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We consider the effect of dephasing on a quantum dot which injects singleelectrons on a chiral edge channel of the quantum Hall effect. Dephasing isdescribed by the coupling of the dot to a bosonic bath which represents theelectromagnetic environment. Using the input-output formalism of quantumoptics, we derive the density matrix of the edge degrees of freedom. Resultsare illustrated by computing the zero frequency current-current correlationswhen two such single electron emitters achieve a collision at the location of aquantum point contact, in the same spirit as the Hong Ou Mandel experiment ofquantum optics. Such correlations are directly linked to the quantum mechanicalpurity. We show that as observed in a recent experiment, the effect ofdephasing leads to a non-vanishing of the Hong Ou Mandel dip when the timedelay between the two electron wave packets is zero. Generalizations to timefiltered wave packets as well as to asymmetric, detuned injection betweenopposite edges are obtained.

Dephasing in single-electron generation due to environmental noise probed by Hong Ou Mandel interferometry