Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below $\hbar$

2021 
We present a magnetic sensor with energy resolution per bandwidth $E_R < \hbar$. We show how a Rb-87 single domain spinor Bose-Einstein condensate, detected by non-destructive Faraday-rotation probing, achieves single shot dc magnetic sensitivity of $49(11)\,\mathrm{fT}/\sqrt{\mathrm{Hz}}$ in a volume $V=1091(30)\,\mu m^3$, and thus $E_R = 0.070(16)\,\hbar$. We measure experimentally the condensate volume, spin coherence time, and readout noise, and use phase-space methods, backed by 3+1D mean-field simulations, to compute the spin noise. Contributions to the spin noise include one-body and three-body losses and shearing of the projection noise distribution, due to competition of ferromagnetic contact interactions and quadratic Zeeman shifts. Nonetheless, the fully-coherent nature of the single-domain, ultracold two-body interactions allows the system to escape the coherence vs. density trade-off that imposes an energy resolution limit on traditional spin-precession sensors. We predict that other Bose-condensed alkalis, especially the antiferromagnetic Na-23, can further improve the energy resolution of this method.
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