Hannover 2020 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 29: Quantum Effects (Entanglement and Decoherence)

Q 29.3: Talk

Wednesday, March 11, 2020, 11:30–11:45, f442

Lie algebra methods for solving the quantum evolution of lossy bosonic chains — •Lucas Teuber and Stefan Scheel — Institut für Physik, Universität Rostock, Albert-Einstein--Str. 23-24, 18059 Rostock, Germany

We solve the quantum evolution of coupled harmonic oscillators experiencing Markovian loss by means of Lie algebraic methods. The coupled oscillators are described in a Liouville space formalism and their dynamics is given by a quantum master equation in Lindblad form. In Liouville space this master equation is generated by a Liouvillian just as the familiar Schrödinger equation is generated by a Hamiltonian. Utilising the Lie algebraic structure induced by the Liouvillian we can find its eigendecomposition which allows to formulate an analytic solution for the quantum state evolution. The analysis of the eigenvalues and eigenvectors enables us to find optimally transported states that mitigate the negative effects of the losses. Furthermore, knowledge of the algebraic structure grants insight into the construction of systems emulating effective non-Hermitian Hamiltonians.