Universal phase structure of dilute Bose gases with Rashba spin-orbit coupling

A Bose gas subject to a light-induced Rashba spin-orbit coupling possesses a dispersion minimum on a circle in momentum space; we show that kinematic constraints due to this dispersion cause interactions to renormalize to universal, angle-dependent values that govern the phase structure in the dilute-gas limit. We find that, regardless of microscopic interactions, (a) the ground state involves condensation at two opposite momenta and is, in finite systems, a fragmented condensate and and (b) there is a nonzero-temperature instability toward the condensation of pairs of bosons. We discuss how our results can be reconciled with the qualitatively different mean-field phase diagram, which is appropriate for dense gases.

Figure 1

Zero-temperature phase diagram as a function of the interaction anisotropy $\gamma \equiv c_2/c_0$ and the chemical potential $\mu$, showing the phases and transitions discussed in the main text. The (dashed) phase boundaries in the crossover region are schematic; the thick line indicates a first-order transition predicted by mean-field theory [9].

Figure 2

(a) Loop correction in the particle-particle channel, which governs the hierarchy of couplings at the QCP. (b) Loop correction in the particle-hole channel. These corrections vanish at $T=0$. (c) Kinematic constraints due to the dispersion structure: (left) case of $\theta \ne 0$, outgoing momenta are constrained to lie in the shaded region, of area $\sim$${\Lambda }^2$; (right) case of $\theta =0$, for which the shaded region's area scales as $\Lambda \sqrt{k_0\Lambda }$.