Abstract
We proved that the spin-1 Bose–Einstein condensate with one-dimensional spin-orbit coupling at the tricritical point is stable against excitations of Goldstone modes. The dispersion relations of these modes are anisotropic and cubic in some directions in the momentum space, which are much softer than the ordinary ones with linear form. A particular scaling form of the quantum depletions fraction on spin-orbit coupling strength is found, which is due to the special form of the dispersion relations of the Goldstone modes.
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