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 ${Z}_{2}$ 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.
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 ${Z}_{2}$ 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.
Motivated by experiments exploring the physics of neutral atoms in artificial magnetic fields, we study the ground state of bosons interacting with long-range dipolar interactions on a two-leg ladder. We focus on the limit where the number of particles per site is large and the interactions are weak. Using two complementary variational approaches, we find rich physics driven by the long-range forces. Generically, long-range interactions tend to destroy the Meissner phase in favor of modulated density wave phases. For example, nearest-neighbor interactions produce an interleg charge density wave phase, where the total density remains uniform but the density on each leg of the ladder is modulating in space, out of phase with one another. Next-nearest-neighbor interactions lead to a fully modulated biased ladder phase, where all of the particles are on one leg of the ladder. This state simultaneously breaks Z2 reflection symmetry and U(1) translation symmetry. For values of the flux near $\ensuremath{\phi}=\ensuremath{\pi}$, we find a switching effect for arbitrarily weak interactions, where the density is modulated but the chiral current changes sign on every plaquette. Arbitrarily weak attractive interactions along the rungs destroy the Meissner phase completely, in favor of a modulated density wave phase. Remarkably, varying the rung to ladder hopping produces a cascade of first-order transitions between modulated density wave states with different wave vectors, which manifests itself as discrete jumps in the chiral current. Polarizing the dipoles along the ladder direction yields a region of phase space where a stable biased ladder phase occurs even at arbitrarily weak rung hopping. We discuss the experimental consequences of our work and draw connections between our work and recent experiments on cold atoms in synthetic dimensions.
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.
Abstract The realization and detection of chiral physics with ultracold atomic gases provide a unique path for the exploration of topological phases. Here, we show that the interplay of magnetic field and interacting particles in an extended two-leg ladder leads to rich chiral Bloch dynamics. Considering both the on-site contact interaction and nearest-neighbor interactions, the ground state and Bloch dynamics of the system are studied analytically and numerically. When the system is in the ground state, the threshold and phase diagram for the transition between zero-momentum state and plane-wave state are analytically obtained, showing the nearest-neighbor interactions along the legs and rungs have opposite impact on the ground state transition, providing new opportunity to manipulate the ground state transition. When the ladder is perturbated under an external linear force, chiral dephasing of Bloch oscillations (BOs), i.e. symmetry breaking damped BOs (the damping rate of BOs on one leg is larger than the other), are observed. This chirality is absent for vanishing the magnetic field and atomic interaction. Particularly, the chirality of damped BOs is inversed when the magnetic field (chiral current) is inversed. In addition, the damping of BOs induced by different types of atomic interactions is different, and the strength and damping rate of BOs initialized in different ground states are distinct, offering dynamic ways to detect the different ground states. Furthermore, the persistent chiral Bloch oscillations observed in single particle case is predicted analytically, which is a crucial requirement for observation and application of chiral BOs in nonlinear regime. Our results provide an interesting path towards the exploration of topological atomic superfluids.
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.
Grand-canonical phase diagram and chiral-current suppression at π 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 2×4 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.
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.