Continuous Faraday measurement of spin precession without light shifts

We describe a dispersive Faraday optical probe of atomic spin which performs a weak measurement of spin projection of a quantum gas continuously for more than one second. To date, focusing bright far-off-resonance probes onto quantum gases has proved invasive due to strong scalar and vector light shifts exerting dipole and Stern-Gerlach forces. We show that tuning the probe near the magic-zero wavelength at 790 nm between the fine-structure doublet of Rb87 cancels the scalar light shift, and careful control of polarization eliminates the vector light shift. Faraday rotations due to each fine-structure line reinforce at this wavelength, enhancing the signal-to-noise ratio for a fixed rate of probe-induced decoherence. Using this minimally invasive spin probe, we perform microscale atomic magnetometry at high temporal resolution. Spectrogram analysis of the Larmor precession signal of a single spinor Bose-Einstein condensate measures a time-varying magnetic field strength with 1 μG accuracy every 5 ms; or, equivalently, makes more than 200 successive measurements each at 10pT/Hz sensitivity.