Critical steady states of all-to-all squeezed and driven superradiance: An analytic approach

TL;DR

This paper analytically investigates steady state phase transitions in driven-dissipative spin models, revealing finite size effects, spin squeezing properties, and the challenges of numerical characterization for large systems.

Contribution

It provides an analytical framework for understanding finite size scaling and spin squeezing in all-to-all driven-dissipative spin models, including logarithmic corrections.

Findings

Finite size scaling laws with numerical prefactors derived analytically.

Logarithmic corrections to spin squeezing identified and explained.

Numerical benchmarks confirm analytical predictions.

Abstract

We analyse the properties across steady state phase transitions of two all-to-all driven-dissipative spin models that describe possible dynamics of N two-level systems inside an optical cavity. We show that the finite size behaviour around the critical points can be captured correctly by carefully identifying the relevant non-linearities in the Holstein-Primakoff representation of spin operators in terms of bosonic variables. With these tools, we calculate analytically various observables across the phase transitions and obtain their finite size scalings, including numerical prefactors. In particular, we look at the amount of spin squeezing carried by the steady states, of relevance for quantum metrology applications, and describe in analytical detail the mechanism by which the optimal spin squeezing acquires logarithmic corrections that depend on the system size. We also demonstrate that the logarithmic nature of these corrections is difficult to characterize through numerical procedures for any experimentally realistic and/or simulable values of particle number. We complement all of our analytical arguments with numerical benchmarks.