Multicriticality, Metastability, and Roton Feature in Bose-Einstein Condensates with Three-Dimensional Spin-Orbit Coupling

We theoretically study homogeneously trapped atomic Bose-Einstein condensates where all three momentum components couple to a pseudo-spin-$1/2$ degree of freedom. Tuning the anisotropies of spin-orbit coupling and the spin-dependent interactions is shown to provide access to a rich phase diagram with a tetracritical point, first-order phase transitions, and multiple metastable phases of stripe and plane-wave character. The elementary excitation spectrum of the axial plane-wave phase features an anisotropic roton feature and can be used to probe the phase diagram. In addition to providing a versatile laboratory for studying fundamental concepts in statistical physics, the emergence of metastable phases creates new opportunities for observing false-vacuum decay and bubble nucleation in ultra-cold-atom experiments.