Feynman relation of Bose-Einstein condensates with spin-orbit coupling

Abstract

We find that the Feynman relation of Bose-Einstein condensates with spin-orbit coupling, which relates the energy of excitations, the static structure factor in condensed phase, and the dispersion of free bosons, is not satisfied in the whole momentum space. The dispersion is highly anisotropic and more divergent in the infrared limit compared to that without spin-orbit coupling because of spontaneous breaking of the O(2) symmetry of the ground state. And the dispersion also exhibits time reversal asymmetry for plane-wave condensates, which is condensed on a momentum with a finite value. We also find that larger spin-orbit coupling makes the excitations out of condensates more coherent.

Drag force on a moving impurity in a spin-orbit-coupled Bose-Einstein condensate

“…where m ν is the mass for δρ fluctuations, and it equals 2gρ 0 in the classical limit [50]. From the last term on the right-hand side of Eq.…”

“…Since ω ± k are not even functions of k x [50], there is generally F T = 0. In short, merely from the symmetry analysis, we find that the anisotropy of the BEC will generally leads to a nonzero transverse force.…”

“…are eigenenergies of excitations with momentum k in the upper and lower bands, respectively [50]. For momenta k satisfying ω + k = ω − k , the two coefficients before the two delta functions in Eq.…”

“…(9) to obtain the momenta k of excitations created by the motion of the impurity. The dispersions of the BEC system, ω k , satisfy [35,50] …”

“…(2) Neglecting the possibility of vortex excitations for point-like impurity, the boson fields including fluctuations induced by the particle-particle interactions and the impurity potential are written as [50,51] …”