Stabilizing Non-Hermitian Systems by Periodic Driving

TL;DR

This paper explores how periodic driving can stabilize the dynamics of non-Hermitian quantum systems, enabling real eigenphases and simulating complex band structures like Hofstadter's butterfly, with implications for quantum Hall physics.

Contribution

It demonstrates that periodic driving can stabilize non-Hermitian systems and maps their stability to lattice band structures, introducing new methods for quantum simulation.

Findings

Periodic driving stabilizes non-Hermitian systems with real eigenphases.

Stability regions can be mapped to lattice band structures.

Simulation of Hofstadter's butterfly spectrum using driven two-level systems.

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.