Population Trapping in the Excited State of an Open Two-level Atomic System Under Non-Hermitian Feedback Controls

We investigate the excited-state population of an open two-level atomic system under the quantum feedback control with non-Hermitian feedback Hamiltonian. We firstly derive the master equation under non-Hermitian feedback controls for the two-level atomic system by using the general measurement theory and then respectively discuss the effect of different feedback parameters on the excited-state population. The results show that the excited-state population can be effectively protected from dissipative environments by adjusting feedback parameters. Furthermore, two schemes to realize long-time excited-state population trapping are proposed. The one is under the quantum feedback control with parity-time (PT)-symmetric feedback Hamiltonian, and the other recovers to the Hermitian quantum-jump-based feedback control. These originally come from the fact that the decay of the open two-level atomic system can be completely balanced by feedback controls with proper feedback parameters.