Submillisecond, nondestructive, time-resolved quantum-state readout of a single, trapped neutral atom

We achieve fast, nondestructive quantum-state readout via fluorescence detection of a single ${}^{87}\mathrm{Rb}$ atom in the $5S_{1/2}$ $(F=2)$ ground state held in an optical dipole trap. The atom is driven by linearly polarized readout laser beams, making the scheme insensitive to the distribution of atomic population in magnetic sublevels. We demonstrate a readout fidelity of $97.6\pm 0.2\%$ in a readout time of $160\pm 20\mu \mathrm{s}$ with the atom retained in $>97\%$ of the trials, representing an advancement over other magnetic-state-insensitive techniques. We demonstrate that the $F=2$ state is partially protected from optical pumping by the distribution of the dipole matrix elements for the various transitions and the ac-Stark shifts from the optical trap. Our results are likely to find application in neutral-atom quantum computing and simulation.