Generalized mean-field approach to simulate large dissipative spin ensembles with long range interactions

TL;DR

This paper develops a generalized mean-field method to simulate large dissipative spin ensembles with long-range interactions, significantly improving computational efficiency and accuracy over traditional quantum models.

Contribution

The authors introduce a pair correlation inclusion in a mean-field framework, enabling simulations of thousands of spins with high accuracy, surpassing previous limitations.

Findings

The method accurately captures properties of infinite systems in 1D and 2D.

It extends feasible simulation sizes from about ten spins to tens of thousands.

The approach provides error estimates useful for optical lattice applications.

Abstract

We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we improve the numerical approximation of the full master equation by including pair correlations at any distance. This truncations enable us to drastically increase the number of spins in our numerical simulations from about ten spins in case of the full quantum model to several ten-thousands in the mean-field approximation and a few hundreds if pair correlations are included. Extensive numerical tests help us identify interaction strengths and geometric configurations where these approximations perform well and allow us to state fairly simple error estimates. By simulating systems of increasing size we show that in one and two dimensions we can include as many spins as needed to capture the properties of infinite size systems with high accuracy, while in 3D the method does not converge to desired accuracy within the system sizes we can currently implement. Our approach is well suited to give error estimates of magic wavelength optical lattices for atomic clock applications and corresponding super radiant lasers.