The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.
The two-leg magnetic ladder is the simplest and ideal model to reflect the coupling effects of lattice and magnetic field. It is of great significance to study some novel phases, topological characteristics, and chiral characteristics in condensed matter physics. In particular, the left-right leg degree of freedom can be regarded as a pseudospin, and the two-leg magnetic ladder also provides an ideal platform for the study of spin dynamics. Here the ground state, Bloch oscillations (BOs), and spin dynamics of the interacting two-leg magnetic ladder subject to an external linear force are studied by using variational approach and numerical simulation. In the absence of the external linear force, the critical condition of transition between the zero-momentum state and plane-wave state is obtained analytically, and the physical mechanism of the ground-state transition is revealed. When the external linear force presents, the occurrence of BOs excites the spin dynamics, and we reveal the chiral BOs and the accompanied spin dynamics of the system in different ground states. In particular, we further study the influence of periodically modulated linear force on BOs and spin dynamics. The frequencies of the linear force corresponding to the resonances and pseudoresonances are obtained analytically, which result in rich nonlinear dynamics. In resonances, stable and strong BOs (with larger amplitude) are observed. In pseudoresonances, because the pseudoresonance frequencies are related to the initial momentum and phase of the wave packet, a dispersion effect takes place and strong diffusion of wave packet occurs. When the frequency is nonresonant, drift and weak dispersion of wave packet occur simultaneously with the wave-packet oscillation. In all cases, the wave-packet dynamics is accompanied with periodic but anharmonic pseudospin oscillation. The BOs and spin dynamics are effectively controlled by periodically modulating the linear force.
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.
The bosonic magnetic ladder, a universal and the simplest model to reproduce the coupled effects of orbital magnetic field and optical lattices, provides an ideal platform for studying spin-orbit coupling, quantum phase transition and chiral topological states of matter. Here, considering both the on-site and rungwise interactions, the ground-state and chiral nonequilibrium dynamics of the bosonic magnetic ladder under an external harmonic trap are studied analytically and numerically. The threshold for the ground-state transition from the zero momentum state to the plane wave state is obtained. We find that the external harmonic potential has an important impact on the phase transition, which strongly depends on the magnetic field and an effective atomic interaction introduced by the interplay of on-site and rungwise interactions. The ground-state phase transitions can be well manipulated by changing the strengths of the external harmonic trap and rungwise interaction. Furthermore, by quenching the harmonic trap, rich nonlinear modes coupling and chiral nonequilibrium dynamics are revealed, which have distinct characteristics in different phases. Strong spin-momentum locking, softening of the collective modes and anharmonic collective dynamics are observed near the phase transition region. Particularly, novel nonlinear chiral dynamics induced by the interplay of strong spin-momentum locking and external trapping near the phase transition region are obtained, including the chiral out-of-phase oscillation of particles in the two legs (i.e., chiral opposite oscillation of particles in the two legs), chiral alternate oscillation of particles between the two legs (i.e., particles primarily populate the right (left) leg when moving away (returning to) the initial position), and chiral focusing-expanding transition of atomic wavepacket on the two legs (i.e., the wave packet exhibits a focused (expanded) state when moving toward (away from) the equilibrium point). Chiral dephasing and phase revival occur near the phase transition region, while coherent harmonic collective dynamics persists far away from the phase transition point. The observed chiralities can be well manipulated by the magnetic field.
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.
In this work we study the model of flux lattice, specifically a two-leg Bose–Hubbard ladder lattice subject to effective magnetic flux, which can be implemented using spin–orbit coupled cold atoms trapped in an optical lattice. This model has attracted much recent research interest due to that it provides a platform to study the interplay between artificial gauge fields and interactions. We consider that collective dipole oscillations are activated in this model via quenching an external harmonic trapping potential and show that this system can exhibit unique dynamical behaviors in terms that oscillation amplitude and period critically dependent on the spin–orbit coupling. A dynamical slowing down in collective dipole oscillations will take place near the transition point between the Meissner superfuild and vortex superfluid phases, which agrees quantitatively with a variational analysis. We show that such a quantum phase transition can also be probed via the damping of the collective dipole oscillation. When the quenching displacement is large, the collective center-of-mass motion behaves as damped oscillation and the damping reaches its maximum near the phase transition point. The specific dynamical phenomena are explained with eigenspectra and level populations after the quenching. In the presence of interactions, the time-dependent density–matrix renormalization group (tDMRG) method is hired to study the collective dynamics. The case with weak interactions is similar to that without interactions, except that interactions tend to enhance damping. In addition to that, Bragg reflection can be observed when the quenching displacement exceeds a critical value. The case with strong interactions is also studied, in which case the phase transition points will be dramatically changed and the system can even move into the Mott insulator phase, which will greatly affect the corresponding collective dynamics. The phenomena predicted in this work can be readily observed in current available experiments on atom flux lattices.
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 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.