Unconventional states of bosons with the synthetic spin–orbit coupling

Abstract

Spin-orbit coupling with bosons gives rise to novel properties that are absent in usual bosonic systems. Under very general conditions, the conventional ground state wavefunctions of bosons are constrained by the "no-node" theorem to be positive-definite. In contrast, the linear-dependence of spin-orbit coupling leads to complex-valued condensate wavefunctions beyond this theorem. In this article, we review the study of this class of unconventional Bose-Einstein condensations focusing on their topological properties. Both the 2D Rashba and 3D σ · p-type Weyl spin-orbit couplings give rise to Landau-level-like quantization of single-particle levels in the harmonic trap. The interacting condensates develop the half-quantum vortex structure spontaneously breaking time-reversal symmetry and exhibit topological spin textures of the skyrmion type. In particular, the 3D Weyl coupling generates topological defects in the quaternionic phase space as an SU(2) generalization of the usual U(1) vortices. Rotating spin-orbit coupled condensates exhibit rich vortex structures due to the interplay between vorticity and spin texture. In the Mott-insulating states in optical lattices, quantum magnetism is characterized by the Dzyaloshinskii-Moriya type exchange interactions.

Tunneling-assisted spin-orbit coupling in bilayer Bose-Einstein condensates

“…To calculate the mean-field energy under the variational Ansatz, it's convenient to rewrite the interacting Hamiltonian (16) in the four-spinor representation Ψ, which is given bŷ…”

“…During the last few years these topics have gained an increasing interest for ultracold atomic gases [4][5][6][7][8] which represent the systems simulating many condensed matter phenomena. Recent experimental progress in the spin-orbit coupling (SOC) of degenerate atomic gases [9][10][11][12][13] has stimulated the theoretical studies of diverse new phases due to the SOC [8,[14][15][16][17], such as emergence of the stripe phase in atomic Bose-Einstein condensates (BECs) [18][19][20][21][22], or formation of unconventional bound states [23][24][25][26] and topological superfluidity [27] for atomic fermions. It was demonstrated that for the spin-orbit (SO) coupled BECs, the half-vortex (meron) ground states may develop in harmonic traps [28][29][30][31][32].…”

Properties of spin–orbit-coupled Bose–Einstein condensates

“…In the BCS phase, unconventional states are predicted, such as Fulde-Ferrell-LarkinOvchinnikov (FFLO) superfluids [38]. Even though the field only started very recently, it has developed in a rapid fashion and several review articles on specific topics along this direction already exist [38,39,64,[96][97][98][99][100][101][102].…”

Bright solitons in a two-dimensional spin-orbit-coupled dipolar Bose-Einstein condensate

“…This achievement has ignited tremendous interest in this field because of the dramatic change in the single particle dispersion (induced by spin-orbit coupling) which in conjunction with the interaction leads to many exotic superfluids [35][36][37][38][39][40][41][42][43][44][45](also see [46][47][48][49][50][51][52][53] for review). Such change in dispersion also results in exotic solitons even when the interaction is contact (without dipole-dipole interactions), including 1D bright solitons [54][55][56][57][58][59][60] for a BEC with attractive contact interactions, 1D dark [61,62] and gap solitons [63][64][65] for a BEC with repulsive contact interactions, as well as 1D dark solitons for Fermi superfluids [66,67].…”