Effect of electron-electron interactions on the propagation of ultrashort voltage pulses in a Mach-Zehnder interferometer

Abstract

Electronic interferometers have been identified as possible candidates for building electronic flying qubits. Such a regime requires ultrafast voltage pulses whose duration is shorter than the time of flight through the device. Understanding the corresponding physics in the presence of such short excitations requires a proper treatment of electron-electron interactions. In this article, we take a step in this direction by performing time-resolved simulations of a Mach-Zehnder interferometer treating the interactions at the time-dependent mean-field level. We find that the main effect of the interaction is the renormalization of the pulse velocity. Very importantly, the interference effects appear to be robust to the presence of interactions.

Figures (14)

• Figure 1: Schematic of a Mach-Zehnder interferometer in the quantum Hall regime. The device consists of a ring shaped 2DEG connected to three contacts: two outer contacts (0 and 1) and one inner contact (2). Quantum point contacts (QPC A and QPC B) act as beam splitters for the chiral edge state injected from source contact 0. The edge channel is partially transmitted and reflected at QPC A, with the two paths recombining at QPC B. The resulting current is collected at the inner contact 2 and outer contact 1.
• Figure 2: Schematic representation of the dynamical interference effect. The color blue corresponds to the phase $e^{iky-iEt}$ where $y$ is the distance from contact $0$ following the edge. The color yellow corresponds to the phase $e^{iky-iEt -i2\pi\bar{n}}$. (a) Initially, the edge state coming from contact 0 is at equilibrium, hence in blue. (b) The pulse arrives followed by its yellow tail. (c) The pulse has been splitted by QPC A. (d) After partial recombination at QPC B of the lower part of the pulse, the system enters the transient period where the dynamical interference effect happens. The yellow-blue stripe corresponds to a region where the rear of the lower part of the pulse interferes with the front of the upper part. (e) After both parts of the pulse have reached contact $1$ and $2$, the system is back to equilibrium, albeit with a different global phase.
• Figure 3: Tight-binding models considered in this work. (a) A quasi-one dimensional wire connected to two semi-infinite electrodes 0 and 1. Width: $W=10$ sites, length: $L=200$. (b) a Quantum Point Contact (QPC) connected to three electrodes 0, 1 and 2. $L_{\text{QPC}}=W_{\text{QPC}}=22$. (c) the Mach-Zehnder interferometer (MZI) that contains the QPC and the wire region as subparts. $L_{\text{MZI}}=100$ and $W_{\text{MZI}}=250$ for a total of around $17 000$ sites. The different insets are zoom into different regions.
• Figure 4: DC characterization of the wire model at $\phi_a=0.44$: dispersion relation. (a) Band dispersion $E_n(k)$ of the infinite electrodes for the three lowest Landau levels. The horizontal dashed line marks the Fermi level $E_F/\gamma$. (b) The corresponding band dispersion velocity $v_n(k)$. (c) Same as (b) but versus energy for the lowest Landau level $v_0(E)$. The left and the right red bars are respectively the bottom of the lowest and first Landau levels.
• Figure 5: DC characteristics of the wire model: transmission. (a) Transmission (green) and reflection (red, vanishing) probability of the wire versus energy at $\phi_a=0.44$. (b) Transmission and reflection probability versus magnetic field $\phi_a$ at $E = E_F/\gamma=-3.2$. Inset: Colormap of the local current density injected from contact $0$ at $E = E_F/\gamma=-3.2$ and $\phi_a=0.44$. One clearly observes that the propagation takes place on the right edge.