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

doi:10.1007/s11467-022-1225-7

Front. Phys.

2023, Vol. 18

Issue (1) : 13310 https://doi.org/10.1007/s11467-022-1225-7

RESEARCH ARTICLE

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

Guangqiang Mei, Pengfei Suo, Li Mao, Min Feng, Limin Cao(

)

School of Physics and Technology, Center for Nanoscience and Nanotechnology, and Key Laboratory of Artificial Micro- and Nano-structures of Ministry of Education, Wuhan University, Wuhan 430072, China

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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.

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

Corresponding Author(s): Limin Cao

Issue Date: 23 November 2022

Cite this article:

Guangqiang Mei,Pengfei Suo,Li Mao, et al. Demonstration and operation of quantum harmonic oscillators in an AlGaAs−GaAs heterostructure[J]. Front. Phys. , 2023, 18(1): 13310.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-022-1225-7
https://academic.hep.com.cn/fop/EN/Y2023/V18/I1/13310

Fig.1 Schematics of model calculations for the formation of a hydrogenic Si QHO in AlGaAs/GaAs heterostructure. (a) A hydrogen-like Si⁺ center is formed resulting from the released valence electron being trapped in the heterointerface quantum well. (b) Under external stimulus, such as an electric field, an electron may re-fill the lowest hydrogen-like orbit, forming the neutral hydrogen-like Si atom. Under its ground state, the electron forms the diffuse electron cloud within the spatial extent of radial radius

R = 1.5 R 1

, here R₁ is the effective Bohr radius. (c) A small displacement between the electron cloud center (denoted by O) and Si⁺ nucleus introduces a restoring Coulomb force that is proportional to displacement resembling the Hooke harmonic oscillator. The harmonic restoring force gives rise to an inherent square law potential, which is the signature of a QHO for a microscopic quantum system.

Fig.2 Schematic of the SET-QHO device architecture. The SET is fabricated on the surface of AlGaAs/GaAs 2DEG heterostructure substrate. The hydrogenic QHOs take place in the Si δ-doping layer. The SET is capacitively coupled to the hydrogen-like Si QHOs beneath the surface. The gate electrodes are used to tune the potentials of both SET and QHOs, and manipulate and operate them simultaneously. S, D, and Gate denote the source, drain, and gate electrodes, respectively.

Fig.3 SEM image of the typical device design for the detection and operation of QHOs. D1(2) and S1(2) denote the drain and source terminals of SET1(2), and G_1T(B) and G_2T(B) denote the top and bottom gates of SET1(2), respectively.

Fig.4 Conductance oscillations versus gate bias applied to top gate. (a) Current passing through SET1 as a function of the gate bias, V_G1T, applied to top gate G_1T. The drain-source bias, V_DS1, is fixed at 0.2 mV for the measurements. (b) Zoomed-in view of the fast oscillation region showing rather uniform and equally spaced resonance peaks with average period of ~7.4 mV. However, the spacing between the 1^st and 2^nd peaks is ~11.4 mV, about ~1.54 times that of average value. (c) The spacing between neighboring peaks versus peak position.

Fig.5 Conductance oscillations versus gate bias applied to bottom gate. (a) Current through SET1 as a function of the bottom gate bias, V_G1B, at fixed drain-source bias of 0.2 mV. (b) Zoomed-in view of the fast oscillation region showing evenly spaced resonance peaks with average period of ~7.5 mV. The spacing between the 1^st and 2^nd peaks is ~11.7 mV, about ~1.56 times that of average value. (c) The spacing between neighboring peaks versus peak position.

