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 report on the design, demonstration and operation of nearly perfect QHOs in AlGaAs/GaAs heterostructure. On the basis of model calculations, we demonstrate that, when a substitutional 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 ~8-9 meV. We experimentally confirm this proposal by utilizing Stark effect 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 qualitatively 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.
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