  Understanding the dynamics of electrical signals within neuronal assemblies
is crucial to unraveling complex brain function. Despite recent advances in
employing optically active nanostructures in transmembrane potential sensing,
there remains room for improvement in terms of response time and sensitivity.
Here, we report the development of such a nanosensor capable of detecting
electric fields with a submillisecond response time at the single particle
level. We achieve this by using ferroelectric nanocrystals doped with rare
earth ions producing upconversion (UC). When such a nanocrystal experiences a
variation of surrounding electric potential, its surface charge density
changes, inducing electric polarization modifications that vary, via converse
piezoelectric effect, the crystal field around the ions. The latter variation
is finally converted into UC spectral changes, enabling optical detection of
electric potential. To develop such a sensor, we synthesized erbium and
ytterbium-doped barium titanate crystals of size $\approx160$ nm. We observed
distinct changes in the UC spectrum when individual nanocrystals were subjected
to an external field via a conductive AFM tip, with a response time of 100
$\mu$s. Furthermore, our sensor exhibits a sensitivity to electric fields of
only 4.8 kV/cm/$\sqrt{\rm Hz}$, making possible the time-resolved detection of
a neuron action potential.
