Squeezing-induced Topological Gap Opening on Bosonic Bogoliubov Excitations

TL;DR

This paper explores how squeezing interactions can induce topological gaps in bosonic Bogoliubov excitations, providing a formalism that simplifies analysis and suggests experimental applications.

Contribution

It introduces a squeezing transformation that reduces the Bogoliubov-de Gennes Hamiltonian to an effective non-interacting form, revealing the role of squeezing in topological gap opening.

Findings

Squeezing acts like spin-orbit or Zeeman coupling in the effective Hamiltonian.

The formalism applies to existing models, deepening understanding of their topological properties.

Constructs minimal Clifford algebra-based models for bosonic topological excitations.

Abstract

We investigate the role of squeezing interaction in inducing topological Bogoliubov excitations of a bosonic system. We introduce a squeezing transformation which is capable of reducing the corresponding Bogoliubov-de Gennes Hamiltonian to an effective non-interacting one with the spectra and topology unchanged. In the weak interaction limit, we apply the perturbation theory to investigate the squeezing-induced topological gap opening on bosonic Bogoliubov excitations and find that the squeezing interaction plays an equivalent role as a spin-orbit or Zeeman-like coupling in the effective Hamiltonian. We thus apply this formalism to two existed models for providing deeper understandings of their topological structures. We also construct minimal models based on the elegant Clifford algebra for realizing bosonic topological Bogoliubov excitations. Our construction is potentially applicable for experiments in bosonic systems.