Nonlinear modes coupling and chiral nonequilibrium dynamics in bosonic magnetic ladder under a harmonic trap

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.