Omjyoti Dutta

Non-standard Hubbard models in optical lattices: a review

Originally, the Hubbard model was derived for describing the behavior of strongly correlated electrons in solids. However, for over a decade now, variations of it have also routinely been implemented with ultracold atoms in optical lattices, allowing their study in a clean, essentially defect-free environment. Here, we review some of the vast literature on this subject, with a focus on more recent non-standard forms of the Hubbard model. After giving an introduction to standard (fermionic and bosonic) Hubbard models, we discuss briefly common models for mixtures, as well as the so-called extended Bose-Hubbard models, that include interactions between neighboring sites, next-neighbor sites, and so on. The main part of the review discusses the importance of additional terms appearing when refining the tight-binding approximation for the original physical Hamiltonian. Even when restricting the models to the lowest Bloch band is justified, the standard approach neglects the density-induced tunneling (which has the same origin as the usual on-site interaction). The importance of these contributions is discussed for both contact and dipolar interactions. For sufficiently strong interactions, the effects related to higher Bloch bands also become important even for deep optical lattices. Different approaches that aim at incorporating these effects, mainly via dressing the basis, Wannier functions with interactions, leading to effective, density-dependent Hubbard-type models, are reviewed. We discuss also examples of Hubbard-like models that explicitly involve higher p orbitals, as well as models that dynamically couple spin and orbital degrees of freedom. Finally, we review mean-field nonlinear Schrödinger models of the Salerno type that share with the non-standard Hubbard models nonlinear coupling between the adjacent sites. In that part, discrete solitons are the main subject of consideration. We conclude by listing some open problems, to be addressed in the future.

Dipolar Molecules in Optical Lattices

We study the extended Bose-Hubbard model describing an ultracold gas of dipolar molecules in an optical lattice, taking into account all on-site and nearest-neighbor interactions, including occupation-dependent tunneling and pair tunneling terms. Using exact diagonalization and the multiscale entanglement renormalization ansatz, we show that these terms can destroy insulating phases and lead to novel quantum phases. These considerable changes of the phase diagram have to be taken into account in upcoming experiments with dipolar molecules.

Bose?Hubbard model with occupation-dependent parameters

We study the ground-state properties of ultracold bosons in an optical lattice in the regime of strong interactions. The system is described by a non-standard Bose–Hubbard model with both occupation-dependent tunneling and on-site interaction. We find that for sufficiently strong coupling, the system features a phase transition from a Mott insulator with one particle per site to a superfluid of spatially extended particle pairs living on top of the Mott background—instead of the usual transition to a superfluid of single particles/holes. Increasing the interaction further, a superfluid of particle pairs localized on a single site (rather than being extended) on top of the Mott background appears. This happens at the same interaction strength where the Mott-insulator phase with two particles per site is destroyed completely by particle–hole fluctuations for arbitrarily small tunneling. In another regime, characterized by weak interaction but high occupation numbers, we observe a dynamical instability in the superfluid excitation spectrum. The new ground state is a superfluid, forming a two-dimensional (2D) slab, localized along one spatial direction that is chosen spontaneously.

Coupling Nanomechanical Cantilevers to Dipolar Molecules

We investigate the coupling of a nanomechanical oscillator in the quantum regime with molecular (electric) dipoles. We find theoretically that the cantilever can produce single-mode squeezing of the center-of-mass motion of an isolated trapped molecule and two-mode squeezing of the phonons of an array of molecules. This work opens up the possibility of manipulating dipolar crystals, which have been recently proposed as quantum memory, and more generally, is indicative of the promise of nanoscale cantilevers for the quantum detection and control of atomic and molecular systems.

Ground-state structure and stability of dipolar condensates in anisotropic traps

We study the Hartree ground state of a dipolar condensate of atoms or molecules in a three-dimensional anisotropic geometry and at T=0. We determine the stability of the condensate as a function of the aspect ratios of the trap frequencies and of the dipolar strength. We find numerically a rich phase space structure characterized by various structures of the ground-state density profile.

Few interacting fermions in a one-dimensional harmonic trap

We study spin-1/2 fermions, interacting via a two-body contact potential, in a one-dimensional harmonic trap. Applying exact diagonalization, we investigate their behavior at finite interaction strength, and discuss the role of the ground-state degeneracy which occurs for sufficiently strong repulsive interaction. Even low temperature or a completely depolarizing channel may then dramatically influence the systems behavior. We calculate level occupation numbers as signatures of thermalization, and we discuss the mechanisms to break the degeneracy.

Quantum spin models with long-range interactions and tunnelings: a quantum Monte Carlo study

We use a quantum Monte Carlo method to investigate various classes of two-dimensional spin models with long-range interactions at low temperatures. In particular, we study a dipolar XXZ model with U(1) symmetry that appears as a hard-core boson limit of an extended Hubbard model describing polarized dipolar atoms or molecules in an optical lattice. Tunneling, in such a model, is short-range, whereas density–density couplings decay with distance following a cubic power law. We also investigate an XXZ model with long-range couplings of all three spin components—such a model describes a system of ultracold ions in a lattice of microtraps. We describe an approximate phase diagram for such systems at zero and at finite temperature, and compare their properties. In particular, we compare the extent of crystalline, superfluid and supersolid phases. Our predictions apply directly to current experiments with mesoscopic numbers of polar molecules and trapped ions.

Density-dependent tunneling in the extended Bose–Hubbard model

Recently, it has become apparent that when the interactions between polar molecules in optical lattices become strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two-dimensional extended Bose–Hubbard model. Using quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V , we show that the ground-state phase diagrams differ significantly from those expected from the standard extended Bose–Hubbard model.

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observation of anomalous Hall effect. Two species of attractively interacting ultracold fermions are considered to be trapped in a shaken two dimensional triangular lattice. A combination of interaction induced tunneling and shaking can result in an emergent Dice lattice. In such a lattice the staggered synthetic magnetic flux appears and it can be controlled with external parameters. The obtained synthetic fields are non-Abelian. Depending on the tuning of the staggered flux we can obtain either anomalous Hall effect or its quantized version. Our results are reminiscent of Anomalous Hall conductivity in spin-orbit coupled ferromagnets.

Rice–Mele model with topological solitons in an optical lattice

Attractive ultracold fermions trapped in a one-dimensional periodically shaken optical lattice are considered. For an appropriate resonant shaking, a dimerized structure emerges for which the system realizes paradigmatic physics described by the Rice?Mele model. The emergent nature of the system together with density fluctuations or controlled modifications of lattice filling allow for the creation of defects. Those defects lead to topologically protected localized modes carrying the fractional particle number. Their possible experimental signatures are discussed.