Equation of motion method for Full Counting Statistics: Steady state superradiance

TL;DR

This paper develops an equation of motion approach for calculating the full counting statistics in the multi-mode Dicke model, enabling analytical insights into steady-state superradiance beyond traditional master equation methods.

Contribution

It introduces an equation of motion method for the cumulant generating function that extends analysis to the thermodynamic limit in superradiant systems.

Findings

Analytical expressions for full counting statistics in the thermodynamic limit.

Approximate methods recover master equation results at low computational cost.

Extension of analysis to regimes inaccessible by standard master equations.

Abstract

For the multi-mode Dicke model in a transport setting that exhibits collective boson transmissions, we construct the equation of motion for the cumulant generating function. Approximating the exact system of equations at the level of cumulant generating function and system operators at lowest order, allows us to recover master equation results of the Full Counting Statistics for certain parameter regimes at very low cost of computation. The thermodynamic limit, that is not accessible with the master equation approach, can be derived analytically for different approximations.