Interstate interference of electron wave packet tunneling through a quantum ring

Abstract

We theoretically study the time-developed progress of resonant tunneling for an electron wave packet injected into a two-dimensional quantum ring (QR) by solving the time-dependent (TD) Schr\odinger equation numerically. Focusing on an extraction of the angular momentum ${l}_{z}$, we examine the TD features in the resonant tunneling electron by projection analysis in which the resulting TD wave function at the QR is decomposed into the (static) resonant states by calculating the inner products among them. This analysis reveals that the two-states approach is well applicable for the QR system and the cross terms between these two states are crucial for the TD vacillation of both the expectation value of the angular momentum $⟨{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{l}}_{z}⟩$ and the electron density $\ensuremath{\rho}$. The quasidegeneracy of the resonant states causes a characteristic beating whose frequency is determined by the difference between the eigenenergies. We further study the corresponding TD phenomena under a magnetic field and find that the rotational direction in $\ensuremath{\rho}$ changes in accordance with the strength of the magnetic field. This feature seems to be very different from the classical prospect of the cyclotron motion where the application of the magnetic field determines the rotational direction uniquely.