Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: II. Nonconventional PT -symmetric dynamics and unidirectional coupling

We analyze the existence and degeneracies of quantum exceptional, diabolical, and hybrid points in simple bosonic systems – comprising up to six modes with damping and/or amplification – under two complementary scenarios to those described in arXiv:2405.01666: (i) nonconventional PT-symmetric dynamics confined to a subspace of the full Liouville space, and (ii) systems featuring unidirectional coupling. The system dynamics described by quadratic non-Hermitian Hamiltonians is governed by the Heisenberg-Langevin equations. Conditions for the observation of inherited quantum hybrid points with up to sixth-order exceptional and second-order diabolical degeneracies are revealed, though relevant only for short-time dynamics. This raises the question of whether higher-order inherited singularities exist in bosonic systems under general conditions. Nevertheless, for short times, unidirectional coupling of various types enables the concatenation of simple bosonic systems with second- and third-order exceptional degeneracies such that arbitrarily high exceptional degeneracies are reached. Methods for numerical identifying the quantum exceptional and hybrid points together with their degeneracies are addressed. Following arXiv:2405.01666 rich dynamics of second-order field-operator moments is analyzed from the point of view of the presence of exceptional and diabolical points and their degeneracies.