Topological phases in 1D bosonic Bogoliubov bands with dynamical instability

Topological phases of matter have attracted much attention in solid-state physics, but most of studies treat Hermitian Hamiltonians [1]. Recently, there has been growing interest in non-Hermitian topological phases [2], which exhibit exotic phenomena absent in Hermitian ones [3]. Non-Hermitian Hamiltonian describes an open quantum system in which loss and gain of particles coexist. Here, we note that bosonic Bogoliubov quasiparticles, which are elementary excitations from a Bose-Einstein condensate (BEC), are also described with a non-Hermitian Hamiltonian, where a BEC works as a particle bath. In this sense, topological classification of BECs is an open question. In the case when the non-Hermitian Hamiltonian has real eigenvalues, the topological properties of quasiparticles is discussed [4].
In this talk, we consider more general cases of 1D BECs and find topological invariants in 1D BDI and D classes. As concrete examples, we discuss topological properties in a 1D Kitaev model [4] and in a 1D SSH model.
[1] M. Z. Hasan and C. L. Kane, Rev. Mod. Phys. 82, 3045 (2010).
[2] R. El-Ganainy et al., Nat. Phys. 14, 11 (2018)
[3] Y. Xu, S. T. Wang, and L. M. Duan, Phys. Rev. Lett. 118, 045701 (2017)
[4] G. Engelhardt and T. Brandes Phys. Rev. A, 91, 053621 (2015).