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The Mott insulator-to-superfluid transition exhibited by the Bose-Hubbard model on a two-dimensional square lattice occurs for any value of the chemical potential, but becomes critical at the tips of the so-called Mott lobes only. Employing…
We address computational issues relevant to the study of disordered quantum mechanical systems at very low temperatures. As an example we consider the disordered Bose- Hubbard model in three dimensions directly at the Bose-glass to…
We investigate the quantum phases of ultracold atoms trapped in a vortex lattice using a mixture of two bosonic species (A and B), in the presence of an artificial gauge field. Heavy atoms of species B are confined in the array of vortices…
We analyze theoretically the emergence of different superfluid phases of spin-1 bosons in a three-dimensional cubic optical lattice by generalizing the recently developed Ginzburg-Landau theory for the Bose-Hubbard model to a spinor Bose…
We study the entanglement spectrum (ES) of the Bose-Hubbard model on the two dimensional square lattice at unit filling, both in the Mott insulating and in the superfluid phase. In the Mott phase, we demonstrate that the ES is dominated by…
We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The…
We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386 (2001), whereby bosons in an optical lattice would be subjected to a sudden parameter change from the Mott to the superfluid phase. We analyze the Bose Hubbard…
We establish the full groundstate phase diagram of disordered Bose-Hubbard model in two-dimensions at unity filling factor via quantum Monte Carlo simulations. Similarly to the three-dimensional case we observe extended superfluid regions…
We use quantum Monte Carlo (QMC) simulations to study the combined effects of harmonic confinement and temperature for bosons in a two dimensional optical lattice. The scale invariant, finite temperature, state diagram is presented for the…
We develop a strong-coupling perturbation theory for the extended Bose-Hubbard model with on-site and nearest-neighbor boson-boson repulsions on ($d > 1$)-dimensional hypercubic lattices. Analytical expressions for the ground-state phase…
Regular arrays of electromagnetic resonators, in turn coupled coherently to individual quantum two-level systems, exhibit a quantum phase transition of polaritons from a superfluid phase to a Mott-insulating phase. The critical behavior of…
We have systematically studied the hard-core Bose-Hubbard model with correlated hopping on a triangular lattice using density-matrix renormalization group method. A rich ground state phase diagram is determined. In this phase diagram there…
We investigate a square-lattice architecture of superconducting transmon qubits with inter-qubit interactions mediated by inductive couplers. Therein, the inductive couling between the qubit and couplers is suggested to be designed into the…
We review the recent theoretical developments towards understanding the Mott phases and quantum phase transition of extended Bose-Hubbard models on lattices in two spatial dimensions . We focuss on the description of these systems using the…
We consider effects of artificial magnetic fields on the ground state of the two-dimensional Bose-Hubbard model. Using an asymmetric Bose-Hubbard model, we demonstrate that the frustrating hopping energy localizes bosons and enlarges…
We show anisotropy of the dipole interaction between magnetic atoms or polar molecules can stabilize new quantum phases in an optical lattice. Using a well controlled numerical method based on the tensor network algorithm, we calculate…
We study the equilibrium and nonequilibrium formation of four-particle complexes in a balanced two-species Bose-Hubbard model with repulsive intra- and attractive inter-species interactions. Using exact diagonalization, we characterize the…
We use a combination of numeric and analytic techniques to determine the groun d state phase diagram of the Bose--Hubbard Hamiltonian with longer range repulsi ve interactions. At half filling one finds superfluidity and an insulating solid…
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…
Motivated by recent experiments on toroidal Bose-Einstein condensates in all-optical traps with tunable weak links, we study the one-dimensional Bose-Hubbard model on a ring-shaped lattice with a small region of weak hopping integrals using…