We establish the phase diagram of the strongly-interacting Bose-Hubbard model defined on a two-leg ladder geometry in the presence of a homogeneous flux. Our work is motivated by a recent experiment [Atala et al., Nature Phys. 10, 588 (2014)], which studied the same system, in the complementary regime of weak interactions. Based on extensive density matrix renormalization group simulations and a bosonization analysis, we fully explore the parameter space spanned by filling, inter-leg tunneling, and flux. As a main result, we demonstrate the existence of gapless and gapped Meissner and vortex phases, with the gapped states emerging in Mott-insulating regimes. We calculate experimentally accessible observables such as chiral currents and vortex patterns.Introduction. The quantum states of interacting electrons in the presence of spin-orbit coupling and magnetic fields are attracting significant attention in condensed matter physics because of their connection to Quantum Hall physics [1], topological insulators [2-4] and the emergence of unusual excitations in low dimensions [5,6]. Recent progress with quantum gas experiments has led to the realization of artificial gauge fields [7], both in the continuum [8][9][10] and for bosons in optical lattices [11][12][13][14], paving the way for future experiments on the interplay of interactions, dimensionality, and gauge fields in a systematic manner. This has motivated theoretical research into the physics of strongly interacting particles in the presence of abelian and non-abelian gauge fields and various questions such as the Quantum Hall effect with bosons [15][16][17][18][19][20][21][22], unusual quantum magnetism [23][24][25][26], and the emergence of topologically protected phases [27][28][29] have been addressed.

Raman-assisted hopping may be used to realize the anyon Hubbard model in one-dimensional optical lattices. We propose a feasible scenario that significantly improves the proposal of T. Keilmann et al. [Nat. Commun. 2, 361 (2011)], allowing as well for an exact realization of the two-body hard-core constraint, and for controllable effective interactions without the need of Feshbach resonances. We show that the combination of anyonic statistics and two-body hard-core constraint leads to a rich ground-state physics, including Mott insulators with attractive interactions, pair superfluids, dimer phases, and multicritical points. Moreover, the anyonic statistics results in a novel two-component superfluid of holon and doublon dimers, characterized by a large but finite compressibility and a multipeaked momentum distribution, which may be easily revealed experimentally. DOI: 10.1103/PhysRevLett.115.053002 PACS numbers: 37.10.Jk, 67.85.-d, 05.30.Pr Particles are classified as bosons or fermions depending on whether their wave function is symmetric or antisymmetric under exchange. Other types of quantum statistics are, however, possible in lower dimensions. Remarkably, 2D systems allow for the existence of anyons, i.e., particles with fractional statistics interpolating between bosons and fermions [1][2][3]. Anyons play a fundamental role in key areas of modern physics, as fractional quantum Hall effect [4][5][6][7] and topological quantum computing [8]. Fractional statistics is, however, not exclusive of 2D systems [9]. In particular, 1D anyons have attracted a large deal of interest [10][11][12][13][14][15][16][17][18][19][20][21][22][23], although the experimental realization of a 1D anyon gas is still lacking.Ultracold atoms offer extraordinary possibilities for the analysis of interesting many-body systems [24]. In particular, several ideas have been proposed for the creation and manipulation of anyons in cold gases [25][26][27][28][29]. Particularly interesting is the recent proposal for the realization of the anyon Hubbard model (AHM) using Raman-assisted hopping in 1D optical lattices [30]. In this proposal, the anyonic statistics may be controlled at will, opening the possibility for the observation of statistically induced quantum phase transitions [30], asymmetric momentum distributions [21], and intriguing particle dynamics in the lattice [20,22,23].In this Letter, we first discuss a scheme for realizing the AHM that, although following Ref. [30], solves crucial drawbacks that would render the original proposal, in general, unfeasible. The scheme also allows for controllable effective interactions without the need of Feshbach resonances, and for an exact two-body hard-core constraint (2BHCC), contrary to the approximate realization of 2BHCC resulting from Zeno projection due to large three-body loss rates [31], where non-negligible losses are typically present. Neither the controllable interactions nor the inherent 2BHCC were considered in Ref. [30], which focused exclusively on statistically induced su...

The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.

