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arXiv:1504.06159 · Physical Review A

Population-imbalance instability in a Bose-Hubbard ladder in the presence of a magnetic flux

Shun Uchino, Akiyuki Tokuno

Published Jul 21, 2015• 35 citations
arXivHTMLPDF

Abstract

We consider a two-leg Bose-Hubbard ladder in the presence of a magnetic flux. We make use of Gross-Pitaevskii, Bogoliubov, bosonization, and renormalization group approaches to reveal a structure of ground-state phase diagrams in a weak-coupling regime relevant to cold atom experiments. It is found that, except for a certain flux $\ensuremath{\phi}=\ensuremath{\pi}$, the system shows different properties as changing hoppings, which also leads to a quantum phase transition similar to the ferromagnetic $XXZ$ model. This implies that population-imbalance instability occurs for certain parameter regimes. On the other hand, for $\ensuremath{\phi}=\ensuremath{\pi}$, it is shown that an umklapp process caused by commensurability of a magnetic flux stabilizes a superfluid with chirality and the system does not experience such a phase transition.

DOI
10.1103/physreva.92.013625

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We consider a two-leg Bose-Hubbard ladder in the presence of a magnetic flux. We make use of Gross-Pitaevskii, Bogoliubov, bosonization, and renormalization group approaches to reveal a structure of ground-state phase diagrams in a weak-coupling regime relevant to cold atom experiments. It is found that, except for a certain flux \ensuremathϕ=\ensuremathπ\ensuremath{\phi}=\ensuremath{\pi}\ensuremathϕ=\ensuremathπ, the system shows different properties as changing hoppings, which also leads to a quantum phase transition similar to the ferromagnetic XXZXXZXXZ model. This implies that population-imbalance instability occurs for certain parameter regimes. On the other hand, for \ensuremathϕ=\ensuremathπ\ensuremath{\phi}=\ensuremath{\pi}\ensuremathϕ=\ensuremathπ, it is shown that an umklapp process caused by commensurability of a magnetic flux stabilizes a superfluid with chirality and the system does not experience such a phase transition.
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.
The stability and superfluidity of the Bose-Einstein condensate in two-leg ladder with magnetic field are studied. The dispersion relation and the phase diagram of the system are obtained. Three phases are revealed: the Meissner phase, the biased ladder (BL) phase, and the vortex phase. The dispersion relation and phase transition of the system strongly depend on the magnitude of atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. Particularly, the change of the energy band structure in the phase transition region is modified significantly by the atomic interaction strength. Furthermore, based on the Bogoliubov theory, the energetic and dynamical stability of the system are invested. The stability phase diagram in the full parameter space is presented, and the dependence of superfluidity on the dispersion relation is illustrated explicitly. The atomic interaction strength can produce dynamical instability in the energetic unstable region and can expand the superfluid region. The results show that the stability of the system can be controlled by the atomic interaction strength, the rung-to-leg coupling ratio and the magnetic flux. In addition, the excitation spectrums in the Meissner phase, BL phase and vortex phase are further studied. The modulation of the excitation spectrum and the energetic stability of the system by the atomic interaction strength, the rung-to-leg coupling ratio and magnetic flux is discussed. Finally, through the numerical simulation, the dynamical instability of the system is verified by the time evolution of the Bloch wave and rung current. This provides a theoretical basis for controlling the superfluidity of the system.
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 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.
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.
Grand-canonical phase diagram and chiral-current suppression at πππ flux in a bosonic two-leg ladder
We investigate the ground-state phase diagram of repulsively interacting bosons on a two-leg ladder threaded by a uniform artificial magnetic flux, using the cluster Gutzwiller mean-field method. In the strong-rung-coupling regime, self-consistent calculations are performed on a 2×42\times42×4 cluster. By analyzing the superfluid order parameter, leg-resolved currents, chiral current, the current ratio on adjacent legs, and the density imbalance between the two legs, we distinguish Mott-insulating from superfluid regimes and characterize the observed states as Meissner-like, vortex-like (superfluid or Mott insulating), or biased-ladder. In regions overlapping with previous DMRG studies, our results qualitatively agree with the established phase structure, demonstrating that the cluster Gutzwiller approach balances computational efficiency and physical accuracy. We then construct the first grand-canonical ttt--μμμ phase diagrams for this system, revealing how the magnetic flux modifies the shape, tilt, and extent of the Mott lobes. We further explore previously inaccessible regimes, including higher fillings ρ≳1ρ\gtrsim1ρ≳1 and the intermediate interaction window U/t∈[7.69,9.09]U/t\in[7.69,9.09]U/t∈[7.69,9.09]. Special attention is paid to φ=πφ=πφ=π, where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of φ=πφ=πφ=π and −π-π−π modulo 2π2π2π, a combined symmetry forbids net chiral currents, leading to a nonchiral Mott-insulating state, in contrast to the chiral-superfluid tendency expected away from φ=πφ=πφ=π. Our results offer a computationally efficient route for mapping the global phase structure of bosonic flux ladders and provide guidance for future ultracold-atom experiments in artificial gauge fields.