Phase transitions from Heating to non-heating in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators

TL;DR

This paper investigates phase transitions in SU(1, 1) quantum dynamics, revealing distinct signatures in entanglement and phonon growth in Bose-Einstein condensates and driven oscillators, and maps these onto trajectories on the Poincaré disc.

Contribution

It introduces a novel phase diagram for SU(1, 1) quantum systems, characterizing heating and non-heating phases via entanglement and phonon signatures, including complex behaviors in driven coupled oscillators.

Findings

Distinct growth patterns in phonon populations classify phases.

Entanglement entropy growth rates reveal phase boundaries.

Complex phase diagram with multiple phases in driven oscillators.

Abstract

We study the entanglement properties in non-equilibrium quantum systems with the SU(1, 1) structure. Through M\"obius transformation, we map the dynamics of these systems following a sudden quench or a periodic drive onto three distinct trajectories on the Poincar\'e disc, corresponding the heating, non-heating, and a phase boundary describing these non-equilibrium quantum states. We consider two experimentally feasible systems where their quantum dynamics exhibit the SU(1, 1) structure: the quench dynamics of the Bose-Einstein condensates and the periodically driven coupled oscillators. In both cases, the heating, non-heating phases, and their boundary manifest through distinct signatures in the phonon population where exponential, oscillatory, and linear growths classify these phases. Similarly, the entanglement entropy and negativity also exhibit distinct behaviors (linearly, oscillatory, and logarithmic growths) characterizing these phases, respectively. Notibly, for the periodically driven coupled oscillators, the non-equilibrium properties are characterized by two sets of SU(1, 1) generators. The corresponding two sets of the trajectories on two Poincar\'e discs lead to a more complex phase diagram. We identify two distinct phases within the heating region discernible solely by the growth rate of the entanglement entropy, where a discontinuity is observed when varying the parameters across the phase boundary within in heating region. This discontinuity is not observed in the phonon population.