Quantum dynamics of disordered bosons in an optical lattice

Abstract

We study the equilibrium and non-equilibrium properties of strongly interacting bosons on a lattice in presence of a random bounded disorder potential. Using a Gutzwiller projected variational technique, we study the equilibrium phase diagram of the disordered Bose Hubbard model and obtain the Mott insulator, Bose glass and superfluid phases. We also study the non equilibrium response of the system under a periodic temporal drive where, starting from the superfluid phase, the hopping parameter is ramped down linearly in time, and back to its initial value. We study the density of excitations created, the change in the superfluid order parameter and the energy pumped into the system in this process as a function of the inverse ramp rate τ . For the clean case the density of excitations goes to a constant, while the order parameter and energy relaxes as 1/τ and 1/τ 2 respectively. With disorder, the excitation density decays exponentially with τ , with the decay rate increasing with the disorder, to an asymptotic value independent of the disorder. The energy and change in order parameter also decrease as τ is increased.

Enhancement of the Bose glass phase in the presence of an artificial gauge field

“…In the SF phase as there is phase coherence throughout the system ρ s is large and it is O(1). The phase diagrams of DBHM with α = 0 at different values of D/U have distinctive features [3]. As examples, the phase diagrams for the case of D/U = 0, 0.2, 0.6 and 1.2 obtained from the SGMF method are shown in Fig.…”

“…The DBHM have been studied with diverse techniques: mean field [11], projected Gutzwiller method [3], site independent and multisite mean-field method [12,13], stochastic mean field [14], quantum Monte Carlo [15][16][17], density matrix renormalisation group (DMRG) [18,19] for 1D system and numerous others [20][21][22][23][24]. In all the cases the introduction of disorder leads to the emergence of BG phase which is characterized by finite compressibility and zero superfluid stiffness.…”

Equilibration Dynamics of Strongly Interacting Bosons in 2D Lattices with Disorder

“…GMFT provides qualitatively correct phase diagrams for strongly interacting clean [40][41][42][43] and disordered [44][45][46][47][48] (away from the tip of the Mott lobe) systems. It has also been used to study nonequilibrium effects such as the dynamical generation of molecular condensates [49] and MIs [50], dipole oscillations [51], quantum quenches [48,52,53], expansion dynamics [54,55], and transport in the presence of disorder [48,56]. However, since the Gutzwiller ansatz wavefunction is a product state, it has zero entanglement entropy for any partitioning of the system.…”

Transport of Strongly Correlated Bosons in an Optical Lattice

“…To analyze the dynamics of the Bose‐Hubbard model beyond mean‐field theory, we have also implemented the projection operator approach . This method uses a canonical transformation such that it systematically eliminates hopping processes which connect states with a large energy difference.…”

“…The energy cut‐off is set as U . From the time dependent variational principle, we obtain improved equations of motion for the coefficients …”