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

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.
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https://hal.archives-ouvertes.fr/hal-02351933
Contributor : Karyn Le Hur <>
Submitted on : Wednesday, November 6, 2019 - 3:53:32 PM
Last modification on : Friday, November 8, 2019 - 1:21:39 AM

### Citation

Andrea Pizzi, Fabrizio Dolcini, Karyn Le Hur. Quench-induced dynamical phase transitions and $\pi$-synchronization in the Bose-Hubbard Model. Physical Review B : Condensed matter and materials physics, American Physical Society, 2019, ⟨10.1103/PhysRevB.99.094301⟩. ⟨hal-02351933⟩

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