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

TL;DR

This paper demonstrates a Bose-Einstein condensate-based magnetometer with energy resolution below $ abla$, achieving high sensitivity through non-destructive probing and phase-space analysis, surpassing traditional limits.

Contribution

It introduces a single-domain spinor Bose-Einstein condensate magnetometer with energy resolution below $ abla$, utilizing phase-space methods and mean-field simulations to understand spin noise.

Findings

Achieved dc magnetic sensitivity of 72(8) fT in a small volume.

Measured energy resolution per bandwidth below $ abla$ at 0.075(16) $ abla$.

Predicted further improvements with other alkali Bose condensates.

Abstract

We present a magnetic sensor with energy resolution per bandwidth $E_R < \hbar$. 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 $V= 1091(30)~\mu\mathrm{m}^3$ for $3.5~\mathrm{s}$, and thus $E_R = 0.075(16)~\hbar$. 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 $^{23}\mathrm{Na}$, can further improve the energy resolution of this method.