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Ultracold polar molecules, with their long-range electric dipolar interactions, offer a unique platform for studying correlated quantum many-body phenomena such as quantum magnetism. However, realizing a highly degenerate quantum gas of…
We study the expansion dynamics of harmonically trapped bosons in a two-dimensional lattice within the extended Bose-Hubbard model. We evaluate the dynamics of the system following a sudden removal of the confining potential, starting with…
We investigate the physics of dipolar bosons in a two dimensional optical lattice. It is known that due to the long-range character of dipole-dipole interaction, the ground state phase diagram of a gas of dipolar bosons in an optical…
We show that ultracold polar diatomic or linear molecules, oriented in an external electric field and mutually coupled by dipole-dipole interactions, can be used to realize the exact Heisenberg XYZ, XXZ and XY models without invoking any…
Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order…
Rotation of atoms in a lattice is studied using a Hubbard model. It is found that the atoms are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in…
Multi-orbital optical lattices have been attracting rapidly growing research interests in the last several years, providing fascinating opportunities for orbital-based quantum simulations. Here, we consider bosonic atoms loaded in the…
A self-bound dipolar quantum droplet modulated by an shallow optical latticeare studied. It is found that the behaviors of the droplets in an optical lattice are similar with those without the optical lattice. In the shallow enough limit…
Strongly correlated quantum particles in lattice potentials are the building blocks for a large variety of quantum insulators, for instance Mott phases and density waves breaking the lattice symmetry. Such collective states are accessible…
We present an architecture for the quantum simulation of many-body spin interactions based on ultracold polar molecules trapped in optical lattices. Our approach employs digital quantum simulation, i.e., the dynamics of the simulated system…
We describe here a quantum simulator of extended bipartite Hubbard model with broken sublattice symmetry. The simulator consists of a structured lateral gate confining two dimensional electrons in a quantum well into artificial minima…
Microwave-dressed polar molecules offer a route to lattice quantum simulators in which the angular form of long-range dipolar interactions, not only their overall strength, can be engineered. We study this setting in a minimal hard-core…
We investigate the dynamics of continuous-time two-particle quantum walks on a one-dimensional noisy lattice. Depending on the initial condition, we show how the interplay between particle indistinguishability and interaction determines…
The recent experimental realization of cold polar molecules in the rotational and vibrational ground state opens the door to the study of a wealth of phenomena involving long-range interactions. By applying an optical lattice to a gas of…
In this review chapter we focus on the many-body dynamics of cold polar molecules in the strongly interacting regime. In particular, we discuss a toolbox for engineering many-body Hamiltonians based on the manipulation of the electric…
Neutral-atom quantum simulators offer a promising approach to the exploration of strongly interacting many-body systems, with applications spanning condensed matter, statistical mechanics, and high-energy physics. Through a combination 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 study the quantum phase diagram of a Bose-Hubbard chain whose dynamics conserves both boson number and boson dipole moment, a situation which can arise in strongly tilted optical lattices. The conservation of dipole moment has a dramatic…
Ultracold ground state dipolar 40K-87Rb molecules have recently been produced in a loose harmonic trap by employing a magnetic field sweep across a Feshbach resonance followed by stimulated Raman adiabatic passage [K.-K. Ni et al., Science…
We consider two particles performing continuous-time nearest neighbor random walk on $\mathbb Z$ and interacting with each other when they are at neighboring positions. Typical examples are two particles in the partial exclusion process or…