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By using a dual vortex method, we study phases such as superfluid, solids, supersolids and quantum phase transitions in a unified scheme in extended boson Hubbard models at and slightly away from half filling on bipartite optical lattices…
The 2D quantum phase transition that occurs in a square lattice of $p+ip$ superconductors is used to show how four-body interactions in $d=2$ reproduce nonperturbative effects familiar from the study of two-body interactions in $d=1$. This…
We study quantum phases of ultracold bosonic atoms in a two-dimensional optical superlattice. The extended Bose-Hubbard model derived from the system of ultracold bosonic atoms in an optical superlattice is solved numerically with…
We introduce a new measure called reduced entropy of sublattice to quantify entanglement in spin, electron and boson systems. By analyzing this quantity, we reveal an intriguing connection between quantum entanglement and quantum phase…
Strongly interacting bosons in 2D in a rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order…
Adding a sublattice bias to the two dimensional Bose Hubbard model greatly enriches the available physics, and introduces knobs which can be used to control and interrogate the quantum state. We describe the physics of this checkerboard…
Atomic many-body phase transitions and quantum criticality have recently attracted much attention in non-standard optical lattices. Here we perform an experimental study of finite-temperature superfluid transition of bosonic atoms confined…
Like a quantum computer designed for a particular class of problems, a quantum simulator enables quantitative modeling of quantum systems that is computationally intractable with a classical computer. Quantum simulations of quantum…
We demonstrate tunneling spectroscopy of synthetic quantum matter in superconducting circuit lattices. We measure site-resolved excitation spectra by coupling the lattice to engineered driven-dissipative particle baths that serve as local…
Many one--dimensional quantum systems, in particular interacting electron and spin systems, can be described a Luttinger liquids. Here, some basic ideas of this picture of one--dimensional systems are briefly reviewed. I then discuss the…
We study the interplay between large-spin, spin-orbit coupling, and superfluidity for bosons in a two dimensional optical lattice, focusing on the spin-1 spin-orbit coupled system recently realized at the Joint Quantum Institute [Campbell…
We show that a two-dimensional (2D) array of 1D interacting boson tubes has a deconfinement transition between a 1D Mott insulator and a 3D superfluid for commensurate fillings and a dimensional crossover for the incommensurate case. We…
We develop a theoretical approach to the low-energy properties of 1D electron systems aimed to encompass the mixed features of Luttinger liquid and Coulomb blockade behavior observed in the crossover between the two regimes. For this aim we…
We investigate the interaction-driven instability of a quadratic band crossing arising for ultracold bosonic atoms loaded into a two-dimensional optical lattice. We consider the case when the degenerate point becomes a local minimum of both…
We investigate systems of interacting bosonic particles confined within slab-like boxes of size L^2 x Z with Z<<L, at their three-dimensional (3D) BEC transition temperature T_c, and below T_c where they experience a quasi-2D…
We consider a classical, two-dimensional system of identical particles which interact via a finite-ranged, repulsive pair potential. We assume that the system is in a crystalline phase. We calculate the normal vibrational modes of a…
We experimentally investigate a superconducting circuit composed of two flux qubits ultrastrongly coupled to a common LC resonator. Owing to the large anharmonicity of the flux qubits, the system can be described well by a generalized Dicke…
We consider a system of weakly interacting bosons confined on a planar double lattice ring subjected to two artificial gauge fields. This system is known to display three phases, the Meissner phase where the flow of particles is carried at…
Recent experimental advances in realizing degenerate quantum dipolar gases in optical lattices and the flexibility of experimental setups in attaining various geometries offer the opportunity to explore exotic quantum many-body phases…
We study the dimensional crossover from 2D to 1D type behavior, which takes place in the thermal excited rippling of a graphene honeycomb lattice, when one of the dimensions of the layer is reduced. Through a joint study, by Monte Carlo…