Quench-induced dynamical phase transitions and $\pi$-synchronization in the Bose-Hubbard Model

TL;DR

This paper studies the non-equilibrium dynamics of a fully-connected Bose-Hubbard model after a quench, revealing a dynamical phase transition to either self-trapping or $ ext{ extpi}$-synchronization, with implications for experiments.

Contribution

It predicts a dynamical phase transition and introduces the concept of $ ext{ extpi}$-synchronization in the Bose-Hubbard model, linking it to fixed points and disorder effects.

Findings

Identification of a critical quench strength inducing a phase transition.

Discovery of $ ext{ extpi}$-synchronization as a long-time dynamical regime.

$ ext{ extpi}$-synchronization persists without fine-tuning and is affected by disorder.

Abstract

We investigate the non-equilibrium behavior of a fully-connected (or all-to-all coupled) Bose-Hubbard model after a Mott to superfluid quench, in the limit of large boson densities and for an arbitrary number $V$ of lattice sites, with potential relevance in experiments ranging from cold atoms to superconducting qubits. By means of the truncated Wigner approximation, we predict that crossing a critical quench strength the system undergoes a dynamical phase transition between two regimes that are characterized at long times either by an inhomogeneous population of the lattice (i.e. macroscopical self-trapping) or by the tendency of the mean-field bosonic variables to split into two groups with phase difference $\pi$, that we refer to as $\pi$-synchronization. We show the latter process to be intimately connected to the presence, only for $V \ge 4$, of a manifold of infinitely many fixed points of the dynamical equations. Finally, we show that no fine-tuning of the model parameters is needed for the emergence of such $\pi$-synchronization, that is in fact found to vanish smoothly in presence of an increasing site-dependent disorder, in what we call a synchronization crossover.