Relaxation dynamics and dissipative phase transition in quantum oscillators with period tripling
Jennifer Gosner, Björn Kubala, Joachim Ankerhold
备注：
- Additional references [10] and [47,48] - Typos and minor stylistic changes in the rest of the text - New versions and captions of Fig. 5 and 14 - Explanation added in section IV. concerning the structure of the eigen-densities in (16) - Minor changes at the beginning of section V. - Removed Eq. (29) and unnecessary technical details
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.
Parametrically driven oscillators can display period-tripling in response to a drive at thrice the resonance frequency. In contrast to the parametric instability for period doubling, the symmetric fixed-point corresponding to the state of rest remains stable at arbitrary strong driving for the tripling transition. Previously, it has been shown that fluctuations can circumvent this and induce a period-tripling instability. In this article, we explore an alternative way of inducing a period-tripling transition by investigating properties of period-tripling due to parametric down-conversion beyon…
We study a minimal model that has a driven-dissipative quantum phase transition, namely a Kerr non-linear oscillator subject to driving and dissipation. Using mean-field theory, exact diagonalization, and the Keldysh formalism, we analyze the critical phenomena in this system, showing which aspects can be captured by each approach and how the approaches complement each other. Then critical scaling and finite-size scaling are calculated analytically using the quantum Langevin equation. The physics contained in this simple model is surprisingly rich: it includes a continuous phase transition, $Z…
