Time crystallinity in open quantum systems

Andreu Riera-Campeny1, Maria Moreno-Cardoner1, and Anna Sanpera1,2

1Física Teòrica: Informació i Fenòmens Quàntics. Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
2ICREA, Passeig Lluís Companys 23, 08001 Barcelona, Spain.

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Time crystals are genuinely non-equilibrium quantum phases of matter that break time-translational symmetry. While in non-equilibrium closed systems time crystals have been experimentally realized, it remains an open question whether or not such a phase survives when systems are coupled to an environment. Although dissipation caused by the coupling to a bath may stabilize time crystals in some regimes, the introduction of incoherent noise may also destroy the time crystalline order. Therefore, the mechanisms that stabilize a time crystal in open and closed systems are not necessarily the same. Here, we propose a way to identify an open system time crystal based on a single object: the Floquet propagator. Armed with such a description we show time-crystalline behavior in an explicitly short-range interacting open system and demonstrate the crucial role of the nature of the decay processes.

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