Photon-Assisted Tunneling in Double Quantum Dot: Application of Scattering Theory

Abstract

We theoretically examine the photon-assisted tunneling (PAT) in a double quantum dot (DQD) in parallel when one of the quantum dots (QDs) is irradiated by an AC field. First, we formulate the PAT in a single QD by solving the time-dependent Schrödinger equation using the scattering theory. The QD has an oscillating energy level, $\varepsilon(t)=\varepsilon_0+eV_{\mathrm{AC}}\cosωt$, and is connected to two leads by the tunnel coupling $Γ$. We show that the resonant tunneling takes place through energy levels of the polariton, $\varepsilon_0+N\hbarω$ ($N=0,\pm 1, \pm 2, \cdots$), when $Γ\ll \hbarω$ (PAT) and through the energy level $\varepsilon(t)$ when $Γ\gg \hbarω$ (adiabatic transport). Then, the scattering theory is applied to the PAT in the DQD in the presence of magnetic flux penetrating between the QDs. We observe the Aharonov--Bohm effect not only in the main peak ($N=0$) but also in subpeaks ($N \ne 0$), indicating coherent transport through the polariton states. Our theory is also applicable to the DQD in the three-terminal geometry. We demonstrate the phase measurement through the irradiated QD and show that the measured phase shift changes continuously from 0 to $π$ around both the main peak and subpeaks.