Affiliation:
1. Vienna Center for Quantum Science and Technology
2. University of Strathclyde
3. Vienna University of Technology
Abstract
The effect of \mathcal{PT}𝒫𝒯-symmetry
breaking in coupled systems with balanced gain and loss has recently
attracted considerable attention and has been demonstrated in various
photonic, electrical and mechanical systems in the classical regime.
However, it is still an unsolved problem how to generalize the concept
of \mathcal{PT}𝒫𝒯
symmetry to the quantum domain, where the conventional definition in
terms of non-Hermitian Hamiltonians is not applicable. Here we introduce
a symmetry relation for Liouville operators that describe the
dissipative evolution of arbitrary open quantum systems. Specifically,
we show that the invariance of the Liouvillian under this symmetry
transformation implies the existence of stationary states with preserved
and broken parity symmetry. As the dimension of the Hilbert space grows,
the transition between these two limiting phases becomes increasingly
sharp and the classically expected \mathcal{PT}𝒫𝒯-symmetry
breaking transition is recovered. This quantum-to-classical
correspondence allows us to establish a common theoretical framework to
identify and accurately describe \mathcal{PT}𝒫𝒯-symmetry
breaking effects in a large variety of physical systems, operated both
in the classical and quantum regimes.
Funder
Austrian Science Fund
Österreichischen Akademie der Wissenschaften
Subject
General Physics and Astronomy
Cited by
41 articles.
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