SKM 2023 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 16: Poster: Transport

TT 16.18: Poster

Montag, 27. März 2023, 15:00–18:00, P2/OG4

Solving non-interacting open bosonic systems — •Steven Kim and Fabian Hassler — JARA Institute for Quantum Information, RWTH Aachen University

Open quantum systems that interact with their Markovian environment are described by a Lindblad master equation. We study non-interacting bosonic systems that are subject to single photon loss. The corresponding Liouvillian superoperator is at most of quadratic order in ladder operators. An analysis of the eigenvalues can give insight into possible instabilites as well as phase transitions. Especially the latter has gained growing interest for PT-symmetric systems. The difficulty in solving such systems for its eigenmodes lies in preserving the canonical commutation relation, which is why the standard way of diagonalization is not possible. In this work, we propose a new method to obtain the diagonalized form of any non-interacting bosonic system using symplectic transformations. We are able to diagonalize a general complex matrix, while maintaining the symplectic form that encodes the commutation relations of the bosonic ladder operators. We show that non-Hermitian Hamiltonians naturally appear while solving the Lindblad master equation and that the eigenmodes can be obtained by solving a reduced system. Including counting fields into the Lindbladian makes the efficient calculation of the cumulant generating functions of arbitrary observables possible.