  We propose a new type of the Unruh-DeWitt detector which measures the
decoherence of the reduced density matrix of the detector interacting with the
massless quantum scalar field. We find that the decoherence decay rates are
different in the inertial and accelerated reference frames. We show that the
exponential phase decay can be observed for relatively low accelerations, that
can significantly improve the conditions for measuring the Unruh effect.
