Ultracold bosonic atoms trapped in a two-leg ladder pierced by a magnetic field provide a minimal and quasi-one-dimensional instance to study the interplay between orbital magnetism and interactions.Using time-dependent matrix-product-state simulations, we investigate the properties of the so-called 'Meissner' and 'vortex' phases which appear in such a system, focusing on the experimentally accessible observables.We discuss how to experimentally monitor the phase transition, and show that the response to the modulation of the density imbalance between the two legs of the ladder is qualitatively different in the two phases.We argue that this technique can be used as a tool for many-body spectroscopy, allowing us to quantitatively measure the spin gap in the Meissner phase.We finally discuss its experimental implementation.
Ultracold bosonic atoms trapped in a two-leg ladder pierced by a magnetic field provide a minimal and quasi-one-dimensional instance to study the interplay between orbital magnetism and interactions.Using time-dependent matrix-product-state simulations, we investigate the properties of the so-called 'Meissner' and 'vortex' phases which appear in such a system, focusing on the experimentally accessible observables.We discuss how to experimentally monitor the phase transition, and show that the response to the modulation of the density imbalance between the two legs of the ladder is qualitatively different in the two phases.We argue that this technique can be used as a tool for many-body spectroscopy, allowing us to quantitatively measure the spin gap in the Meissner phase.We finally discuss its experimental implementation.
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 [M. Atala et al., Nat. 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, interleg 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.
Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to a strong magnetic field and a lattice potential. The recent realization of flux ladders in ultracold quantum gases with artificial magnetic fields has attracted great interest. In this thesis, we study various aspects of interacting bosonic flux ladders using extensive matrix-product-state based calculations. Specifically, the numerical techniques include the variational ground-state optimization by means of the density-matrix renormalization-group method, a purification approach for the study of finite-temperature states, as well as time-evolution methods for the simulation of quench dynamics. In an introductory part, we recapitulate key features and important ground-state phases of the flux-ladder model and discuss the numerical methods. Subsequently, the main results are presented as follows. First, the emphasis is put on model parameters which are envisioned to be realized in a future quantum gas experiment exploiting the internal states of potassium atoms as a synthetic dimension. Considering a particle filling of one boson per rung, we map out the ground-state phase diagram and report on a Mott-insulating Meissner phase as well as on biased-ladder phases, which might exist on top of superfluids and Mott insulators. Moreover, we demonstrate that quantum quenches of suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of particle hopping along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase and the Meissner phase can be observed in the transient dynamics. Second, we study the effect of finite temperatures in flux ladders. So far, most of the theoretical work on these systems has concentrated on zero-temperature phases while the finite-temperature regime remains largely unexplored. However, the question if and up to which temperature characteristic features of the ground-state phases persist is relevant in experimental realizations. In order to explore the finite-temperature regime, a matrix-product-state based purification approach for the simulation of strongly interacting bosons has been implemented. Our study is focused on chiral currents and momentum-distribution functions, which are key observables in ultracold quantum gases, and our main results concern the most prominent vortex liquid-to-Meissner crossover. We demonstrate that signatures of the vortex-liquid phase can still be detected at elevated temperatures from characteristic finite-momentum maxima in the momentum-distribution functions, while the vortex-liquid phase leaves weaker fingerprints in the chiral current. In order to determine the range of temperatures over which these signatures can be observed, we introduce a suitable measure for the contrast of these maxima. The results are condensed into a finite-temperature crossover diagram. Third, we investigate the Hall response in bosonic flux ladders. While flux ladders are the most simple lattice models giving rise to the Hall effect, the theoretical description of the many-body ground-state Hall response in these systems remains a tricky problem and an active line of research. In view of current quantum gas experiments, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Most importantly, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases using a semiclassical approach. In conclusion, we present a brief summary of our work and touch on possible follow-up studies which are directly connected to the contents of this thesis.
A boson two-leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and density matrix renormalization group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is ρπ and close to it, where ρ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung–rung correlation function and the spin–spin and charge–charge static structure factors.
Flux ladders constitute the minimal setup enabling a systematic understanding of the rich physics of interacting particles subjected simultaneously to strong magnetic fields and a lattice potential. In this paper, the ground-state phase diagram of a flux-ladder model is mapped out using extensive density-matrix renormalization-group simulations. The emphasis is put on parameters which can be experimentally realized exploiting the internal states of potassium atoms as a synthetic dimension. The focus is on accessible observables such as the chiral current and the leg-population imbalance. Considering a particle filling of one boson per rung, we report the existence of a Mott-insulating Meissner phase as well as biased-ladder phases on top of superfluids and Mott insulators. Furthermore, we demonstrate that quantum quenches from suitably chosen initial states can be used to probe the equilibrium properties in the transient dynamics. Concretely, we consider the instantaneous turning on of hopping matrix elements along the rungs or legs in the synthetic flux-ladder model, with different initial particle distributions. We show that clear signatures of the biased-ladder phase can be observed in the transient dynamics. Moreover, the behavior of the chiral current in the transient dynamics is discussed. The results presented in this paper provide guidelines for future implementations of flux ladders in experimental setups exploiting a synthetic dimension.
Quasi-one-dimensional lattice systems such as flux ladders with artificial gauge fields host rich quantum-phase diagrams that have attracted great interest. However, so far, most of the work on these systems has concentrated on zero-temperature phases while the corresponding finite-temperature regime remains largely unexplored. The question if and up to which temperature characteristic features of the zero-temperature phases persist is relevant in experimental realizations. We investigate a two-leg ladder lattice in a uniform magnetic field and concentrate our study on chiral edge currents and momentum-distribution functions, which are key observables in ultracold quantum-gas experiments. These quantities are computed for hard-core bosons as well as noninteracting bosons and spinless fermions at zero and finite temperatures. We employ a matrix-product-state based purification approach for the simulation of strongly interacting bosons at finite temperatures and analyze finite-size effects. Our main results concern the vortex-fluid-to-Meissner crossover of strongly interacting bosons. We demonstrate that signatures of the vortex-fluid phase can still be detected at elevated temperatures from characteristic finite-momentum maxima in the momentum-distribution functions, while the vortex-fluid phase leaves weaker fingerprints in the local rung currents and the chiral edge current. In order to determine the range of temperatures over which these signatures can be observed, we introduce a suitable measure for the contrast of these maxima. The results are condensed into a finite-temperature crossover diagram for hard-core bosons.
We characterize the Hall response of non-interacting fermionic M-leg ladders in the presence of an artificial magnetic flux, that can be realized in one-dimensional optical lattices supplemented with a synthetic dimension. We focus on the Hall imbalance, which can be directly measured in experiments with ultracold fermionic atoms. At relatively large synthetic flux we find a dependence of the density that contrasts with previously reported density-independent behavior. In particular, the Hall imbalance can be significantly enhanced in the limit of small density of particles (or holes), or it can vanish and change sign at specific fluxes, which we obtain analytically in the large inter-leg coupling regime. This behavior is explained in terms of Lifshitz transitions of the band structure, where the number of Fermi points changes as a function of the flux and density. Finally, we explore the connection between these transitions and the so-called Meissner-vortex transition for fermionic ladders by computing the site-resolved leg and rung currents and discussing the similarities and differences with the bosonic counterpart.