1	A. Nielsen M.L. Chuang I., Quantum Computation and Quantum Information, Cambridge University Press, New York, USA, 2000
2	J. Wineland D.. Nobel lecture: Superposition, entanglement, and raising Schrödinger’s cat. Rev. Mod. Phys., 2013, 85(3): 1103 https://doi.org/10.1103/RevModPhys.85.1103
3	J. Wineland D., Monroe C., M. Itano W., Leibfried D., E. King B., M. Meekhof D.. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl. Inst. Stand. Technol., 1998, 103(3): 259 https://doi.org/10.6028/jres.103.019
4	Leibfried D., Blatt R., Monroe C., J. Wineland D.. Quantum dynamics of single trapped ions. Rev. Mod. Phys., 2003, 75(1): 281 https://doi.org/10.1103/RevModPhys.75.281
5	Kielpinski D., Monroe C., J. Wineland D.. Architecture for a large-scale ion-trap quantum computer. Nature, 2002, 417(6890): 709 https://doi.org/10.1038/nature00784
6	D. Bruzewicz C., Chiaverini J., McConnell R., M. Sage J.. Trapped-ion quantum computing: Progress and challenges. Appl. Phys. Rev., 2019, 6(2): 021314 https://doi.org/10.1063/1.5088164
7	J. Ballance C., P. Harty T., M. Linke N., A. Sepiol M., M. Lucas D.. High-fidelity quantum logic gates using trapped-ion hyperfine qubits. Phys. Rev. Lett., 2016, 117(6): 060504 https://doi.org/10.1103/PhysRevLett.117.060504
8	P. Gaebler J., R. Tan T., Lin Y., Wan Y., Bowler R., C. Keith A., Glancy S., Coakley K., Knill E., Leibfried D., J. Wineland D.. High-fidelity universal gate set for 9Be+ ion qubits. Phys. Rev. Lett., 2016, 117(6): 060505 https://doi.org/10.1103/PhysRevLett.117.060505
9	Srinivas R., C. Burd S., T. Sutherland R., C. Wilson A., J. Wineland D., Leibfried D., Allcock C., H. Slichter D.. Trapped-ion spin-motion coupling with microwaves and a near-motional oscillating magnetic field gradient. Phys. Rev. Lett., 2019, 122(16): 163201 https://doi.org/10.1103/PhysRevLett.122.163201
10	R. Brown K., Ospelkaus C., Colombe Y., C. Wilson A., Leibfried D., J. Wineland D.. Coupled quantized mechanical oscillators. Nature, 2011, 471(7337): 196 https://doi.org/10.1038/nature09721
11	C. McCormick K., Keller J., C. Burd S., J. Wineland D., C. Wilson A., Leibfried D.. Quantum-enhanced sensing of a single-ion mechanical oscillator. Nature, 2019, 572(7767): 86 https://doi.org/10.1038/s41586-019-1421-y
12	Kienzler D., Y. Lo H., Keitch B., de Clercq L., Leupold F., Lindenfelser F., Marinelli M., Negnevitsky V., P. Home J.. Quantum harmonic oscillator state synthesis by reservoir engineering. Science, 2015, 347(6217): 53 https://doi.org/10.1126/science.1261033
13	Flühmann C., L. Nguyen T., Marinelli M., Negnevitsky V., Mehta K., P. Home J.. Encoding a qubit in a trapped-ion mechanical oscillator. Nature, 2019, 566(7745): 513 https://doi.org/10.1038/s41586-019-0960-6
14	D. O’Connell A., Hofheinz M., Ansmann M., C. Bialczak R., Lenander M., Lucero E., Neeley M., Sank D., Wang H., Weides M., Wenner J., M. Martinis J., N. Cleland A.. Quantum ground state and single-phonon control of a mechanical resonator. Nature, 2010, 464(7289): 697 https://doi.org/10.1038/nature08967
15	Chan J., P. M. Alegre T., H. Safavi-Naeini A., T. Hill J., Krause A., Groblacher S., Aspelmeyer M., Painter O.. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature, 2011, 478(7367): 89 https://doi.org/10.1038/nature10461
16	Arrangoiz-Arriola P., A. Wollack E., Y. Wang Z., Pechal M., T. Jiang W., P. McKenna T., D. Witmer J., Van Laer R., H. Safavi-Naeini A.. Resolving the energy levels of a nanomechanical oscillator. Nature, 2019, 571(7766): 537 https://doi.org/10.1038/s41586-019-1386-x
17	W. Chu Y., Kharel P., Yoon T., Frunzio L., T. Rakich P., J. Schoelkopf R.. Creation and control of multi-phonon Fock states in a bulk acoustic-wave resonator. Nature, 2018, 563(7733): 666 https://doi.org/10.1038/s41586-018-0717-7
