Dynamics and phase transitions in biased ladder systems with magnetic flux

Abstract

The ground states and the dynamics of a biased two-leg flux ladder in the presence of a gravitational field are discussed. In the absence of the gravitational field, the ground states and the critical condition of phase transition are obtained analytically. We identify the Meissner phase, Vortex phase, and interestingly, two new Plane Wave phases, that break both Z2 and time-reversal symmetry, characterized by the imbalance particle density distribution, asymmetry double well energy band structure in Plane Wave I (PWI) phase and asymmetry single well energy band structure in Plane Wave II (PWII) phase, respectively. In the presence of a longitudinal dc gravitational field, rich chiral Bloch oscillation and Landau-Zener tunneling are predicted theoretically and confirmed numerically. The characteristics of the chiral Bloch oscillation can distinguish the novel phases intuitively. Our work gives an interesting way to discuss the quantum phase transitions in a dynamical way.