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  • Open Access

Quantum-limited acoustoelectric amplification in a piezoelectric-2DEG heterostructure

Eric Chatterjee1, Daniel Soh1, and Matt Eichenfield1,2,3,*

  • *Contact author: matt.eichenfield@colorado.edu
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Phys. Rev. Research 8, 023185 – Published 19 May, 2026

DOI: https://doi.org/10.1103/9zjg-gx79

Abstract

We provide a quantum mechanical description of phonon amplification in a heterostructure consisting of a two-dimensional electron gas (2DEG) stacked on top of a piezoelectric material. An applied drift voltage effectively creates a population inversion in the momentum states of the 2DEG electrons, giving rise to spontaneous emission of phonons. Once an acoustic wave is launched, the pumped electrons release phonons via stimulated emission, returning to depleted ground states before being pumped back to the excited states. We show that whereas efficient amplification using a one-dimensional electron gas requires the acoustic wavelength to roughly equal the mean distance between electrons, a 2DEG enables efficient amplification for any wavelength greater than this distance. We derive the imaginary and real parts of the 2DEG’s first-order acoustic susceptibility as functions of electronic drift velocity in specific limits and derive the gain per unit length for the signal and the quantum noise, with the gain matching the classical result in the short-electronic-lifetime (low-mobility) regime. Moreover, we analyze the gain clamping due to pump depletion and calculate the maximum achievable intensity. Our results provide a framework for designing acoustic devices including a quantum phononic laser and phase-insensitive quantum phononic amplifiers.

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References (41)

