Effects of entanglement in controlled dephasing

In controlled dephasing a controlled environment causes dephasing of transport through a mesoscopic system. As a result of their interaction the states of the two subsystems are entangled. In this paper we discuss how their entanglement influences dephasing using as an example the “which path detector,” where the dephasing of transport through a quantum dot (QD) due to the interaction with a quantum point contact (QPC) is detected by means of an Aharonov-Bohm (AB) interferometer. In particular, we calculate the suppression $\nu$ of AB oscillations as a function of the bias $\mathrm{eV}$ applied to the QPC and the coupling $\Gamma$ of the QD to the leads. At low temperatures the entanglement produces a smooth crossover from $\nu \propto (eV/\Gamma {)}^2,$ when $\mathrm{eV}\ll \Gamma$ to $\nu \propto eV/\Gamma ,$ for $\mathrm{eV}\gg \Gamma .$