Sub-Projection-Noise Sensitivity in Broadband Atomic Magnetometry

We demonstrate sub-projection-noise sensitivity of a broadband atomic magnetometer using quantum nondemolition spin measurements. A cold, dipole-trapped sample of rubidium atoms provides a long-lived spin system in a nonmagnetic environment, and is probed nondestructively by paramagnetic Faraday rotation. The calibration procedure employs as known reference state, the maximum-entropy or “thermal” spin state, and quantitative imaging-based atom counting to identify electronic, quantum, and technical noise in both the probe and spin system. The measurement achieves a sensitivity 1.6 dB (2.8 dB) better than projection-noise (thermal state quantum noise) and will enable squeezing-enhanced broadband magnetometry.

Figure 1

(a) Atomic transitions for probing, preparation, and imaging light fields. (b) Atomic ensemble with probing, pumping, and imaging light fields. The polarimeter measures in the 45° basis, i.e., the Stokes component ${\widehat{S}}_y$.

Figure 2

Measured variance of ${\widehat{S}}_y$ plotted as black dots and a fit to the data using Eq. (4) as colored surface. The left plot shows the atom-number scaling for $N_L={10}^9$. See Fig. 3 for more details. The right plot shows the photon-number scaling for $N_A=7.6\times {10}^5$. In the left and right plot curves indicate (from top to bottom): ($a$) total noise, ($b$) quantum spin noise plus light noise, ($c$) light shot and technical noise, and ($d$) light shot noise.

Figure 3

Measured variance of ${\widehat{S}}_y$ with statistical errors for $N_L={10}^9$ as a function of atom number. Dashed curve: theoretical curve including technical noise sources. Solid line: pure spin quantum noise. Dotted line: shot noise and technical light noise. Thin solid line: light shot noise. The electronic noise is not plotted because it is negligible for this number of photons.