We show that density-dependent synthetic gauge fields may be engineered by combining periodically modulated interactions and Raman-assisted hopping in spin-dependent optical lattices. These fields lead to a density-dependent shift of the momentum distribution, may induce superfluid-to-Mott insulator transitions, and strongly modify correlations in the superfluid regime. We show that the interplay between the created gauge field and the broken sublattice symmetry results, as well, in an intriguing behavior at vanishing interactions, characterized by the appearance of a fractional Mott insulator. DOI: 10.1103/PhysRevLett.113.215303 PACS numbers: 67.85.-d, 03.65.Vf, 03.75.Lm, 37.10.Jk The emulation of synthetic electromagnetism in cold neutral gases has attracted major interest [1,2]. Artificial electric and magnetic fields have been induced using lasers [3][4][5]. Moreover, these setups may be extended to generate non-Abelian fields, and in particular, spin-orbit coupling [6][7][8][9][10][11][12][13]. Synthetic fields may be generated as well in optical lattices, and recent experiments have created artificial staggered [14][15][16] and uniform [17,18] magnetic fields. These fields are, however, static, as they are not influenced by the atoms.The dynamical feedback between matter and gauge fields plays an important role in various areas of physics, ranging from condensed matter [19] to quantum chromodynamics [20], and its realization in cold lattice gases is attracting growing attention [21]. Schemes have been recently proposed for multicomponent lattice gases, such that the low-energy description of these systems is that of relevant quantum field theories [22][23][24][25][26][27][28][29][30][31]. The backaction of the atoms on the value of a synthetic gauge field is expected to lead to interesting physics, including statistically induced phase transitions and anyons in 1D lattices [32], and chiral solitons in Bose-Einstein condensates [33].Periodically modulated optical lattices open interesting possibilities for the engineering of lattice gases [16][17][18][34][35][36][37][38][39][40]. In particular, periodic lattice shaking results in a modified hopping rate [34][35][36], which has been employed to drive the superfluid (SF) to Mott insulator (MI) transition [37], to simulate frustrated classical magnetism [38], and to create tunable gauge potentials [16]. Interestingly, a periodically modulated magnetic field may be employed in the vicinity of a Feshbach resonance to induce periodically modulated interactions, which result in a nonlinear hopping rate that depends on the occupation differences at neighboring sites [41][42][43].In this Letter, we show that combining periodic interactions and Raman-assisted hopping may induce a densitydependent gauge field in 1D lattices. The created field results in a density-dependent shift of the momentum distribution that may be probed in time-of-flight (TOF) experiments. Moreover, contrary to the Peierls phase induced in shaken lattices [16], the created field cannot be ga...

We study the quantum phases of bosons with repulsive contact interactions on a two-leg ladder in the presence of a uniform Abelian gauge field. The model realizes many interesting states, including Meissner phases, vortex fluids, vortex lattices, charge density waves, and the biased-ladder phase. Our work focuses on the subset of these states that breaks a discrete symmetry. We use density matrix renormalization group simulations to demonstrate the existence of three vortex-lattice states at different vortex densities and we characterize the phase transitions from these phases into neighboring states. Furthermore, we provide an intuitive explanation of the chiral-current reversal effect that is tied to some of these vortex lattices. We also study a charge-density-wave state that exists at 1/4 particle filling at large interaction strengths and flux values close to half a flux quantum. By changing the system parameters, this state can transition into a completely gapped vortex-lattice Mott-insulating state. We elucidate the stability of these phases against nearest-neighbor interactions on the rungs of the ladder relevant for experimental realizations with a synthetic lattice dimension. A charge-density-wave state at 1/3 particle filling can be stabilized for flux values close to half a flux quantum and for very strong on-site interactions in the presence of strong repulsion on the rungs. Finally, we analytically describe the emergence of these phases in the low-density regime, and, in particular, we obtain the boundaries of the biased-ladder phase, i.e., the phase that features a density imbalance between the legs. We make contact with recent quantum-gas experiments that realized related models and discuss signatures of these quantum states in experimentally accessible observables.

We study the ground state of frustrated spin-S chains in a strong magnetic field in the immediate vicinity of saturation. In strongly frustrated chains, the magnon dispersion has two degenerate minima at inequivalent momenta ±Q, and just below the saturation field the system can be effectively represented as a dilute one-dimensional lattice gas of two species of bosons that correspond to magnons with momenta around ±Q. We present a theory of effective interactions in such a dilute magnon gas that allows us to make quantitative predictions for arbitrary values of the spin. With the help of this method, we are able to establish the magnetic phase diagram of frustrated chains close to saturation and study phase transitions between several nontrivial states, including a two-component Luttinger liquid, a vector chiral phase, and phases with bound magnons. We study those phase transitions numerically and find a good agreement with our analytical predictions.

Ultracold bosons in zig-zag optical lattices present a rich physics due to the interplay between frustration induced by lattice geometry, two-body interactions, and a three-body constraint. Unconstrained bosons may develop chiral superfluidity and become a Mott insulator even at vanishingly small interactions. Bosons with a three-body constraint allow for a Haldane-insulator phase in nonpolar gases, as well as pair superfluidity and density-wave phases for attractive interactions. These phases may be created and detected within the current state-of-the-art techniques.

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