# Magic-wavelength Faraday probe measures spin continuously and without light shifts

## TL;DR

This paper introduces a minimally-invasive, continuous Faraday optical probe for atomic spins that cancels light shifts at a magic-zero wavelength, enabling high-resolution magnetometry of quantum gases without significant disturbance.

## Contribution

The authors demonstrate a novel dispersive Faraday probe tuned near 790 nm that cancels scalar and vector light shifts, allowing for continuous, high-precision spin measurements of quantum gases.

## Key findings

- Achieved over one second of continuous, minimally-invasive spin measurement.
- Measured magnetic field variations with 1 μG accuracy every 5 ms.
- Performed >200 successive measurements with 10 pT/√Hz sensitivity.

## Abstract

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 $^{87}$Rb 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 {\mu}G accuracy every 5 ms; or equivalently makes > 200 successive measurements each at $10\,\mathrm{pT/\sqrt{Hz}}$ sensitivity.