Phonon emission and arrival times of electrons from a single-electron source

Abstract

In recent charge-pump experiments, single electrons are injected into quantum Hall edge channels at energies significantly above the Fermi level. We consider here the relaxation of these hot edge-channel electrons through longitudinal-optical phonon emission. Our results show that the probability for an electron in the outermost edge channel to emit one or more phonons en route to a detector some microns distant along the edge channel suffers a double-exponential suppression with increasing magnetic field. This explains recent experimental observations. We also describe how the shape of the arrival-time distribution of electrons at the detector reflects the velocities of the electronic states post phonon emission. We show how this can give rise to pronounced oscillations in the arrival-time-distribution width as a function of magnetic field or electron energy.

Energy relaxation in hot electron quantum optics via acoustic and optical phonon emission

“…In this regime, therefore, we expect the conclusions of Ref. [27] to hold. At lower energies, however, the effective rates develop a "knee", which is more pronounced at lower fields and also more extreme in γ 0 than γ 01 .…”

“…For this reason we expect the LO emission rates from the inner channels to be significantly increased over those for the outermost channel, see Ref. [27] for more details.…”

“…Furthermore, we assume that these wave packets remain coherent during their transmission to the detector and that their shape remains constant. The absence of significant dispersion over the relevant timescales was discussed in [27]. The maintenance of coherence under phonon emission can be justified by considering the Bloch-Redfield equations for the coherences, analogous to those for the populations in Eq.…”

“…If LO-phonon emission was the only process operative here then the survival probability P 0 would show an exponential decay as a function of time with rate given by the LO-phonon emission rate [27]. Let us therefore assume that a similar relation exists in the presence of LA-phonon emission and write an exponential relation between the survival probability, P 0 ≈ e −γ0t , where γ 0 is an effective rate parameter describing the total decay of the survival probability.…”

Time‐resolved single‐electron wave‐packet detection

“…One particular aspect of these studies is the transport characteristics of electron wave packets in quantum‐Hall edge states such as decoherence , , . For this purpose, measurements of the size of electron wave packets, or their arrival‐time distribution are useful tools.…”