G. Fève 1, 2, Pascal Degiovanni 3, 4, Th. Jolicoeur 5
Physical Review B 77 (2008) 035308
We consider a model of a detector of ballistic electrons at the edge of a two-dimensional electron gas in the integer quantum Hall regime. The electron is detected by capacitive coupling to a gate which is also coupled to a passive RC circuit. Using a quantum description of this circuit, we determine the signal over noise ratio of the detector in term of the detector characteristics. The back-action of the detector on the incident wavepacket is then computed using a Feynman-Vernon influence functional approach. Using information theory, we define the appropriate notion of quantum limit for such an ‘on the fly’ detector. We show that our particular detector can approach the quantum limit up to logarithms in the ratio of the measurement time over the RC relaxation time. We argue that such a weak logarithmic effect is of no practical significance. Finally we show that a two-electron interference experiment can be used to probe the detector induced decoherence.
- 1. Laboratoire Pierre Aigrain (LPA),
CNRS : UMR8551 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot – Ecole Normale Supérieure de Paris – ENS Paris - 2. Laboratoire de photonique et de nanostructures (LPN),
CNRS : UPR20 - 3. Laboratoire de Physique de l’ENS Lyon (Phys-ENS),
CNRS : UMR5672 – École Normale Supérieure – Lyon - 4. Physics Department [Boston] (BU-Physics),
Boston University - 5. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
CNRS : UMR8626 – Université Paris XI – Paris Sud