Related papers: The Bose-Hubbard model with localized particle los…
We study the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting bosons on the unit interval in the Gross-Pitaevskii regime. We prove that Bose Einstein condensation survives even a…
We show how to perfectly transfer, without state initialization and remote collaboration, arbitrary functions in interacting boson lattices. We describe a possible implementation of state transfer through bosonic atoms trapped in optical…
In response to a recent manuscript [cond-mat/0609685] on the analysis of interference patterns produced by ultracold atoms released from an optical lattice, we point out that in the presence of a Bose-Einstein condensate the interference…
We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the…
Quantum many-body systems are expected to relax to a thermal state over time, with some exceptions such as systems with atypical eigenstates. In this study, we investigate the effect of the existence of spatially localized eigenstates on…
The impact of interparticle correlations on the behavior of Bose-Einstein Condensates (BECs) is discussed using two approaches. In the first approach, the wavefunction of a BEC is encoded in the $N$-particle sector of an extended "catalytic…
We investigate the particle-hole pair excitations of dipolar molecules in optical lattice, which can be described with an extended Bose-Hubbard model. For strong enough dipole-dipole interaction, the particle-hole pair excitations can form…
A grand canonical system of hard-core bosons in an optical lattice is considered. The bosons can occupy randomly $N$ equivalent states at each lattice site. The limit $N\to\infty$ is solved exactly in terms of a saddle-point integration,…
We present a study of the superfluid properties of atomic Bose gases in optical lattice potentials using the Bose-Hubbard model. To do this, we use a microscopic definition of the superfluid fraction based on the response of the system to a…
Aligning self-propelled particles undergo a nonequilibrium flocking transition from apolar to polar phases as their interactions become stronger. We propose a thermodynamically consistent lattice model, in which the internal state of the…
We study the spectrum and eigenstates of the quantum discrete Bose-Hubbard Hamiltonian in a finite one-dimensional lattice containing two bosons. The interaction between the bosons leads to an algebraic localization of the modified extended…
I describe in these notes the physical properties of one dimensional interacting quantum particles. In one dimension the combined effects of interactions and quantum fluctuations lead to a radically new physics quite different from the one…
We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic…
We analyze quantum phase transitions in a system of optical lattice bosons coupled to an array of atomic quantum dots, or pseudospins-1/2. The system parallels the Bose-Hubbard model with a single difference of the direct tunneling between…
Quantum gases in optical lattices offer an opportunity to experimentally realize and explore condensed matter models in a clean, tunable system. We investigate the Bose-Hubbard model on a microscopic level using single atom-single lattice…
We investigate the real-time dynamics of open quantum spin-$1/2$ or hardcore boson systems on a spatial lattice, which are governed by a Markovian quantum master equation. We derive general conditions under which the hierarchy of…
We consider a pair of bosonic particles in a one-dimensional tight-binding periodic potential described by the Hubbard model with attractive or repulsive on-site interaction. We derive explicit analytic expressions for the two-particle…
We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes…
The stationary properties of the Bose-Hubbard model under squeezed dissipation are investigated. The dissipative model does not possess a $U(1)$ symmetry, but parity is conserved: $\langle a_j \rangle \to -\langle a_j \rangle$. We find that…
After almost half a century since the work of Anderson [Phys. Rev. {\bf 109}, 1492 (1958)], at present there is no well established theoretical framework for understanding the dynamics of interacting particles in the presence of disorder.…