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

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 δ-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 ~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.

Graphical abstract

Keywords

quantum harmonic oscillator / AlGaAs/GaAs semiconductor heterostructure / single-electron transistor / gate tuning

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Electronic supplementary material

Supplementary materials are available in the online version of this article at https://doi.org/10.1007/s11467-022-1225-7 and https://journal.hep.com.cn/fop/EN/10.1007/s11467-022-1225-7 and are accessible for authorized users.

Acknowledgements

We gratefully acknowledge Prof. A. M. Chang for his generous supports in experiments at Duke University, and Dr. F. Altomare for his sincere helps in experiments and careful reading of the manuscript. Fruitful discussions with Profs. Y. Zhang, J. Chen, J. Zhao, and C. Lin are greatly appreciated. M. Feng thanks financial support from the National Key R&D Program of China (Grant No. 2018YFA0305802), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XD30000000), and the National Natural Science Foundation of China (Grant Nos. 11574364 and 11774267). L. Mao thanks financial support from the National Key R&D Program of China by the Ministry of Science and Technology of China (Grant No. 2015C8932400).

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