Findings

Entanglement can be suddenly frozen or thawed periodically.

A maximum limit for the sum of bipartite entanglements is identified.

Permanent freezing of entanglement can occur under certain conditions.

Abstract

Within the one-excitation context of two identical two-level atoms interacting with a common cavity, we examine the dynamics of all bipartite one-to-other entanglements between each qubit and the remaining part of the whole system. We find a new non-analytic "sudden" dynamical behavior of entanglement. Specifically, the sum of the three one-to-other entanglements of the system can be suddenly frozen at its maximal value or can be suddenly thawed from this value in a periodic manner. We calculate the onset timing of sudden freezing and sudden thawing under several different initial conditions. The phenomenon of permanent freezing for entanglement is also found. We also identify a non-trivial upper limit for the sum of three individual entanglements, which exposes the concept of entanglement sharing in a shrunken "volume". Further analyses about freezing and thawing processes reveal quantitative and qualitative laws of entanglement sharing.