Exploring Unconventional Hubbard Models with Doubly Modulated Lattice Gases

Abstract

Recent experiments show that periodic modulations of cold atoms in optical lattices may be used to engineer and explore interesting models. We show that double modulation combining lattice shaking and modulated interactions allows for the engineering of a much broader class of lattice with correlated hopping, which we study for the particular case of one-dimensional systems. We show, in particular, that by using this double modulation it is possible to study Hubbard models with asymmetric hopping, which, contrary to the standard Hubbard model, present insulating phases with both parity and string order. Moreover, double modulation allows for the simulation of lattice models in unconventional parameter regimes, as we illustrate for the case of the spin-1=2 Fermi-Hubbard model with correlated hopping, a relevant model for cuprate superconductors. Introduction.-Ultracold gases in optical lattices have attracted a lot of attention as emulators of fundamental models of quantum many-body systems. Their unprecedented levels of controllability, tunability, and cleanness have permitted the realization of Hubbard models with cold atoms [1][2][3], the creation of synthetic magnetic fields in neutral lattice gases [4,5], first steps towards the emulation of quantum magnetism [6][7][8][9][10][11][12], and more [13,14]. Recent progress in measurement techniques has allowed for singlesite resolved detection [15,16], which has permitted a deeper insight into the properties of Mott insulators (MI) [16][17][18] and the dynamical properties of cold lattice gases [19].The possibility of tuning parameters in real time in cold lattice gases has aroused particular interest. Fast periodic modulations provide a new tool for the engineering of relevant lattice models [4,5,[20][21][22][23][24][25][26][27][28][29]. In particular, a fastenough modulation of the lattice position (lattice shaking) results in the effective change of the tunneling rate [20] allowing, for example, driving the superfluid (SF) to MI transition [24], inducing photon-assisted hopping in tilted lattices [22], simulating frustrated classical magnetism [25], generating gauge potentials [28], and inducing effective ferromagnetic domains [29]. Moreover, a fast modulation of the interparticle interactions results in an effective hopping that depends on the occupation differences at neighboring sites [30][31][32][33] and may induce density-dependent gauge fields [34].In this Letter, we show that double modulation (DM), i.e., the combination of lattice shaking and periodically modulated interactions, permits the selective control of different hopping processes, hence, allowing for the engineering of a broad range of lattice models that cannot be realized with either lattice shaking or modulated interaction

Schrieffer-Wolff Transformation for Periodically Driven Systems: Strongly Correlated Systems with Artificial Gauge Fields

“…[45] and expected to produce novel topological phases. By utilizing resonance phenomena, this scheme only requires shaking of the on-site potentials, which is easier in practice than other schemes which have suggested modulating the interaction strength to realize similar Hamiltonians [77,78].…”

“…For instance, H 1 can be a local Hamiltonian or can be written as a sum of local commuting terms. The method also works if the interaction strength is periodically modulated [77][78][79].…”

Compacton matter waves in binary Bose gases under strong nonlinear management

“…Properties of the superfluid -Mott transition in a 2D square and a 3D cubic optical lattice with periodic modulation of the atomic scattering length have been investigated in [6]. Modulations of the interactions were used also to design new correlatedhopping models for fermions in optical lattices [7] and, in combination with OL shaking, for engineering unconventional Bose-Hubbard models [8].…”

Hidden Order and Symmetry Protected Topological States in Quantum Link Ladders

“…Moreover, a defect pair cannot split due to Gauss' law. This selective pair creation induces O 2 P = 0 and O 2 S = 0 for any µ [50], precluding a Haldanelike phase (which would have O 2 P = 0 and O 2 S = 0). At µ/J x ≃ 0.45 there is an Ising-like phase transition into the so-called non-zero flux (NZ) phase [49].…”