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.

References in corpus (10)

• Making Sense of Non-Hermitian Hamiltonians
• Loss-induced suppression and revival of lasing
• Driven quantum transport on the nanoscale
• PT-Symmetric Phonon Laser
• Reversing the Pump-Dependence of a Laser at an Exceptional Point
• Visualization of Coherent Destruction of Tunneling in an Optical Double Well System
• PT-Symmetric Wave Chaos
• PT spectroscopy of the Rabi problem
• Proposal of a Cold-atom Realization of Quantum Maps with Hofstadter's Butterfly Spectrum
• Aspects of Floquet Bands and Topological Phase Transitions in a Continuously Driven Superlattice

Cited by in corpus (3)

• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling
• Protecting coherence in the non-Hermitian two-level system
• Relativistic Zitterbewegung in non-Hermitian photonic waveguide systems