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 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.
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.
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.
We investigate the ground-state properties of ultracold atoms trapped in a two-leg ladder potential in the presence of an artificial magnetic field in a staggered configuration. We focus on the strongly interacting regime and use the Landau theory of phase transitions and a mean field Gutzwiller variational method to identify the stable superfluid phases and their boundaries with the Mott-insulator regime as a function of magnetic flux. In addition, we calculate the local and chiral currents of these superfluid phases, which show a staggered vortex-antivortex configuration. The analytical results are confirmed by numerical simulations using a cluster mean-field-theory approach.
We investigate the ground-state properties of ultracold atoms with long-range interactions trapped in a two-leg ladder configuration in the presence of an artificial magnetic field. Using a Gross-Pitaevskii approach and a mean-field Gutzwiller variational method, we explore both the weakly interacting and strongly interacting regimes, respectively. We calculate the boundaries between the density-wave--supersolid and the Mott-insulator--superfluid phases as a function of magnetic flux and uncover regions of supersolidity. The mean-field results are confirmed by numerical simulations using a cluster mean-field approach.
Motivated by a recent experiment with optical lattices that has realized a ladder geometry with an effective magnetic field [Atala et al., Nat. Phys. 10, 588 (2014)], we study the dynamics of bosons on a tight-binding two-leg ladder with complex hopping amplitudes. This system displays a quantum phase transition even without interactions. We study the nonequilibrium dynamics without and with interactions, in the presence of a harmonic trapping potential. In particular we consider dynamics induced by quenches of the trapping potential and of the magnitude of the rung hopping. We present a striking ``slowing down'' effect in the collective mode dynamics near the phase transition. This manifestation of a slowing down phenomenon near a quantum phase transition can be visualized unusually directly: The collective mode dynamics can be followed experimentally in real time and real space by imaging the atomic cloud.