  1. V. Fiore, Y. Yang, M. C. Kuzyk, R. Barbour, L. Tian, and H. Wang, Storing optical information as a mechanical excitation in a silica optomechanical resonator, Phys. Rev. Lett. 107, 133601 (2011).
  2. C. Galland, N. Sangouard, N. Piro, N. Gisin, and T. J. Kippenberg, Heralded single-phonon preparation, storage, and readout in cavity optomechanics, Phys. Rev. Lett. 112, 143602 (2014).
  3. I. Söllner, L. Midolo, and P. Lodahl, Deterministic single-phonon source triggered by a single photon, Phys. Rev. Lett. 116, 234301 (2016).
  4. H. H. Diamandi, Y. Luo, D. Mason, T. B. Kanmaz, S. Ghosh, M. Pavlovich, T. Yoon, R. Behunin, S. Puri, J. G. E. Harris, and P. T. Rakich, Optomechanical control of long-lived bulk acoustic phonons in the quantum regime, Nat. Phys. 21, 1482 (2025).
  5. M. D. Anderson, S. Tarrago Velez, K. Seibold, H. Flayac, V. Savona, N. Sangouard, and C. Galland, Two-color pump-probe measurement of photonic quantum correlations mediated by a single phonon, Phys. Rev. Lett. 120, 233601 (2018).
  6. M. Mirhosseini, A. Sipahigil, M. Kalaee, and O. Painter, Superconducting qubit to optical photon transduction, Nature (London) 588, 599 (2020).
  7. M. D. Urmey, S. Mittal, K. Adachi, L. G. Talamo, S. Dickson, S.-X. Lin, R. D. Delaney, B. M. Brubaker, J. M. Kindem, N. E. Frattini, K. W. Lehnert, and C. A. Regal, Stable optomechanical Fabry-Pérot architecture in a continuous microwave-to-optical transducer, in Proceedings of SPIE, Quantum Computing, Communication, and Simulation IV, San Francisco, California, USA (SPIE, 2024), Vol. 12911, p. 1291109.
  8. A. N. Cleland and M. R. Geller, Superconducting qubit storage and entanglement with nanomechanical resonators, Phys. Rev. Lett. 93, 070501 (2004).
  9. R. Ruskov and C. Tahan, Coherent phonons as a new element of quantum computing and devices, J. Phys.: Conf. Ser. 398, 012011 (2012).
  10. K. J. Satzinger, Y. P. Zhong, H.-S. Chang, G. A. Peairs, A. Bienfait, M.-H. Chou, A. Y. Cleland, C. R. Conner, E. Dumur, J. Grebel, I. Gutierrez, B. H. November, R. G. Povey, S. J. Whiteley, D. D. Awschalom, D. I. Schuster, and A. N. Cleland, Quantum control of surface acoustic-wave phonons, Nature (London) 563, 661 (2018).
  11. F. Pistolesi, A. N. Cleland, and A. Bachtold, Proposal for a nanomechanical qubit, Phys. Rev. X 11, 031027 (2021).
  12. H. Qiao, E. Dumur, G. Andersson, H. Yan, M.-H. Chou, J. Grebel, C. R. Conner, Y. J. Joshi, J. M. Miller, R. G. Povey, X. Wu, and A. N. Cleland, Splitting phonons: Building a platform for linear mechanical quantum computing, Science 380, 1030 (2023).
  13. J. D. Cohen, S. M. Meenehan, G. S. MacCabe, S. Gröblacher, A. H. Safavi-Naeini, F. Marsili, M. D. Shaw, and O. Painter, Phonon counting and intensity interferometry of a nanomechanical resonator, Nature (London) 520, 522 (2015).
  14. S. Hong, R. Riedinger, I. Marinkovic, A. Wallucks, S. G. Hofer, R. A. Norte, M. Aspelmeyer, and S. Gröblacher, Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator, Science 358, 203 (2017).
  15. M. J. Weaver, D. Newsom, F. Luna, W. Löffler, and D. Bouwmeester, Phonon interferometry for measuring quantum decoherence, Phys. Rev. A 97, 063832 (2018).
  16. A. Bienfait, Y. P. Zhong, H.-S. Chang, M.-H. Chou, C. R. Conner, E. Dumur, J. Grebel, G. A. Peairs, R. G. Povey, K. J. Satzinger, and A. N. Cleland, Quantum erasure using entangled surface acoustic phonons, Phys. Rev. X 10, 021055 (2020).
  17. A. Zivari, N. Fiaschi, R. Burgwal, E. Verhagen, R. Stockill, and S. Gröblacher, On-chip distribution of quantum information using traveling phonons, Sci. Adv. 8, eadd2811 (2022).
  18. X. Ma, J. J. Viennot, S. Kotler, J. D. Teufel, and K. W. Lehnert, Non-classical energy squeezing of a macroscopic mechanical oscillator, Nat. Phys. 17, 322 (2021).
  19. H. Zhao, W. D. Chen, A. Kejriwal, and M. Mirhosseini, Quantum-enabled microwave-to-optical transduction via silicon nanomechanics, Nat. Nanotechnol. 20, 602 (2025).
  20. A. D. O’Connell, A macroscopic mechanical resonator operated in the quantum limit, Doctoral dissertation, University of California, Santa Barbara, 2010.
