Multiple quantum exceptional, diabolical, and hybrid points in multimode bosonic systems: I. Inherited and genuine singularities

TL;DR

This paper investigates the complex singularities in multimode bosonic systems with damping or amplification, revealing conditions for various exceptional and diabolical degeneracies through analytical spectral analysis.

Contribution

It introduces a detailed analysis of inherited and genuine quantum singularities in multimode bosonic systems, including conditions for observing higher-order degeneracies.

Findings

Observation of inherited hybrid points with up to third-order exceptional degeneracies

Identification of genuine exceptional and diabolical points in system dynamics

Analytical reduction of spectral problem due to specific matrix structures

Abstract

The existence and degeneracies of quantum exceptional, diabolical, and hybrid (i.e., diabolically degenerated exceptional) singularities of simple bosonic systems composed of up to five modes with damping and/or amplification are analyzed. Their dynamics governed by quadratic non-Hermitian Hamiltonians is followed using the Heisenberg-Langevin equations. Their dynamical matrices generally exhibit specific structures that allow for an effective reduction of their dimension by half. This facilitates analytical treatment and enables efficient spectral analysis based on characteristic second-order diabolical degeneracies. Conditions for the observation of inherited quantum hybrid points, observed directly in the dynamics of field operators, having up to third-order exceptional and second-order diabolical degeneracies are revealed. Surprisingly, exceptional degeneracies of only second and third orders are revealed, even though the systems with up to five modes are considered. Exceptional and diabolical genuine points and their degeneracies observed in the dynamics of second-order field-operator moments are also analyzed. Each analyzed bosonic system exhibits its own unique and complex dynamical behavior.