Spatiotemporal Evolution of Topological Order Upon Quantum Quench Across the Critical Point

We consider a topological superconducting wire and use the string order parameter to investigate the spatiotemporal evolution of the topological order upon a quantum quench across the critical point. We also analyze the propagation of the initially localized Majorana bound states after the quench, in order to examine the connection between the topological order and the unpaired Majorana states, which has been well established at equilibrium but remains illusive in dynamical situations. It is found that after the quench the string order parameters decay over a finite time and that the decaying behavior is universal, independent of the wire length and the final value of the chemical potential (the quenching parameter). It is also found that the topological order is revived repeatedly although the amplitude gradually decreases. Further, the topological order can propagate into the region which was initially in the non-topological state. It is observed that all these behaviors are in parallel and consistent with the propagation and dispersion of the Majorana wave functions. Finally, we propose a local probing method which can measure the non-local topological order.
Comment: 21 pages; 11 figures