Effective Zitterbewegung of bosonic Bogoliubov quasi-particle with effective spin-orbital coupling

The conventional Zitterbewegung (ZB) refers to the jittering motion of a particle or wavepacket in space induced by the spin-orbital coupling. Here we show that the analogue of Zitterbewegung of bosonic Bogoliubov quasi-particle manifests itself in a form of periodic distortion of wave packet because of its dynamics is governed by a non-hermitian operator. The effective spin-orbital coupling (SOC) is due to the fact that the two modes (pseudo-spin) in the Bogoliubov de Gennes (BdG) equation are coupled to the spatial momentum. These results are illustrated with spin wave excitations in antiferromagnet and phonon excitations in BEC system.