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

TL;DR

This paper investigates quantum exceptional, diabolical, and hybrid degeneracies in multimode bosonic systems with damping or amplification, focusing on nonconventional PT-symmetric dynamics and unidirectional coupling to reveal conditions for high-order degeneracies.

Contribution

It introduces new scenarios for quantum degeneracies in bosonic systems, including nonconventional PT-symmetry and unidirectional coupling, and develops methods to identify these degeneracies.

Findings

Inherited quantum hybrid points can exhibit high-order degeneracies for short times.

Unidirectional coupling enables the construction of systems with arbitrarily high exceptional degeneracies.

Numerical methods for identifying quantum degeneracies are proposed.

Abstract

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 Quantum 9, 1932 (2025): (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 Quantum 9, 1932 (2025) 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.