Symmetry classification of spin-orbit-coupled spinor Bose-Einstein condensates

Abstract

We develop a symmetry classification scheme to find ground states of pseudo-spin-1 2 , spin-1, and spin-2 spin-orbit-coupled spinor Bose-Einstein condensates and show that as the SO(2) symmetry of simultaneous spin and space rotations is broken into discrete cyclic groups, various types of lattice structures emerge in the absence of a lattice potential. Examples include two different kagome lattices for pseudo-spin-1 2 condensates and a nematic vortex lattice in which uniaxial and biaxial spin textures align alternatively for spin-2 condensates. For the pseudo-spin-1 2 system, although mean-field states always break time-reversal symmetry, there exists a timereversal invariant many-body ground state, which is fragmented and expected to be observed in a microcondensate.

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

“…First we note that the triangular lattice phases have been found for a trapped spin-1/2 BEC with Rashba-type SOC [28,29]. Furthermore, the triangular and square lattice phases have also been observed for a spin-2 BEC [69]. Yet, for a spin-1/2 BEC in a 2D homogeneous system, the ground states are found to be plane wave or stripe phases comprised of a single wave vector or a pair of wave vectors, and it is hard to form the ground state which involves an interference of more than one pair of wave vectors [18].…”

Highly symmetric POVMs and their informational power

“…Such points are called inert states in physical literature; they are critical regardless of the exact form of F, see, e.g., [127]. Of course, an invariant function can have other critical points than those guaranteed by the above theorem (non-inert states).…”

Condensation Transition of Ultracold Bose Gases with Rashba Spin-Orbit Coupling

“…More exotic phases are predicted at nonzero temperatures [13] and in harmonic traps [14][15][16][17][18]. Atoms with isotropic in-plane Rashba spin-orbit coupling have circularly degenerate single particle energy minima; as a consequence non-interacting bosons with such coupling do not Bose condense in three dimensions, owing to the density of states being two-dimensional at low energy [19].…”

“…As noted, expressions (17) and (18) are valid when the spin-orbit coupling strength κ is large compared with √ mgn 0 . When κ = 0, the system reduces to the ordinary two-component Bose gas without spin-orbit coupling, and thus has a second order phase transition to a condensate phase at nonzero temperature.…”

“…Approximating the coupling g by 4πa/m, so that 2mκg ∼ 0.69, we obtain T c ∼ 2nK with a jump in the condensate fraction at the transition, n 0 /n ∼ 0.1. In addition, T c /ǫ κ ∼ 0.019 and ∆µ/ǫ κ ∼ 4.3 × 10 −4 putting the system in a regime where the approximations leading to (17) are valid. Future experiments could, depending on their specific configurations, be able to increase the transition temperature and the jump in the condensate density via increasing κ, n, or a.…”