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Results in Physics

Bosonic flux ladder considering the next nearest neighbor kinetic tunneling

Dian-Cheng Zhang

Published Dec 4, 2023• 0 citations
Publisher

Abstract

We investigate interacting bosons in a two-leg lattice, which is subject to an uniform artificial magnetic field. Its Hamiltonian takes into account the next nearest neighbor kinetic tunneling term, along the principal diagonal direction. With the help of an inhomogeneous dynamical Gutzwiller mean-field theory, we figure out four novel quantum phases of the system site by site, three of which are the dual vortex lattice, the triplet vortex lattice, and the composite vortex lattice. They particularly present parallelogram vortical particle currents, inside those conventional rectangular vortical currents, due to the import of next nearest neighbor kinetic tunneling. Under certain parameters, we further identify the crossed circulation lattice featuring alternating sequences on local currents and occupancies, whose minimal periods are determined by the value of flux quanta.

DOI
10.1016/j.rinp.2023.107228

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We investigate interacting bosons in a two-leg lattice, which is subject to an uniform artificial magnetic field. Its Hamiltonian takes into account the next nearest neighbor kinetic tunneling term, along the principal diagonal direction. With the help of an inhomogeneous dynamical Gutzwiller mean-field theory, we figure out four novel quantum phases of the system site by site, three of which are the dual vortex lattice, the triplet vortex lattice, and the composite vortex lattice. They particularly present parallelogram vortical particle currents, inside those conventional rectangular vortical currents, due to the import of next nearest neighbor kinetic tunneling. Under certain parameters, we further identify the crossed circulation lattice featuring alternating sequences on local currents and occupancies, whose minimal periods are determined by the value of flux quanta.
Abstract We conduct a dynamical Gutzwiller mean-field study of interacting bosons on a four-leg ladder, subject to a uniform flux. The ground states dependent on the magnetic flux and kinetic tunneling strength are explored. Consequently, we identify the super-vortical lattice, as well as the inner-Meissner phase, which presents Meissner currents just along the intimal legs within the flux ladder. The staggered-current phase is also allowed, with its formation condition altered because of the four-leg construction. The number of legs on the flux ladder can make an effect.
We examine a bosonic two-leg ladder model subject to a magnetic flux and especially focus on a regime where the lower-energy band has two minima. By using a low-energy field theory approach, we study several issues discussed in the system: the existence of local patterns in density and current, chiral-current reversal, and the effect of a nearest-neighbor interaction along the rung direction. In our formalism, the local patterns are interpreted as a result of breaking of discrete symmetry. The chiral-current reversal occurs through a competition between a current component determined at a commensurate vortex density causing an enlargement of the unit cell and another component, which is proportional to the magnetic-field doping from the corresponding commensurate flux. The nearest-neighbor interaction along the rung direction available with the technique on a synthetic dimension is shown to favor a population-imbalance solution in an experimentally relevant regime.
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 investigate the nonequilibrium dynamics of interacting bosons in a two-leg ring ladder pierced by an artificial magnetic flux, where the particles are initially localized in the central sites of both rings, and the ac-driven local energy shifts are applied to the remaining lattice sites. Within the mean-field approximation, we demonstrate the emergence of nonlinear self-trapping for strong interparticle interactions, and characterize the distinct excitation regimes in the absence of the inter-ring tunneling. The artificial magnetic flux typically introduces Peierls phase factors, which induces complex-valued hopping amplitudes and leads to directed net particle currents along the chains. By further incorporating the finite inter-ring coupling and biased intra-ring hopping, we reveal that the tuning of the drive frequency and Peierls phase allows the precise control over both the intensity and direction of particle currents, which facilitates the transition between chiral and antichiral dynamics. These findings offer insights into the coherent manipulation of matter-wave transports in closed-loop lattice configurations and the exploration of nonequilibrium synthetic quantum systems in related fields.
We consider a system of weakly interacting bosons confined on a planar double ring lattice subjected to two artificial gauge fields. We determine its ground state by solving coupled discrete nonlinear Schr\"odinger equations at mean-field level. At varying inter-ring tunnel coupling, flux, and interactions, we identify the vortex, Meissner, and biased-ladder phases also predicted for a bosonic linear ladder by a variational ansatz. We also find peculiar features associated to the ring geometry, in particular parity effects in the number of vortices, and the appearance of a single vortex in the Meissner phase. We show that the persistent currents on the rings carry precise information on the various phases. Finally, we propose a way of observing the Meissner and vortex phases via spiral interferogram techniques.
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.