Fig. 2. Experimental protocol.

After Doppler cooling, Raman sideband cooling, and optical pumping, the initial vibronic state $\mid D\rangle \langle D\mid \otimes {\mathrm{\rho }}_{-}$ is prepared by a $\mathrm{\pi }/2$ pulse along the $x$ axis and by displacing the motional state via a spin-dependent force. Before the final measurement, another $\mathrm{\pi }/2$ pulse along the $x$ axis rotates the final spin state back into the qubit basis.