Evolution of entanglement under an Ising-like Hamiltonian with particle losses

TL;DR

This paper provides an analytical solution for the evolution of entanglement in two collective spins under an Ising-like Hamiltonian with particle losses, highlighting how losses affect entanglement and identifying conditions for EPR-like correlations.

Contribution

It offers a compact analytical solution for the density matrix and correlation functions in a system with particle losses, advancing understanding of entanglement dynamics under realistic conditions.

Findings

Particle losses introduce non-local phase noise that destroys highly entangled states.

EPR-like entangled states can survive at short times despite losses.

Optimal atom number for EPR correlations in BECs is estimated.

Abstract

We present analytical compact solution for the density matrix and correlation functions of two collective-macroscopic spins evolving via Ising-like Hamiltonian in the presence of particle losses. The losses introduce non-local phase noise which destroys highly entangled states arising in the evolution. On the other hand, the states appearing at relatively short timescales, possessing EPR-like entanglement will survive. Applying our solutions to the recently proposed scheme to entangle two Bose-Einstein condensates, we estimate the optimal number of atoms for EPR correlations.