Exceptional swallowtail degeneracies in driven-dissipative quadrature squeezing

TL;DR

This paper uncovers swallowtail catastrophe structures in driven-dissipative quadrature squeezing systems, revealing complex eigenvalue braiding and topologically nontrivial control of Gaussian states.

Contribution

It demonstrates the natural occurrence of swallowtail degeneracies in two-mode driven-dissipative systems with engineered losses, linking degeneracy geometry to topological state control.

Findings

Swallowtail degeneracies exist in the dynamics of the system.

Eigenvalues can braid nontrivially around exceptional lines.

The work advances understanding of degeneracy geometry in non-Hermitian systems.

Abstract

We show that swallowtail catastrophe consisting of various-order non-Hermitian and Hermitian degeneracies naturally exists in the dynamics of two-mode driven-dissipative quadrature squeezing systems that break pseudo-Hermiciticy by judiciously engineered losses. We reveal that the swallowtail degeneracy structure enables nontrivial braiding of complex eigenvalues by looping around an exceptional line in the parameter space. Our findings provide a comprehensive understanding of the degeneracy geometry in two-mode driven-dissipative bosonic quadratic systems, opening new pathways toward topologically nontrivial control of Gaussian states.