  The sensing of external fields using quantum systems is a prime example of an
emergent quantum technology. Generically, the sensitivity of a quantum sensor
consisting of $N$ independent particles is proportional to $\sqrt{N}$. However,
interactions invariably occuring at high densities lead to a breakdown of the
assumption of independence between the particles, posing a severe challenge for
quantum sensors operating at the nanoscale. Here, we show that interactions in
quantum sensors can be transformed from a nuisance into an advantage when
strong interactions trigger a dissipative phase transition in an open quantum
system. We demonstrate this behavior by analyzing dissipative quantum sensors
based upon nitrogen-vacancy defect centers in diamond. Using both a variational
method and numerical simulation of the master equation describing the open
quantum many-body system, we establish the existence of a dissipative first
order transition that can be used for quantum sensing. We investigate the
properties of this phase transition for two- and three-dimensional setups,
demonstrating that the transition can be observed using current experimental
technology. Finally, we show that quantum sensors based on dissipative phase
transitions are particularly robust against imperfections such as disorder or
decoherence, with the sensitivity of the sensor not being limited by the $T_2$
coherence time of the device. Our results can readily be applied to other
applications in quantum sensing and quantum metrology where interactions are
currently a limiting factor.
