The interplay between spontaneous symmetry breaking in many-body systems, the wavelike nature of quantum particles and lattice effects produces an extraordinary behavior of the chiral current of bosonic particles in the presence of a uniform magnetic flux defined on a two-leg ladder. While noninteracting as well as strongly interacting particles, stirred by the magnetic field, circulate along the system's boundary in the counterclockwise direction in the ground state, interactions stabilize vortex lattices. These states break translational symmetry, which can lead to a reversal of the circulation direction. Our predictions could readily be accessed in quantum gas experiments with existing setups or in arrays of Josephson junctions.
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.
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.
We study the magnetic orbital effect of a doped two-leg ladder in the presence of a magnetic field component perpendicular to the ladder plane. Combining both low-energy approach (bosonization) and numerical simulations (density-matrix renormalization group) on the strong coupling limit ($t\text{\ensuremath{-}}J$ model), a rich phase diagram is established as a function of hole doping and magnetic flux. Above a critical flux, the spin gap is destroyed and a Luttinger liquid phase is stabilized. Above a second critical flux, a reentrance of the spin gap at high magnetic flux is found. Interestingly, the phase transitions are associated with a change of sign of the orbital susceptibility. Focusing on the small magnetic field regime, the spin-gapped superconducting phase is robust, but immediately acquires algebraic transverse (i.e., along rungs) current correlations which are commensurate with the
4kF density correlations. In addition, we have computed the zero-field orbital susceptibility for a large range of doping and interaction ratio
J∕t: we found strong anomalies at low
J∕t only in the vicinity of the commensurate fillings corresponding to $\ensuremath{\delta}=1∕4$ and
1∕2. Furthermore, the behavior of the orbital susceptibility reveals that the nature of these insulating phases is different: while for $\ensuremath{\delta}=1∕4$ a
4kF charge density wave is confirmed, the $\ensuremath{\delta}=1∕2$ phase is shown to be a bond order wave.
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.
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.