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A quantum limit on the measurement of magnetic field has been recentlypointed out, stating that the so-called Energy Resolution $E_\mathrm{R}$ isbounded to $E_\mathrm{R} \gtrsim \hbar$. This limit holds indeed true for thevast majority of existing quantum magnetometers, including SQUIDs, solid statespins and optically pumped atomic magnetometers. However, it can be surpassedby highly correlated spin systems, as recently demonstrated with asingle-domain spinor Bose-Einstein Condensate. Here we show that similar andpotentially much better resolution can be achieved with a hard ferromagnetlevitated above a superconductor at cryogenic temperature. We demonstrate$E_\mathrm{R}=\left( 0.064 \pm 0.010 \right) \, \hbar$ and anticipate that$E_\mathrm{R}<10^{-3} \, \hbar$ is within reach with near-future improvements.This finding opens the way to new applications in condensed matter, biophysicsand fundamental science. In particular, we propose an experiment to search foraxionlike dark matter and project a sensitivity orders of magnitude better thanin previous searches.

Levitated ferromagnetic magnetometer with energy resolution well below $\hbar$