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arXiv:1411.0749 · Physical Review A

Mott transition in a two-leg Bose-Hubbard ladder under an artificial magnetic field

Ahmet Keleş, Mehmet Özgür Oktel

Published Jan 28, 2015• 57 citations
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Abstract

We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field and investigate the superfluid--to--Mott insulator transition in this setting. Recently, this system has been experimentally realized [M. Atala et al., Nature Phys. 10, 588 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion, and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions, indicating the possibility of correlated phases.

DOI
10.1103/physreva.91.013629

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We consider the Bose-Hubbard model on a two-leg ladder under an artificial magnetic field and investigate the superfluid--to--Mott insulator transition in this setting. Recently, this system has been experimentally realized [M. Atala et al., Nature Phys. 10, 588 (2014)], albeit in a parameter regime that is far from the Mott transition boundary. Depending on the strength of the magnetic field, the single-particle spectrum has either a single ground state or two degenerate ground states. The transition between these two phases is reflected in the many-particle properties. We first investigate these phases through the Bogoliubov approximation in the superfluid regime and calculate the transition boundary for weak interactions. For stronger interactions the system is expected to form a Mott insulator. We calculate the Mott transition boundary as a function of the magnetic field and interleg coupling with mean-field theory, strong-coupling expansion, and density matrix renormalization group (DMRG). Finally, using the DMRG, we investigate the particle-hole excitation gaps of this system at different filling factors and find peaks at simple fractions, indicating the possibility of correlated phases.
We investigate the ground-state properties of ultracold atoms with long-range interactions trapped in a two-leg ladder configuration in the presence of an artificial magnetic field. Using a Gross-Pitaevskii approach and a mean-field Gutzwiller variational method, we explore both the weakly interacting and strongly interacting regimes, respectively. We calculate the boundaries between the density-wave--supersolid and the Mott-insulator--superfluid phases as a function of magnetic flux and uncover regions of supersolidity. The mean-field results are confirmed by numerical simulations using a cluster mean-field approach.
We investigate the ground-state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex-antivortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field-theory approach.
Bosons in periodic potentials with very strong local interactions, known as constrained bosons, often exhibit interesting physical behavior. We investigate the ground-state properties of a two-leg Bose-Hubbard ladder by imposing a three-body constraint in one leg and a hard-core constraint in the other. By using the cluster mean-field theory approximation and the density matrix renormalization group method, we show that at unit filling, for strong two-body attraction among the three-body constrained bosons, the system becomes a gapped pair-Mott insulator where all the bosons form strong bound pairs and occupy the leg with the three-body constraint. With increase in hopping strength, this pair-Mott insulator phase undergoes a phase transition to the gapless superfluid phase for equal leg and rung hopping strengths. However, when the rung hopping is stronger compared to the leg hopping, we obtain a crossover to another gapped phase which is called the rung-Mott insulator phase where the bosons prefer to delocalize on the rungs rather than the legs. By moving away from unit filling, the system remains in the superfluid phase except for a small region below the gapped phase where a pair superfluid phase is stabilized in the regime of strong attractive interaction. We further extend our studies by considering the three-body constraint in both the legs and find that the crossover from the gapped to gapped phase does not occur; rather, the system undergoes a transition from a pair-rung-Mott insulator phase to the superfluid phase at unit filling. Moreover, in this case, we find the signature of the pair superfluid phase on either side of this gapped phase.
We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.
Abstract We investigate the ground state properties of interacting bosons on a triangular ladder subject to an artificial magnetic field. By means of the mean-field approximation, rich phases are revealed in the limit of weak interaction and large bosons occupation per site, including the Meissner superfluid, vortex superfluid, biased chiral superfluid (C-SF), C-SF and insulating phases. The quantum phases can be precisely identified and the underlying physics of phase transitions can be clarified by utilizing order parameters based on the atomic density, the effective rung current, and the current asymmetry ratio. Meanwhile, the phase transition of the system can be effectively controlled by adjusting the rung-to-leg coupling ratio, the magnetic flux and the atomic interaction. Furthermore, using Bogoliubov theory, we have mapped the stability phase diagram across all parameters, and clarified the interdependence between superfluidity and the dispersion relation. The excitation spectrum, which effectively describes the system’s energetic stability, is governed by the rung-to-leg coupling ratio, the magnetic flux, and the atomic interaction. Numerical simulations validate the dynamical instability of the system. This work offers a theoretical foundation for identifying new quantum phases exhibited by ultracold atoms in optical lattices and new experimental approaches for achieving system superfluidity.
We study the fully gapped chiral Mott insulator (CMI) of frustrated Bose-Hubbard models on ladders and two-dimensional lattices by perturbative strong-coupling analysis and density matrix renormalization group (DMRG). First we show the existence of a low-lying exciton state on several geometries carrying the correct quantum numbers responsible for the condensation of excitons and formation of the CMI in the intermediate interaction regime. Then we perform systematic DMRG simulations on several two-leg ladder systems with $\ensuremath{\pi}$ flux and carefully characterize the two quantum phase transitions. We discuss the possibility to extend the generally very small CMI window by including repulsive nearest-neighbor interactions or changing density and coupling ratios.