Electron quantum optics in ballistic chiral conductors

Abstract

The edge channels of the quantum Hall effect provide one dimensional chiral and ballistic wires along which electrons can be guided in an optics-like setup. Electronic propagation can then be analyzed using concepts and tools derived from optics. After a brief review of electron optics experiments performed using stationary current sources which continuously emit electrons in the conductor, this paper focuses on triggered sources, which can generate on-demand a single particle state. It first outlines the electron optics formalism and its analogies and differences with photon optics and then turns to the presentation of single electron emitters and their characterization through the measurements of the average electrical current and its correlations. This is followed by a discussion of electron quantum optics experiments in the Hanbury-Brown and Twiss geometry where two-particle interferences occur. Finally, Coulomb interactions effects and their influence on single electron states are considered.

Time-resolved energy dynamics after single electron injection into an interacting helical liquid

“…The injection of a single polarized electron into the EC can thus be achieved with an abrupt change of the top gate potential at time t = 0. Consequently, the most energetic electron in the QD, chosen here with spin up, is suddenly brought above E F and leaves it [19,48] tunneling into the helical edges. In this paper, we will assume that the spin-preserving tunneling is the dominant mechanism, and we thus restrict the discussion to this case.…”

“…Moreover, we explicitly take into account the finite lifetime 1/2γ of the QD level [19,71] by assuming the time evolution of QD correlator d † (t 1 )d(t 2 ) = β * (t 1 )β(t 2 ), with…”

“…Nevertheless, an accurate description and understanding of energy dynamics for time-dependent single electron injection in an interacting system is still lacking, despite the fact that it will play an important role in the fast developing field of electron quantum optics [18,19]. This very promising field relies on the possibility of injecting single electrons and holes into one-dimensional (1D) systems.…”

First-order correlation function of a stream of single-electron wave packets

“…For other energies the correlation function is zero, what is specific for purely electronic excitations. 39 Note that G…”

“…A non-zero value of G (1),in ac in the electron-hole sector, n ≥ 0, ν ≤ 0 or n < 0, ν > 0, indicates the presence of electron-hole correlations. 32,33,39 Note that in the electron-hole sector the sum on the RHS of the second line of Eq. (7) is zero due to cancellation of electron and hole contributions, which is specific for states with equal number of electrons and holes.…”