Dynamic phase diagram for the quantum phase model

Abstract

We address the stability of superfluid currents in a system of interacting lattice bosons. We consider various Gutzwiller trial states for the quantum phase model which provides a good approximation for the Bose-Hubbard model in the limit of large interactions and boson populations. We thoroughly analyze the current-carrying stationary states of the dynamics ensuing from a Gaussian ansatz, and derive analytical results for the critical lines signaling their modulational and energetic instability, as well as the maximum of the carried current. We show that these analytical results are in good qualitative agreement with those obtained numerically in previous works on the Bose-Hubbard model, and in the present work for the quantum phase model.

Triangular Bose-Hubbard trimer as a minimal model for a superfluid circuit

“…This unexpected quasi-stability is effective enough to stabilize metastable vortex-states even if the device is non-rotating! Note added in proof.-Relevant works have been brought to our attention recently [61][62][63].…”

Transport of Strongly Correlated Bosons in an Optical Lattice

“…The experimental results are compared to time dependent mean‐field calculations within the Gutzwiller ansatz. This method has been widely used to study time‐dependent bosonic lattice problems, such as the creation of molecular Bose‐Einstein condensate by dynamically melting a Mott‐insulator, many‐body dynamics after a sudden shift of the harmonic trap, creation of exotic condensates via quantum‐phase‐revival dynamics, the Higgs‐amplitude mode of strongly correlated lattice bosons, collective modes of a harmonically trapped, strongly interacting Bose gas in an optical lattice, quantum dynamics of interacting bosons in a three‐dimensional disordered optical lattice, and many more . We also present results from a projection operator approach with a finite energy cut‐off, which we find to agree well with the Gutzwiller ansatz for our parameters.…”