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 a straightforward 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.
- Publication:
-
Physical Review A
- Pub Date:
- April 2015
- DOI:
- 10.1103/PhysRevA.91.042135
- arXiv:
- arXiv:1412.3549
- Bibcode:
- 2015PhRvA..91d2135G
- Keywords:
-
- 03.65.-w;
- 05.70.Ln;
- 11.30.Er;
- 42.82.Et;
- Quantum mechanics;
- Nonequilibrium and irreversible thermodynamics;
- Charge conjugation parity time reversal and other discrete symmetries;
- Waveguides couplers and arrays;
- Quantum Physics
- E-Print:
- doi:10.1103/PhysRevA.91.042135