Time-periodic driving like lattice shaking offers a low-demanding method to generate artificial gauge fields in optical lattices. We identify the relevant symmetries that have to be broken by the driving function for that purpose and demonstrate the power of this method by making concrete proposals for its application to two-dimensional lattice systems: We show how to tune frustration and how to create and control band touching points like Dirac cones in the shaken kagome lattice. We propose the realization of a topological and a quantum spin Hall insulator in a shaken spin-dependent hexagonal lattice. We describe how strong artificial magnetic fields can be achieved for example in a square lattice by employing superlattice modulation. Finally, exemplified on a shaken spin-dependent square lattice, we develop a method to create strong non-abelian gauge fields.

We present the theoretical mean-field zero-temperature phase diagram of a Bose-Einstein condensate (BEC) with dipolar interactions loaded into an optical lattice with a staggered flux. Apart from uniform superfluid, checkerboard supersolid, and striped supersolid phases, we identify several supersolid phases with staggered vortices, which can be seen as combinations of supersolid phases found in earlier work on dipolar BECs and a staggered-vortex phase found for bosons in optical lattices with staggered flux. By allowing for different phases and densities on each of the four sites of the elementary plaquette, more complex phase patterns are found.

We consider ultracold bosons in a 2D square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. It is therefore necessary to account for higher-order hopping terms, which are renormalized differently by the shaking, and introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates, with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott-insulator and the different superfluid phases, and present the time-of-flight images expected to be observed experimentally. Our results open up new possibilities for the realization of bosonic analogs of the FFLO phase describing inhomogeneous superconductivity.

As a minimal fermionic model with kinetic frustration, we study a system of spinless fermions in the lowest band of a triangular lattice with nearest-neighbor repulsion. We find that the combination of interactions and kinetic frustration leads to spontaneous symmetry breaking in various ways. Time-reversal symmetry can be broken by two types of loop current patterns, a chiral one and one that breaks the translational lattice symmetry. Moreover, the translational symmetry can also be broken by a density wave forming a kagome pattern or by a Peierls-type trimerization characterized by enhanced correlations among the sites of certain triangular plaquettes (giving a plaquette-centered density wave). We map out the phase diagram as it results from leading-order Ginzburg-Landau mean-field theory. Several experimental realizations of the type of system under study are possible with ultracold atoms in optical lattices.

We study chaoticity and thermalization in Bose-Einstein condensates in disordered lattices, described by the discrete nonlinear Schrödinger equation (DNLS). A symplectic integration method allows us to accurately obtain both the full phase space trajectories and their maximum Lyapunov exponents (mLEs), which characterize their chaoticity. We find that disorder destroys ergodicity by breaking up phase space into subsystems that are effectively disjoint on experimentally relevant timescales, even though energetically, classical localisation cannot occur. This leads us to conclude that the mLE is a very poor ergodicity indicator, since it is not sensitive to the trajectory being confined to a subregion of phase space. The eventual thermalization of a BEC in a disordered lattice cannot be predicted based only on the chaoticity of its phase space trajectory.Introduction In this Letter, we bring together the topics of disorder, nonlinearity, chaos, ergodicity, and Bose-Einstein condensation (BEC) in optical lattices. Inspired by the realisation of disordered optical potentials in experiments with ultracold atomic gases [1, 2], we explore the question of thermalisation in such systems. Previous theoretical works have, amongst others, addressed the topics of Bose and Anderson glasses [3], Anderson localisation [4,5], and Lifshits glasses [6]. In [6], various regimes of interaction strengths were investigated, and it was found that for sufficiently strong interactions, a disordered BEC is expected. We will focus on this regime, and study the Bose-Hubbard model [7,8], which describes a bosonic gas in a lattice, in the mean-field approximation. The resulting model can be obtained by discretising the Gross-Pitaevskii equation, and is also known as the discrete nonlinear Schrödinger equation (DNLS) [9]. In this Letter, we pose and answer the following question: what is the effect of disorder on thermalisation and ergodicity in the mean-field Bose-Hubbard model / DNLS?The connection between chaoticity and thermalisation was recently discussed in the disorder-free case [10]. Intuitively, one would expect chaotic trajectories to thermalise, since unlike regular ones, they are not confined to the neighborhood of stable periodic orbits. Not being confined, the expectation is that they are able to cover the available phase space, and that the system is therefore well-described by the microcanonical ensemble, since only the energy and particle number are conserved. We show that this expectation is not correct, by explicitly demonstrating the absence of equiprobability of states on the microcanonical shell. Since the energies involved are higher than the disorder potential, classical localisation cannot be responsible for this effect.The most commonly employed method of chaos detection, which quantifies the sensitive dependence on initial conditions, is the evaluation of the maximum Lyapunov exponent (mLE) [11][12][13][14]. In [10], a positive mLE, which

We calculate the finite-temperature shift of the critical wave vector Q c of the Pokrovsky-Talapov model using a renormalization-group analysis. Separating the Hamiltonian into a part that is renormalized and one that is not, we obtain the flow equations for the stiffness and an arbitrary potential. We then specialize to the case of a cosine potential, and compare our results to well-known results for the sine-Gordon model, to which our model reduces in the limit of vanishing driving wave vector Q = 0. Our results may be applied to describe the commensurate-incommensurate phase transition in several physical systems and allow for a more realistic comparison with experiments, which are always carried out at a finite temperature.

We investigate two theoretical pseudomagnon-based models for a bilayer quantum Hall system ͑BQHS͒ at total filling factor t = 1. We find a unifying framework which elucidates the different approximations that are made. We also consider the effect of an in-plane magnetic field in BQHSs at t = 1, by deriving an equation for the ground-state energy from the underlying microscopic physics. Although this equation is derived for small in-plane fields, its predictions agree with recent experimental findings at stronger in-plane fields, for low electron densities. We also take into account finite-temperature effects by means of a renormalization group analysis, and find that they are small at the temperatures that were investigated experimentally.

We investigate quantum phase transitions occurring in a system of strongly interacting ultracold bosons in a 1D optical lattice. After discussing the commensurate-incommensurate transition, we focus on the phases appearing at incommensurate filling. We find a rich phase diagram, with superfluid, supersolid and solid (kink-lattice) phases. Supersolids generally appear in theoretical studies of systems with long-range interactions; our results break this paradigm and show that they may also emerge in models including only short-range (contact) interactions, provided that quantum fluctuations are properly taken into account. PACS numbers:The rapid progress in trapping and cooling atoms has rendered the study of "tailor-made" low-dimensional (D) systems [1] experimentally accessible. Both the dimensionality and the interactions can be controlled, allowing great flexibility in realizing almost arbitrary stronglycorrelated physical systems. A superfluid-Mott insulator (SF-MI) quantum phase transition, driven by increasing the potential depth of the optical lattice (and hence the relative strength of interactions) beyond a critical value, has been observed for bosons loaded into an optical lattice in 3D [2], 2D [3], and 1D [4]. In addition, the Tonks-Girardeau gas, where bosons avoid spatial overlap and acquire fermionic properties due to strong repulsive interactions, has been experimentally realized in 1D [5].Recently, a new type of quantum phase transition was observed in 1D in the very strongly interacting regime: for an arbitrarily weak optical lattice potential commensurate with the atomic density of the Bose gas, a quantum phase transition into an insulating, gapped state, was observed, with the atoms pinned at the lattice minima [6]. Theoretical studies of 1D systems based on the sine-Gordon model indeed predict that above a critical interaction strength, the SF should become a MI even for a vanishingly weak optical lattice [7].