18	Porrati M., Putterman S.. Prediction of short time qubit readout via measurement of the next quantum jump of a coupled damped driven harmonic oscillator. Phys. Rev. Lett., 2020, 125(26): 260403 https://doi.org/10.1103/PhysRevLett.125.260403
19	Mirrahimi M., Leghtas Z., Albert V., Touzard S., J. Schoelkopf R., Jiang L., H. Devoret M.. Dynamically protected cat-qubits: A new paradigm for universal quantum computation. New J. Phys., 2014, 16(4): 045014 https://doi.org/10.1088/1367-2630/16/4/045014
20	W. Gurney R., F. Mott N.. Conduction in polar crystals (III): On the colour centres in alkali-halide crystals. Trans. Faraday Soc., 1938, 34: 506 https://doi.org/10.1039/tf9383400506
21	R. Tibbs S.. Electron energy levels in NaCl. Trans. Faraday Soc., 1939, 35: 1471 https://doi.org/10.1039/tf9393501471
22	Y. Yu P.Cardona M., Fundamentals of Semiconductors: Physics and Material Properties, Springer-Verlag, Berlin, Germany, 2001
23	Zhang Y.. Electronic structures of impurities and point defects in semiconductors. Chin. Phys. B, 2018, 27(11): 117103 https://doi.org/10.1088/1674-1056/27/11/117103
24	Zhang Y., W. Wang J.. Bound exciton model for an acceptor in a semiconductor. Phys. Rev. B, 2014, 90(15): 155201 https://doi.org/10.1103/PhysRevB.90.155201
25	M. Cao L., Altomare F., L. Guo H., Feng M., M. Chang A.. Coulomb blockade correlations in a coupled single-electron device system. Solid State Commun., 2019, 296: 12 https://doi.org/10.1016/j.ssc.2019.04.004
26	J. Schoelkopf R., Wahlgren P., A. Kozhevnikov A., Delsing P., E. Prober D.. The radio-frequency single-electron transistor (RF-SET): A fast and ultrasensitive electrometer. Science, 1998, 280(5367): 1238 https://doi.org/10.1126/science.280.5367.1238
27	H. Devoret M., J. Schoelkopf R.. Amplifying quantum signals with the single-electron transistor. Nature, 2000, 406(6799): 1039 https://doi.org/10.1038/35023253
28	Lu W., Q. Ji Z., Pfeiffer L., W. West K., J. Rimberg A.. Real-time detection of electron tunnelling in a quantum dot. Nature, 2003, 423(6938): 422 https://doi.org/10.1038/nature01642
29	Bylander J., Duty T., Delsing P.. Current measurement by real-time counting of single electrons. Nature, 2005, 434(7031): 361 https://doi.org/10.1038/nature03375
30	Lu W., J. Rimberg A., D. Maranowski K., C. Gossard A.. Single-electron transistor strongly coupled to an electrostatically defined quantum dot. Appl. Phys. Lett., 2000, 77(17): 2746 https://doi.org/10.1063/1.1320455
31	Berman D., B. Zhitenev N., C. Ashoori R., Shayegan M.. Observation of quantum fluctuations of charge on a quantum dot. Phys. Rev. Lett., 1999, 82(1): 161 https://doi.org/10.1103/PhysRevLett.82.161
32	C. Chen J., H. An Z., Ueda T., Komiyama S., Hirakawa K., Antonov V.. Metastable excited states of a closed quantum dot probed by an aluminum single-electron transistor. Phys. Rev. B, 2006, 74(4): 045321 https://doi.org/10.1103/PhysRevB.74.045321
33	Sun L., R. Brown K., E. Kane B.. Coulomb blockade in a Si channel gated by an Al single-electron transistor. Appl. Phys. Lett., 2007, 91(14): 142117 https://doi.org/10.1063/1.2793712
34	W. Dellow M., H. Beton P., J. G. M. Langerak C., J. Foster T., C. Main P., Eaves L., Henini M., P. Beaumont S., D. W. Wilkinson C.. Resonant tunneling through the bound states of a single donor atom in a quantum well. Phys. Rev. Lett., 1992, 68(11): 1754 https://doi.org/10.1103/PhysRevLett.68.1754
35	Tsu R., L. Li X., H. Nicollian E.. Slow conductance oscillations in nanoscale silicon clusters of quantum dots. Appl. Phys. Lett., 1994, 65(7): 842 https://doi.org/10.1063/1.112178
36	D. McCluskey M., Janotti A.. Defects in semiconductors. J. Appl. Phys., 2020, 127(19): 190401 https://doi.org/10.1063/5.0012677

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