Fig. 1: Schematic illustration of the experiment.

a Schematic representation of spin-space quantum transport. By spin rotation, quantum transport is induced in spin space. Black lines show the Fermi-Dirac distribution function, and a red line shows the differential distribution function Δf(ε) = f(ε − μ₊) − f(ε − μ₋). b Quantum-circuit representation of a typical experimental sequence. The ³P₀ excitation (R_π) transfers the \(\left|g\right\rangle \left|{m}_{F}=-5/2\right\rangle\) state to \(\left|e\right\rangle \left|{m}_{F^{\prime} }=-5/2\right\rangle\). The initially prepared \(\left|\uparrow \right\rangle\) state is rotated by the first Raman pulse (R_{θ = π/2}), subjected to the interaction with the impurity acquiring a spin-dependent phase shift (U) during the hold time, rotated again by the second Raman pulse (R_{π − θ}), and finally detected by an OSG light. Although a single spin-flip event is shown in the circuit for simplicity, the multiple impurity scattering should occur in experiments. c Raman Rabi oscillation between the \(\left|\uparrow \right\rangle\) and \(\left|\downarrow \right\rangle\) states. Error bars show the standard deviations of the mean values obtained by averaging three measurements. Solid lines represent fits to the data. d Typical example of simultaneous observation of both spin states in false color time-of-flight (ToF) image of the two-component ¹⁷³Yb gas subjected to the OSG light. The distorted shape of the atom cloud in the \(\left|\downarrow \right\rangle\) state is ascribed to the photon scattering by the OSG light.