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.
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 investigate the localization of a Bose-Einstein condensate trapped in a two-leg ladder in the presence of an artificial magnetic field via Bose-Hubbard model and discuss its abundant localized phenomena using variational approximation and direct numerical simulation. A two-leg bosonic ladder provides an ideal platform to study the complex dynamics of Bose-Einstein condensates in an optical lattice subject to an artificial magnetic field. As a main result, the system displays rich interesting localized states including self-trapping, soliton and breather. The coupling of the repulsive atomic interaction, artificial magnetic field, the rung-to-leg coupling ratio of the ladder, and the initial population difference of atoms between the two legs of the ladder results in the transitions between the localized states. The critical conditions for the transitions between the localized states are given analytically and are intuitively demonstrated in the phase diagram. Particularly, when the rung-to-leg coupling radio of the ladder satisfies a critical condition, we have the localized states with no local atomic currents between the two legs, otherwise, we observe the localized states with local atomic currents between the two legs. Finally, the results obtained via variational method are confirmed by the numerical simulations of the full discrete nonlinear Schrödinger equation describing the system.
We calculate the ground state of a Bose gas trapped on a two-leg ladder where Raman-induced hopping mimics the effect of a large magnetic field. In the mean-field limit, where there are large numbers of particles per site, this maps onto a uniformly frustrated two-leg ladder classical spin model. The net particle current always vanishes in the ground state, but generically there is a finite ``chiral current,'' corresponding to equal and opposite flow on the two legs. We vary the strength of the hopping across the rungs of the ladder and the interaction between the bosons. We find the following three phases. (1) A ``saturated chiral current phase'' (SCCP), where the density is uniform and the chiral current is simply related to the strength of the magnetic field. In this state the only broken symmetry is the U(1) condensate phase. (2) A ``biased ladder phase'' (BLP), where the density is higher on one leg than the other. The fluid velocity is higher on the lower density leg, so the net current is zero. In addition to the U(1) condensate phase, this has a broken
Z2 reflection symmetry. (3) A ``modulated density phase'' (MDP), where the atomic density is modulated along the ladder. In addition to the U(1) condensate phase, this has a second broken U(1) symmetry corresponding to translations of the density wave. We further study the fluctuations of the condensate in the BLP, finding a roton-maxon-like excitation spectrum. Decreasing the hopping along the rungs softens the spectrum. As the energy of the ``roton'' reaches to zero, the BLP becomes unstable. We describe the experimental signatures of these phases, including the response to changing the frequency of the Raman transition.
The realization and detection of various phase transitions in interacting two-leg bosonic flux ladders are at the frontier of the present theoretical and experimental research in condensed-matter physics. We develop a biased two-leg Bose-Hubbard flux ladder model and first achieve the ground states and phase transition conditions of this system by the mean-field approach and variational analysis. Rich phases are revealed, including two different kinds of plane-wave phase, i.e., plane wave I (characterized with one single energy minimum of the energy band) and plane wave II (characterized with two nondegenerate local energy minima of the energy band), and interestingly the asymmetry vortex phase with the breaking of both
Z2 reflection symmetry and translational symmetry of space, which is characterized by the vortex with imbalanced density distributions on two legs. Moreover, the corresponding quantum phases can also be distinguished by the order parameters and the excitation spectra of the plane-wave phase intuitively. Furthermore, we demonstrate that this biased ladder system also makes it possible to realize a different dynamical asymmetric vortex state, which shows a dynamical supersolidlike property.
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.
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
2×4 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
t--
μ 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≳1 and the intermediate interaction window
U/t∈[7.69,9.09]. Special attention is paid to
φ=π, where the effective triangular-ladder mapping becomes singular. Owing to the equivalence of
φ=π and
−π modulo
2π, 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=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.