Lindblad dynamics of Gaussian states and their superpositions in the semiclassical limit

Abstract

The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function, where the Lindblad terms generally introduce a non-Hamiltonian flow. In addition to this, the Gaussian approximation yields dynamical equations for the covariances. The approximation becomes exact for linear Lindblad operators and a quadratic Hamiltonian. By viewing the Wigner function as a wave function on a coordinate space of doubled dimension, and the phase-space Lindblad equation as a Schrödinger equation with a non-Hermitian Hamiltonian, a further set of semiclassical equations are derived. These are capable of describing the interference terms in Wigner functions arising in superpositions of Gaussian states, as demonstrated for a cat state in an anharmonic oscillator subject to damping.

substantially revised version, 20 pages, 8 figures, published in Journal of Physics A

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• Making Sense of Non-Hermitian Hamiltonians
• Quantum trajectories and open many-body quantum systems
• The Dissipative Bose-Hubbard Model. Methods and Examples
• Wave packet evolution in non-Hermitian quantum systems

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• Impossibility of bosonic autonomous entanglement engines in the weak-coupling limit
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