Abstract
We investigate the combined effect of the particle-particle interaction and non-Hermiticity on the quantum states and energy spectra for a non-Hermitian Bose-Hubbard dimer with complex coupling constant. It is analytically and numerically found that a real energy appears uniquely when a balance between the interaction strength and non-Hermiticity is established. The corresponding quantum state is a stationary state which does not decay in time evolution. The result provides a route for enhancing survival probability of an open many-body system and for incoherently controlling quantum transition between the stationary states by modulating the interaction strength to fit the different balance conditions.
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