Quantum master equation with balanced gain and loss

Abstract

We present a quantum master equation describing a Bose-Einstein condensate with particle loss on one lattice site and particle gain on the other lattice site whose mean-field limit is a non-Hermitian PT-symmetric Gross-Pitaevskii equation. It is shown that the characteristic properties of PT-symmetric systems, such as the existence of stationary states and the phase shift of pulses between two lattice sites, are also found in the many-particle system. Visualizing the dynamics on a Bloch sphere allows us to compare the complete dynamics of the master equation with that of the Gross-Pitaevskii equation. We find that even for a relatively small number of particles the dynamics are in excellent agreement and the master equation with balanced gain and loss is indeed an appropriate many-particle description of a PT-symmetric Bose-Einstein condensate.

7 pages, 6 figures, additions in the text, to be published in Phys. Rev. A

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• Interaction effects on $\mathcal{P}\mathcal{T}$-symmetry breaking transition in atomic gases
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• Realizing PT-symmetric BEC subsystems in closed hermitian systems
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• Bifurcations and exceptional points in a PT-symmetric dipolar Bose-Einstein condensate
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• Skin Effect Induced Anomalous Dynamics from Charge-Fluctuating Initial States
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• Non-Hermitian interaction of a discrete state with a continuum
• Using mixed many-body particle states to generate exact $\mathcal{P}\mathcal{T}$-symmetry in a time-dependent four-well system
• Exact solution to a Bhatnagar-Gross-Krook-type equation for quantum lattice gases with dephasing noise
• Balancing gain and loss in symmetrised multi-well potentials
• Exact $\mathcal{N}$-point function mapping between pairs of experiments with Markovian open quantum systems
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery
• Approaching the scaling limit of transport through lattices with dephasing
• PT symmetry and the evolution speed in open quantum systems