We present the deepest optical spectrum acquired to date of Balmer-dominated shocks in the NW rim of SN 1006. We detect the broad and narrow components of H-alpha, H-beta and H-gamma and report the first detection of the He I 6678 emission line in this supernova remnant. We may have detected, at the 1.5-sigma level, faint He II 4686 emission. We measure a full width half maximum of 2290 +/- 80 km/s in the broad component H-alpha line, with broad-to-narrow flux ratios of 0.84^+(0.03)_(-0.01) and 0.93^(+0.18)_(-0.16) in H-alpha and H-beta, respectively. To match these observations, our nonradiative shock models require a low degree of electron-proton equilibration at the shock front, T_e/T_p <= 0.07, and a shock speed of 2890 +/- 100 km/s. These results agree well with an earlier analysis of ultraviolet lines from SN 1006. The He I/H-alpha and He I/He II flux ratios also indicate low equilibration. Furthermore, our models match the observations for mostly ionized (~ 90%) preshock H and mostly neutral (>~ 70%) preshock He, respectively. We conclude that the high H ionization fraction cannot be explained by either photoionization from the reverse shock or relic ionization from EUV photons released in the 1006 A.D. supernova. The most plausible explanation appears to be photoionization from the Galactic Lyman continuum.
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