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Arrays of Rydberg atoms interacting via dipole-dipole interactions offer a powerful platform for probing quantum many-body physics. However, these intrinsic interactions also determine and constrain the models -- and parameter regimes…
We show that multi-orbital and density-induced tunneling have a significant impact on the phase diagram of bosonic atoms in optical lattices. Off-site interactions lead to density-induced hopping, the so-called bond-charge interactions,…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
Localized defects, unavoidable in real solids, may be simulated in (generically defect-free) cold-atom systems, e.g., via modifications of the optical lattice. We study the Hubbard model on a square lattice with single impurities, pairs of…
Ultracold fermions in a one-dimensional, spin-dependent, optical lattice are described by a non-standard Hubbard model with next-nearest-neighbour correlated hopping. Periodic driving of the lattice allows wide tuning of the system…
A theoretical approach was developed for an exact numerical description of a pair of ultracold atoms interacting via a central potential that are trapped in a three-dimensional optical lattice. The coupling of center-of-mass and…
We use inverse methods of statistical mechanics to explore trade-offs associated with designing interactions to stabilize self-assembled structures against changes in density or temperature. Specifically, we find isotropic,convex-repulsive…
With the recent production of polar molecules in the quantum regime, long-range dipolar interactions are expected to facilitate the understanding of strongly interacting many-body quantum systems and to realize lattice spin models for…
We show that by coupling two hyperfine states of an atom in an optical lattice one can independently control two-, three-, and four-body on-site interactions in a non-perturbative manner. In particular, under typical conditions of current…
We consider a strongly repulsive two-component Fermi gas in a one-dimensional (1D) optical lattice described in terms of a Hubbard Hamiltonian. We analyze the response of the system to a periodic modulation of the hopping amplitude in…
Inspired by recent advances in atomic homo and heterostructures, we consider the vertical stacking of plasmonic lattices as a new degree of freedom to create a coupled system showing a modified optical response concerning the monolayer. The…
Motivated by the recent rapid development of the field of quantum gases in optical lattices, we present a comprehensive study of the spectrum of ultracold atoms in a one-dimensional optical lattice subjected to a periodic lattice…
We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered…
Recent experiments have revealed the tantalizing possibility of fabricating lattice electronic systems strongly coupled to quantum fluctuations of electromagnetic fields, e.g., by means of geometry confinement from a cavity or artificial…
We develop a model to describe the motional (i.e., external degree of freedom) energy spectra of atoms trapped in a one-dimensional optical lattice, taking into account both axial and radial confinement relative to the lattice axis. Our…
Extended Bose Hubbard models with nearest neighbour interaction describe minimally the effect of long range interaction on ultra cold atoms in deep optical lattices. Rotation of such optical lattices subject such neutral cold atoms to the…
We propose a scheme to control and enhance atomic Bloch oscillations via photon-mediated interactions in an optical lattice supported by a standing-wave cavity with incommensurate lattice and cavity wavelengths. Our scheme uses…
Engineering long-range interacting spin systems with ultra cold atoms offers the possibility to explore exotic magnetically ordered phases in strongly-correlated scenarios. Quantum gases in optical cavities provide a versatile experimental…
Spin lattice models play central role in the studies of quantum magnetism and non-equilibrium dynamics of spin excitations -- magnons. We show that a spin lattice with strong nearest-neighbor interactions and tunable long-range hopping of…
Hexagonal optical lattices offer a tunable platform to study exotic orbital physics in solid state materials. Here, we present a versatile high-precision scheme to implement a hexagonal optical lattice potential, which is engineered by…