Periodically driving a quantum many body system offers a powerful means to generate and control dynamical quantum phases of matter that find no analogue in thermodynamic equilibrium. In particular, the periodic driving allows for accessing physics in a synthetic space where the time itself places the role of extra dimension. In this talk, I will show how this idea could be utilized to braid anyons in strictly spatially one-dimensional system by going into this synthetic space . Using the periodically driven Majorana chain as a concrete example , I will show it supports two classes of topologically protected Majorana modes: the Majorana zero modes, which are identical to the Majorana zero modes in equilibrium (MZM), and the Majorana pi modes (MPM), which are unique to driven systems. The MZM and MPM occupy different corners of the synthetic space, thereby permitting braiding . The idea is quite general and could potentially provide a novel platform for topological quantum information processing.
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Raditya Weda Bomantara and Jiangbin Gong, "Simulation of Non-Abelian Braiding in Majorana Time Crystals", Phys. Rev. Lett. 120, 230405 (2018).