Quantum interference and exceptional points in a nonreciprocal two-level system

Non-Hermitian systems with complex-valued energy spectra and exceptional points show unconventional dynamics. Here we investigate the quantum interference of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. We propose the multiple-passage Landau-Zener-Stuckelberg-Majorana scheme to realize the quantum interferometry of such a non-Hermitian system, that is, the energy bias between two levels is periodically modulated, which may result in constructive or destructive interference. In the absence of nonlinear self-interaction, it exhibits obvious interference fringes in the weak nonreciprocal regime, whereas the interference is completely suppressed in the strong nonreciprocal regime due to the parity-time-symmetry breaking. The explicit expressions for the occupation probabilities are obtained within an effective rotating-wave approximation, which is consistent with the numerical results. In the presence of nonlinear interaction, the system shows a rich variety of dynamics and interference fringes. We further obtain phase diagrams for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate quantum interference within the nonlinear non-Hermitian system. The present work unlocks quantum interference characteristics from a nonreciprocal two-level system and provides a theoretical perspective for the manipulation of quantum states in non-Hermitian systems.