Braiding of dynamical eigenvalues of Hermitian bosonic Kitaev chains

Abstract

In quantum mechanics, observables correspond to Hermitian operators, and the spectra are restricted to be real. However, the dynamics of the underlying fields may allow complex eigenvalues and therefore create the possibility of braiding structures. Here we study the braiding of dynamical eigenvalues in quantum systems by considering Hermitian bosonic Kitaev chains with multiple bands. The dynamics of the quantum fields in these systems are described by their dynamic matrices, which have complex eigenvalues. We show that there are symmetry constraints imposed on these dynamic eigenvalues. Despite these constraints, braiding is possible for frequencies within the effective gain and loss regions of the complex plane. We explicitly construct two- and three-strand braidings using the exceptional points found in the system and discuss possible implementations.

16 pages, 4 figures

References in corpus (16)

• Topological Photonics
• Observation of Acoustic Non-Hermitian Bloch Braids and Associated Topological Phase Transitions
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Knot topology of exceptional point and non-Hermitian no-go theorem
• Exceptional Non-Abelian Topology in Multiband Non-Hermitian Systems
• Optomechanical realization of the bosonic Kitaev-Majorana chain
• Probing Complex-energy Topology via Non-Hermitian Absorption Spectroscopy in a Trapped Ion Simulator
• Eigenvalue topology of non-Hermitian band structures in two and three dimensions
• Resolving the topology of encircling multiple exceptional points
• Braid Protected Topological Band Structures with Unpaired Exceptional Points
• Quantum Simulation of the Bosonic Kitaev Chain
• Quantum-Squeezing-Induced Point-Gap Topology and Skin Effect
• Non-Hermitian eigenvalue knots and their isotopic equivalence
• Non-Abelian Braiding of Topological Edge Bands
• Versatile Braiding of Non-Hermitian Topological Edge States
• Hidden exceptional point, localization-delocalization phase transition in Hermitian bosonic Kitaev model