Unconventional Bose—Einstein Condensations from Spin-Orbit Coupling

Abstract

According to the "no-node" theorem, many-body ground state wavefunctions of conventional Bose-Einstein condensations (BEC) are positive-definite, thus time-reversal symmetry cannot be spontaneously broken. We find that multi-component bosons with spin-orbit coupling provide an unconventional type of BECs beyond this paradigm. We focus on the subtle case of isotropic Rashba spin-orbit coupling and the spin-independent interaction. In the limit of the weak confining potential, the condensate wavefunctions are frustrated at the Hartree-Fock level due to the degeneracy of the Rashba ring. Quantum zero-point energy selects the spin-spiral type condensate through the "orderfrom-disorder" mechanism. In a strong harmonic confining trap, the condensate spontaneously generates a half-quantum vortex combined with the skyrmion type of spin texture. In both cases, time-reversal symmetry is spontaneously broken. These phenomena can be realized in both cold atom systems with artificial spin-orbit couplings generated from atom-laser interactions and exciton condensates in semi-conductor systems.

Two- and three-dimensional topological insulators with isotropic and parity-breaking Landau levels

“…[44] in the case of strong SO coupling, i.e., α ≫ 1, the physics picture is mostly clear in momentum representation. The lowest energy states are reorganized from the plane-wave states ψ + ( k) with k near the SO ring.…”

“…In the context of ultra-cold atoms, the Bose-Einstein condensation with Rashba SO coupling plus harmonic potential was studied by one of the author and Mondragon in Ref. [45], in which the spontaneous generation of halfquantum vortex is found. Later on there has been great experimental progress in generating the synthetic gauge field from light-atom interaction 46 , which inspires a great deal of theoretical interest [47][48][49][50][51][52] .…”

Harmonically trapped two-atom systems: Interplay of short-ranges-wave interaction and spin-orbit coupling

“…In Eqs. (2) and (3), H (12) soc,a ( r 12 ) and H (12) soc,soc ( r 12 ) account for the atom-atom interaction. We note that the single particle Hamiltonian H (1) ( r j ) and variants thereof have been investigated extensively in quantum optics and molecular physics [40,41].…”

“…3. In the second step, we utilize the eigenstates and eigenenergies determined in the first step to treat the interactions H (12) soc,a and H (12) soc,soc (see Secs. III B and III C) perturbatively.…”

“…A variety of intriguing phenomena such as non-equilibrium dynamics [9,10], the spin-orbit coupling assisted formation of molecules [7], and the engineering of band structures [11] have been investigated. At the mean-field level, spin-orbit coupled gases exhibit rich phase diagrams [4,[12][13][14][15][16][17][18]. Effects beyond mean-field theory [19][20][21][22], associated with the renormalization of interactions, are enhanced by the spin-orbit coupling, especially in the pure Rashba case, and can qualitatively change the mean-field results.…”