Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling

Abstract

Period tripling in driven quantum oscillators reveals unique features absent for linear and parametric drive, but generic for all higher-order resonances. Here, we focus at zero temperature on the relaxation dynamics towards a stationary state starting initially from a domain around a classical fixed point in phase space. Beyond a certain threshold for the driving strength, the long-time dynamics is governed by a single time constant that sets the rate for switching between different states with broken time translation symmetry. By analyzing the lowest eigenvalues of the corresponding time evolution generator for the dissipative dynamics, we find that near the threshold the gap between these eigenvalues nearly closes. The closing becomes complete for a vanishing quantum parameter. We demonstrate that this behavior, reminiscent of a quantum phase transition, is associated with a transition from a stationary state which is localized in phase space to a delocalized one. We further show, that switching between domains of classical fixed points happens via quantum activation, however, with rates that differ from those obtained by a standard semiclassical treatment. As period tripling has been explored with superconducting circuits mainly in the quasi-classical regime recently, our findings may trigger new activities towards the deep quantum realm. arXiv:1911.08366v2 [cond-mat.mes-hall]

Metastable quantum entrainment

“…[3,50,51]. Moreover, such long-time scales associated with fluctuations between multiple possible phases have also been reported for quantum systems of parametric oscillators [16], period-tripling oscillators [26], and optomechanical oscillators [67]. Thus, slow-relaxation time scales seem a characteristic feature of multistable dynamical systems in the quantum regime, and a seemingly metastable manifold and dynamics could be expected for these examples as well as in further synchronization scenarios with multiple preferred phases.…”

Condensed Matter Physics in Time Crystals

“…[78]. Recently, there is a lot of interest in Z 3 -lattice of triply driven oscillator [113,114,[116][117][118], e.g., nonlocal random walk [116], quantum state preparation [117] and dissipative phase transition [118]. A similar calculation for the band structure of the multiple Z n lattice (34) with tight-binding model has been provided in Ref.…”

Injection locking and synchronization in Josephson photonics devices

“…The p-fold symmetry has been described in the language of a spontaneous breaking of a discrete symmetry and termed phasespace time-crystal. [51][52][53][54][55] The physics of phase locking at higher-order resonances is very rich and considerably more complex compared to the fundamental resonance; for one, due to the fact, that the unlocked (classical) solution only exists in a nonlinear regime. Here, we do not want to discuss locking at higherorder resonances at the same level of detail as done for the fundamental resonance above.…”