Double-driven Parity-Time (PT) and Anti-Parity-Time (APT) Symmetric Floquet Models

In quantum mechanics, one of the key requirements for a system is that it must be Hermitian in order to have real energies and unitary time evolution. Over the past two decades, we have seen tremendous growth of interest in systems that are non-Hermitian, but PT-symmetric. This is due to the fact they have been found to possess real energies, although being open systems, hence generalizing the Hermiticity condition. More recently, there has been increasing interest in non-Hermitian systems with APT-symmetry, which has also been found in many contexts such as optics, diffusive systems, and electronics. In this talk, we will explore various types of single and double-driven time-periodic non-Hermitian PT and APT-symmetric Hamiltonians. Time-dependent systems are generally difficult to solve, but being time-periodic, we can resort to using Floquet theory for our models. PT and APT symmetries in the models give rise to transitions of PT-symmetry breaking and restoring, which as a result leads to observations of many fascinating and rich features and characteristics not seen in Hermitian cases. This could bring about new exciting developments to the probing and control of quantum systems.