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

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.