Interacting bosons in a disordered lattice: Dynamical characterization of the quantum phase diagram

Abstract

We study the quantum dynamics of interacting bosons in a three-dimensional disordered lattice. We show that the superfluid current induced by an adiabatic acceleration of the disordered lattice undergoes a dynamical instability signaling the onset of the Bose-glass phase. The dynamical superfluid-Bose-glass phase diagram is found in very good agreement with static superfluid fraction calculation. A different boundary is obtained when the disorder is suddenly quenched in a moving periodic lattice. In this case we do not observe a dynamical instability but rather a depletion of the superfluid density. Our analysis is based on a dynamical Gutzwiller approach which we show to reproduce the quantum Monte Carlo static phase diagram in the strong interaction limit.How does disorder affect superfluidity? This question [1,2], first posed for liquid helium [3] in the 1980s, remains-to a large extent and in spite of a large body of results-an open and challenging problem. The literature has mainly focused on the ground-state properties of zero-temperature interacting bosons in a disordered potential (the "dirty boson" problem [4]), which is either superfluid (SF) or insulating. The insulating phases can be of two different kinds. If disorder dominates over interaction, the system is found in a gapless Bose-glass (BG) phase consisting of disconnected SF puddles. If interaction is sufficiently strong and dominates over disorder, a lattice system at integer filling is a Mott insulator (MI), characterized by a gap in the excitation spectrum that prevents the exchange of particles between neighboring sites. However, while "static" properties of dirty bosons are well understood, much less is known about the effect of disorder on the dynamical SF properties [5].Experiments with ultracold gases have renewed the interest in disorder [6] and lattice [7] physics. In these systems, the SF-MI transition has been observed in spectacular experiments [8], Anderson localization has been demonstrated in one [9] and three (3D) [10,11] dimensions, and the SF-BG transition is currently under intense investigation [12][13][14][15]. Ultracold gases offer the fine control of relevant parameters and unprecedented diagnostics: spatial and momentum distributions can be directly imaged and, as demonstrated in recent experiments [15][16][17][18], dynamical excitations can be probed.In this Rapid Communication we analyze the dissipation mechanism of the SF current in a system of dilute interact ing bosons at zero temperature in a 3D disordered lattice. The quantum dynamics is investigated in the Gutzwiller approximation. We prepare the system in the ground state of the disordered lattice, which we subsequently accelerate adiabatically up to a final velocity (we refer to this as boost protocol). The current induced by this boost either persists substantially unchanged for the entire-comparatively long-observation time, or rapidly decays due to dynamical instabilities [19]. We recognize two different regions in the disorder versus interaction plane, which...

Cluster Gutzwiller study of the Bose-Hubbard ladder: Ground-state phase diagram and many-body Landau-Zener dynamics

“…Our cluster Gutzwiller meanfield approach can also be extended to investigate the bosonic ladders in the presence of an artificial magnetic field [26,[57][58][59][60][61][62][63], such as the observation of chiral currents [57], the measurement of Chern number in Hofstadter bands [58,63], and the two-leg Bose-Hubbard ladder under a magnetic flux [26,61]. In addition, our cluster Gutzwiller mean-field approach may also use to explore the non-equilibrium dynamics of two coupled onedimensional Luttinger liquids [64] and the dynamical instability of interacting bosons in disordered lattices [65].…”

The dissipative Bose-Hubbard model

“…Likewise, the time-dependent equations (41) proved to be useful in describing dynamic phenomena in systems governed by Hamiltonian (3), such as the creation of a molecular condensate [119], dipole oscillations in a trapped system [129], the excitation of "Higgs" amplitude modes at the two-dimensional superfluid-insulator transition [130], the creation of negativetemperature states [131] and the disorder-induced decay of superfluid currents [132].…”

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