Stabilizing Non-Hermitian Systems by Periodic Driving
Abstract
The time evolution of a system with a time-dependent non-Hermitian Hamiltonian is in general unstable with exponential growth or decay. A periodic driving field may stabilize the dynamics because the eigenphases of the associated Floquet operator may become all real. This possibility can emerge for a continuous range of system parameters with subtle domain boundaries. It is further shown that the issue of stability of a driven non-Hermitian Rabi model can be mapped onto the band structure problem of a class of lattice Hamiltonians. As an application, we show how to use the stability of driven non-Hermitian two-level systems (0-dimension in space) to simulate a spectrum analogous to Hofstadter's butterfly that has played a paradigmatic role in quantum Hall physics. The simulation of the band structure of non-Hermitian superlattice potentials with parity-time reversal symmetry is also briefly discussed.
Keywords
Cite
@article{arxiv.1412.3549,
title = {Stabilizing Non-Hermitian Systems by Periodic Driving},
author = {Jiangbin Gong and Qing-hai Wang},
journal= {arXiv preprint arXiv:1412.3549},
year = {2015}
}