Interaction Effects and Charge Quantization in Single-Particle Quantum Dot Emitters

We discuss a theoretical model of an on-demand single-particle emitter that employs a quantum dot, attached to an integer or fractional quantum Hall edge state. Via an exact mapping of the model onto the spin-boson problem we show that Coulomb interactions between the dot and the chiral quantum Hall edge state, unavoidable in this setting, lead to a destruction of precise charge quantization in the emitted wave packet. Our findings cast doubt on the viability of this setup as a single-particle source of quantized charge pulses. We further show how to use a spin-boson master equation approach to explicitly calculate the current pulse shape in this setup.

Figure 1

Schematic picture of the model. A quantum dot is attached to a quantum Hall edge state (integer or fractional) via a quantum point contact. The voltage on the QPC can be used to control the tunneling $\lambda (t)$ between the dot and the edge. We assume that the dot has a single level with energy $ϵ(t)$, which is controlled by an applied gate voltage. The level can be occupied with an electron in the IQHE case, or with a quasiparticle in the case of FQHE.

Figure 2

Results of the numerical solution of the generalized master equation for the time dependence of $-dN/d(t\mathrm{\Delta })$, which is related to the current on the edge via Eq. (13). In both figures we turn on the tunneling $\lambda (t)$ at the QPC at $t=0$, provided that the dot is filled, and the edge is in equilibrium at $t<0$. (Top) Time evolution of the current after a steplike pulse, see text, which leads to discharging of the dot at long times. In the calculations we use parameters $a=0.005v{\mathrm{\Delta }}^{-1}$, $\alpha =0.05$, ${ϵ}_0=2\mathrm{\Delta }$. (Bottom) Time evolution of the current after a linear ramp $ϵ(t)=\xi (t-t_0)$ with parameters $a=0.005v{\mathrm{\Delta }}^{-1}$, $\alpha =0.01$, $\xi =4{\mathrm{\Delta }}^2$, $t_0=5{\mathrm{\Delta }}^{-1}$. See insets for the corresponding time dependence of $N(t)$.