# Analytical results for a parity-time symmetric two-level system under synchronous combined modulations

## TL;DR

This paper introduces a method for generating exact analytical solutions for a parity-time symmetric two-level system under synchronous modulations, revealing phenomena like stabilization, coherent destruction of tunneling, and population inversion, with implications for quantum control.

## Contribution

It provides a novel analytical approach using combined synchronous modulations to solve and analyze PT-symmetric two-level systems, extending understanding beyond Hermitian cases.

## Key findings

- Exact solutions expressed in elementary functions
- Demonstration of stabilization and population inversion phenomena
- Derivation of a pulse area theorem for non-Hermitian systems

## Abstract

We propose a simple method of combined synchronous modulations to generate the analytically exact solutions for a parity-time symmetric two-level system. Such exact solutions are expressible in terms of simple elementary functions and helpful for illuminating some generalizations of appealing concepts originating in the Hermitian system. Some intriguing physical phenomena, such as stabilization of a non-Hermitian system by periodic driving, non-Hermitian analogs of coherent destruction of tunneling (CDT) and complete population inversion (CPI), are demonstrated analytically and confirmed numerically. In addition, by using these exact solutions we derive a pulse area theorem for such non-Hermitian CPI in the parity-time symmetric two-level system. Our results may provide an additional possibility for pulse manipulation and coherent control of the parity-time symmetric two-level system.