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

Abstract

We present a magnetic sensor with energy resolution per bandwidth $E_R<\hslash$. We show how a ${}^{87}\mathrm{Rb}$ single domain spinor Bose-Einstein condensate, detected by non-destructive Faraday-rotation probing, achieves single shot dc magnetic sensitivity of $72(8)\mathrm{fT}$ measuring a volume $V=1091(30)\hat{I}¼{\mathrm{m}}^3$ for $3.5\mathrm{s}$, and thus $E_R=0.075(16)\hslash$. 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 ${}^{23}\mathrm{Na}$, can further improve the energy resolution of this method.

9 pages, 3 figures