Exact diagonalization of a non-quadratic bosonic Liouvillian with two-body loss

TL;DR

This paper achieves the exact diagonalization of a complex bosonic Liouvillian with two-body loss, providing a comprehensive spectral solution and exploring non-Gaussian open system models.

Contribution

It introduces an exact diagonalization method for a non-quadratic bosonic Liouvillian, extending previous solutions and analyzing non-Gaussian systems via nonlinear pseudomodes.

Findings

Liouvillian diagonalized using confluent hypergeometric functions

Spectral decomposition provides the general solution of the master equation

Explores non-Gaussian open system models through nonlinear pseudomodes

Abstract

We present the full diagonalization of a non-quadratic bosonic Liouvillian with a two-body loss term. The Liouvillian is shown to be exactly diagonalizable in terms of left and right confluent hypergeometric functions, whose distinction arises from the noncommutative nature of superoperators. The resulting spectral decomposition yields the general solution of the master equation, extending previous results. We further investigate the construction of a non-Gaussian open system model through the lens of nonlinear pseudomodes.