Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons

TL;DR

This paper explores the topological properties of Bogoliubov excitations in inversion-symmetric interacting bosonic systems, extending polarization concepts and linking them to edge states, with implications for experimental observation.

Contribution

It introduces a symplectic extension of polarization for Bogoliubov excitations and connects it to inversion eigenvalues and edge states in bosonic systems.

Findings

Topological characterization of Bogoliubov excitations in bosonic systems.

Relation between inversion eigenvalues and edge states.

Feasible experimental example demonstrating the theory.

Abstract

On top of the mean-field analysis of a Bose-Einstein condensate, one typically applies the Bogoliubov theory to analyze quantum fluctuations of the excited modes. Therefore, one has to diagonalize the Bogoliubov Hamiltonian in a symplectic manner. In our article we investigate the topology of these Bogoliubov excitations in inversion-invariant systems of interacting bosons. We analyze how the condensate influences the topology of the Bogoliubov excitations. Analogously to the fermionic case, here we establish a symplectic extension of the polarization characterizing the topology of the Bogoliubov excitations and link it to the eigenvalues of the inversion operator at the inversion-invariant momenta. We also demonstrate an instructive but experimentally feasible example that this quantity is also related to edge states in the excitation spectrum.