  21. A. B. Bozkurt, O. Golami, Y. Yu, H. Tian, and M. Mirhosseini, A mechanical quantum memory for microwave photons, Nat. Phys. 21, 1469 (2025).
  22. L. Hackett, M. Koppa, B. Smith, M. Miller, S. Santillan, S. Weatherred, S. Arterburn, T. A. Friedmann, N. Otterstrom, and M. Eichenfield, Giant electron-mediated phononic nonlinearity in semiconductor-piezoelectric heterostructures, Nat. Mater. 23, 1386 (2024).
  23. K. Länge, B. E. Rapp, and M. Rapp, Surface acoustic wave biosensors: A review, Anal. Bioanal. Chem. 391, 1509 (2008).
  24. X. Ding, P. Li, S.-C. S. Lin, Z. S. Stratton, N. Nama, F. Guo, D. Slotcavage, X. Mao, J. Shi, F. Costanzo, and T. J. Huang, Surface acoustic wave microfluidics, Lab Chip 13, 3626 (2013).
  25. M. J. A. Schuetz, E. M. Kessler, G. Giedke, L. M. K. Vandersypen, M. D. Lukin, and J. I. Cirac, Universal quantum transducers based on surface acoustic waves, Phys. Rev. X 5, 031031 (2015).
  26. D. Mandal and S. Banerjee, Surface acoustic wave (SAW) sensors: Physics, materials, and applications, Sensors 22, 820 (2022).
  27. A. Wendt, M. J. Storey, M. Miller, D. Anderson, E. Chatterjee, W. Horrocks, B. Smith, P.-S. Wong, S. Arterburn, T. A. Friedmann, L. Hackett, and M. Eichenfield, An electrically injected solid-state surface acoustic wave phonon laser, Nature (London) 649, 597 (2026).
  28. L. Hackett, M. Miller, S. Weatherred, S. Arterburn, M. J. Storey, G. Peake, D. Dominguez, P. S. Finnegan, T. A. Friedmann, and M. Eichenfield, Non-reciprocal acoustoelectric microwave amplifiers with net gain and low noise in continuous operation, Nat. Electron. 6, 76 (2023).
  29. E. Chatterjee, A. Wendt, D. Soh, and M. Eichenfield, Ab initio calculations of nonlinear susceptibility and multiphonon mixing processes in a 2DEG-piezoelectric heterostructure, Phys. Rev. Res. 6, 023288 (2024).
  30. L. Bandhu, L. M. Lawton, and G. R. Nash, Macroscopic acoustoelectric charge transport in graphene, Appl. Phys. Lett. 103, 133101 (2013).
  31. L. Bandhu and G. R. Nash, Controlling the properties of surface acoustic waves using graphene, Nano Res. 9, 685 (2016).
  32. A. Hernández-Mínguez, Y.-T. Liou, and P. V. Santos, Interaction of surface acoustic waves with electronic excitations in graphene, J. Phys. D: Appl. Phys. 51, 383001 (2018).
  33. Y. Mou, H. Chen, J. Liu, Q. Lan, J. Wang, C. Zhang, Y. Wang, J. Gu, T. Zhao, X. Jiang, W. Shi, and C. Zhang, Gate-tunable quantum acoustoelectric transport in graphene, Nano Lett. 24, 4625 (2024).
  34. E. Preciado, F. J. R. Schulein, A. E. Nguyen, D. Barroso, M. Isarraraz, G. von Son, I.-H. Lu, W. Michailow, B. Moller, V. Klee, J. Mann, A. Wixforth, L. Bartels, and H. J. Krenner, Scalable fabrication of a hybrid field-effect and acousto-electric device by direct growth of monolayer MoS2/LiNbO3, Nat. Commun. 6, 8593 (2015).
  35. A. V. Kalameitsev, V. M. Kovalev, and I. G. Savenko, Macroscopic acoustoelectric charge transport in graphene, Phys. Rev. Lett. 122, 256801 (2019).
  36. Matt Eichenfield, Acoustoelectric devices: Then and now, Technical Report No. SAND2015-8536PE (Sandia National Laboratory, Albuquerque, NM, 2015).
  37. J. Lindhard, On the properties of a gas of charged particles, Kgl. Danske Videnskab. Selskab Mat.-fys. Medd. 28, 8 (1954).
  38. N. D. Mermin, Lindhard dielectric function in the relaxation-time approximation, Phys. Rev. B 1, 2362 (1970).
  39. Erik Mosekilde, Quantum theory of acoustoelectric interaction, Phys. Rev. B 9, 682 (1974).
  40. G. S. Kino and T. M. Reeder, A normal mode theory for the Rayleigh wave amplifier, IEEE Trans. Electron Devices 18, 909 (1971).
  41. K. Inoue, Quantum mechanical treatment of optical amplifiers based on population inversion, IEEE J. Quantum Electron. 50, 563 (2014).

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Phys. Rev. Research 8, 023185– Published 19 May, 2026
  • Received 10 October 2025
  • Accepted 13 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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