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.

22 pages, 8 figures; added explicit reference to the Truncated Wigner Approximation; added references; improved formatting

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• Influences of weak disorder on dynamical quantum phase transitions of anisotropic XY chain
• Enhancement of many-body quantum interference in chaotic bosonic systems
• Quantum Entangled Fractional Topology and Curvatures
• Synchronization by Magnetostriction
• Thermalization and its Breakdown for a Large Nonlinear Spin
• Discrete Polynomial Optimization with Coherent Networks of Condensates and Complex Coupling Switching
• Persistent oscillations versus thermalization in the quench dynamics of quantum gases with long-range interactions