  We derive an analytical expression for the backaction dephasing rate, which
characterizes the disturbance induced by coupling with an environment
containing a quantum dot detector (QDD). In this letter, we show that charge
noise induces backaction dephasing in an explicit form. In the linear transport
regime through a QDD, this backaction dephasing induced by charge noise can be
explained as a relaxation by an inelastic electron-electron scattering in Fermi
liquid theory. In the low bias voltage regime, the increase or decrease of
dephasing rate depends on the QDD energy level, the linewidth functions, and
how to apply the bias voltage. Unlike quantum point contact, the dephasing rate
would be insensitive to the bias voltage in a high bias voltage regime because
of the saturation of charge noise in a QDD.
