Topological Bogoliubov excitations in inversion-symmetric systems of interacting bosons

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 inversioninvariant momenta. We also demonstrate an instructive but experimentally feasible example that this quantity is also related to edge states in the excitation spectrum.

Bose-Einstein condensate in an optical lattice with Raman-assisted two-dimensional spin-orbit coupling

“…Unlike the singleparticle situation, the Chern number for the excitation spectrum is defined in a symplectic manner [31,32]. In Fig.…”

Interacting quantum fluid in a polariton Chern insulator

“…In bosonic systems, the most well-known collective effect is the Bose-Einstein Condensation 16,17 , leading to fascinating dynamical behaviour such as superfluidity 18 , and, more generally, to the physics of quantum fluids [19][20][21] . So far, the physics of bosonic quantum fluids in topologically non-trivial systems has been addressed only in a couple of works, essentially dealing with atomic condensates [22][23][24] .On the other hand, the mixed exciton-photon quasiparticles called exciton-polaritons represent a very good implementation of quantum fluids of light 21 in which a wide variety of phenomena such as polariton BEC 25 , superfluidity 26 , quantized vortices 27 have been observed. Polaritons possess the same type of spin-orbit coupling as other photonic systems, based on energy splitting between TE and TM polarized eigenmodes.…”

Integer quantum magnon Hall plateau-plateau transition in a spin-ice model

“…[1][2][3][4][5][6][7][8][9][11][12][13]20 On the one hand, these bosonic systems often break conservation of the quasi-particle number even at the level of respective quadratic Hamiltonian. 8,9,[11][12][13][14][15][16]19,[21][22][23][24][25][26][27] Thereby, one naturally wonders if the quasi-particle flow along the topological edge modes is still robust against such particle-number-nonconserving perturbations or not. In other words, one may raise a question whether two quantum Hall regimes with different Chern integers are topologically distinguishable even in the absence of the U(1) symmetry associated with the quasi-particle number conservation.…”