Coalescence of non-Markovian dissipation, quantum Zeno effect and non-Hermitian physics, in a simple realistic quantum system

Diagonalization of the effective Hamiltonian describing an open quantum system is the usual method of tracking its exceptional points. Although, such a method is successful for tracking EPs in Markovian systems, it may be problematic in non-Markovian systems where a closed expression of the effective Hamiltonian describing the open system may not exist. In this work we provide an alternative method of tracking EPs in open quantum systems, using an experimentally measurable quantity, namely the effective decay rate of a qubit. The quantum system under consideration consists of two non-identical interacting qubits, one of which is coupled to an external environment. We develop a theoretical framework in terms of the time-dependent Schrodinger equation of motion, which provides analytical closed form solutions of the Laplace transforms of the qubit amplitudes for an arbitrary spectral density of the boundary reservoir. The link between the peaked structure of the effective decay rate of the qubit that interacts indirectly with the environment, and the onset of the quantum Zeno effect, is discussed in great detail revealing the connections between the latter and the presence of exceptional points. Our treatment and results have in addition revealed an intricate interplay between non-Markovian dynamics, quantum Zeno effect and non-Hermitian physics