Quantum-fluid q -plates in spinor Bose–Einstein condensates

We propose a reconfigurable way to convert the polarization of light into orbital angular momentum using a spinor Bose–Einstein condensate (BEC). In conventional optics, this conversion is performed by a q -plate, a patterned birefringent element that couples circular polarization (spin angular momentum) to a helical wavefront (orbital angular momentum). Here, we show that an in-plane spin (or nematic) texture in a spinor BEC can play the same role: it imprints a geometric phase that converts incident circularly polarized light into a new orbital-angular-momentum channel set by the texture winding number q . In the low-loss, adiabatic regime, we derive a closed-form mapping for the transmitted field, which yields a quantized selection rule Δ ℓ =2 s q ( s =±1) and a simple back-action law for the reaction torque on the condensate. Notably, the predicted torque vanishes at q =1 in the ideal limit, providing a clear experimental signature of angular-momentum exchange. We analyze robustness to smooth azimuthal distortions and identify breakdown when defects form or loss dominates. Monte Carlo sampling and two-component beam-propagation simulations confirm the predicted conversion efficiency, OAM spectrum, and torque response.