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• The ground states and the dynamics of the biased bosonic ladder are discussed. • The Meissner, Vortex and two new Plane Wave phases are predicted analytically. • Interestingly, the Plane Wave phases break both Z 2 and time-reversal symmetry. • Rich chiral Bolch oscillations are predicted to distinguish the novel phases. • The work gives an interesting way to explore phases in condensed physics dynamically. 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 Z 2 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. [ABSTRACT FROM AUTHOR]

The realization and detection of two-leg ladders with the interplay of the artificial gauge field provide an ideal platform for investigations of the quantum phase transition and quantum dynamics. Here, we realize the spatio-temporal evolution dynamics of two-leg ladder systems with magnetic flux analytically and numerically. The quench dynamics induced by giving sudden quenches of initial density distributions of left and right leg components, rung-to-leg coupling ratios and magnetic flux from the ground state are discussed in detail. Affected by the chirality of ladder systems together with the tunneling between the two legs, rich and interesting quench dynamics observed, which including the Josephson Oscillations (JOs), Chiral Density Wave (CDW), Scissors Mode (SM), Periodic Torsional Vortex (PTV) and Periodic Torsional-Scissors Vortex (PTSV). Remarkably, we find that the oscillation frequency of the quench dynamics associated with coupling ratios and magnetic flux can be used to identify the phase transition between the Meissner phase and Vortex phase. Therefore, our work may provide an effective way to distinguish phase transitions by using quench dynamics. [ABSTRACT FROM AUTHOR]