  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.
