Demonstration and operation of quantum harmonic oscillators in an AlGaAs-GaAs heterostructure

TL;DR

This paper demonstrates the creation and control of quantum harmonic oscillators in an AlGaAs-GaAs heterostructure using dopants, confirmed by experimental measurements, and discusses their potential for quantum technology applications.

Contribution

It introduces a new method to realize and manipulate quantum harmonic oscillators in semiconductor heterostructures through dopant engineering and experimental validation.

Findings

QHO states with ~8-9 meV energy spacing observed

Fast oscillations in conductance confirmed QHO behavior

Theoretical and experimental results are quantitatively consistent

Abstract

The quantum harmonic oscillator (QHO), one of the most important and ubiquitous model systems in quantum mechanics, features equally spaced energy levels or eigenstates. Here we present a new class of nearly ideal QHOs formed by hydrogenic substitutional dopants in an AlGaAs/GaAs heterostructure. On the basis of model calculations, we demonstrate that, when a deta-doping Si donor substitutes the Ga/Al lattice site close to AlGaAs/GaAs heterointerface, a hydrogenic Si QHO, characterized by a restoring Coulomb force producing square law harmonic potential, is formed. This gives rise to QHO states with energy spacing of about ~8-9 meV. We experimentally confirm this proposal by utilizing gate tuning and measuring QHO states using an aluminum single-electron transistor (SET). A sharp and fast oscillation with period of ~7-8 mV appears in addition to the regular Coulomb blockade (CB) oscillation with much larger period, for positive gate biases above 0.5 V. The observation of fast oscillation and its behavior is quantitatively consistent with our theoretical result, manifesting the harmonic motion of electrons from the QHO. Our results might establish a general principle to design, construct and manipulate QHOs in semiconductor heterostructures, opening future possibilities for their quantum applications.