Detection of weak and large electric fields through the transient dynamics of a Brownian particle in an electromagnetic field

In this work we present a mechanism to detect the presence of an external electric field of either weak or large amplitude by means of the decay process from an unstable state, described by a bistable potential, of an electrically charged Brownian particle embedded in a uniform electromagnetic field. Since the detection process takes place around the initial unstable state of the bistable potential, our theoretical description is given in the linear approximation of the aforementioned potential. The decay process is characterized through the statistics of the passage time distribution calculated by means of two theoretical approaches relying on the overdamped Langevin equation: one is the quasideterministic approach valid for large times and used for the detection of weak signals, whereas the other one is the rotational approach, valid for intermediate times and adequate for the detection of large electric-field amplitudes.