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 nontopological 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 local probing methods which can measure the nonlocal topological order.
Bibliographical noteFunding Information:
This work was supported by the the National Research Foundation (Grant Nos. 2011-0030046 and 2015- 003689) and the Ministry of Education (through the BK21 Plus Project) of Korea.
© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
- Majorana Fermion
- quantum quenching
- string order parameter
- topological order
- topological phase transition
- topological superconductor
ASJC Scopus subject areas
- Physics and Astronomy(all)