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.
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