Abstract
Quantum van der Pol oscillators are driven-dissipative systems displaying quantum synchronization phenomena. When forced by a squeezed drive, the frequency adjusts to half of the forcing displaying multiple preferred phases. Here we analyze the physical origin of this entrained response, establishing a connection with metastability in open quantum systems. We report a dynamical regime characterized by a huge separation of time scales, in which a dynamical mode displays a lifetime that can be orders of magnitude larger than the rest. In this regime, the long-time dynamics is captured by an incoherent process between two metastable states, which correspond to the preferred phases of the synchronized oscillator. In fact, we show that quantum entrainment is here characterized by fluctuations driving an incoherent process between two metastable phases, which ultimately limits its temporal coherence when moving into the quantum regime. Finally, we discuss connections with the phenomena of dissipative phase transitions and transient synchronization in open quantum systems.
Highlights
The investigation of the properties of the nonequilibrium dynamics of dissipative quantum systems has recently become a major research subject, with focus ranging from their dynamics and control, to phase transitions, collective phenomena or thermodynamic features [10, 14, 18, 19, 28, 54, 62, 69]
While for first order dissipative phase transitions (DPTs) this usually occurs in a narrow region between the different regimes [11, 12], as experimentally observed in Refs. [18, 19], for symmetry-breaking DPTs this occurs in a whole dynamical regime characterized by the emergence of metastable symmetry-broken states [3, 50, 51]
We show that the squeezed quantum van der Pol (QvdP) displays a distinct dynamical scenario in which the main features of the entrained response cannot be captured by a linearized model, a fact rooted in the emergence of bistability in the classical limit
Summary
The investigation of the properties of the nonequilibrium dynamics of dissipative quantum systems has recently become a major research subject, with focus ranging from their dynamics and control, to phase transitions, collective phenomena or thermodynamic features [10, 14, 18, 19, 28, 54, 62, 69]. One of the consequences of the interplay between driving, dissipation and interactions is the possibility of having the dynamics of an open quantum system dominated by a huge separation of time scales, a characteristic of metastability [44] In this case, initially highly excited configurations quickly relax to a set of metastable states that act as attractors of the dynamics for a long intermediate timescale, until final relaxation to the true stationary state occurs. This is precisely how subharmonic entrainment manifests in the quantum regime, and it dominates the behavior of the power spectrum While these phases act as effective attractors of the dynamics (any initial condition quickly relaxes to them), quantum fluctuations turn phase bistability to phase metastability, limiting the temporal coherence of the synchronized response on the long-time
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