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Phonon decoherence produced by two-level tunneling states

Ryan O. Behunin1,2,*, Taylor Ray1,2, Dylan Chapman1,2, Andrew J. Shepherd1,2, Yizhi Luo3, and Peter T. Rakich4

  • 1Department of Applied Physics and Materials Science, Northern Arizona University, Flagstaff, Arizona 86011, USA
  • 2Center for Materials Interfaces in Research and Applications (¡MIRA!) Flagstaff, Arizona, USA
  • 3Department of Applied Physics and E.L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
  • 4Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA

  • *Contact author: ryan.behunin@nau.edu
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Phys. Rev. Applied 26, 034047 – Published 22 September, 2026

DOI: https://doi.org/10.1103/732t-38bj

Abstract

Phonon modes within pristine crystalline resonators now routinely reach the quantum ground state. Such systems are attractive for quantum information science applications, as advanced fabrication and processing can enable relatively long quantum coherence times, and precision control can be realized through optical, electrical, or qubit coupling. In many state-of-the-art systems, the phonon lifetime is limited by disorder. In particular, native oxides or damaged “dead layers” at surfaces can host two-level tunneling states (TLS) that lead to a particularly problematic form of dissipation that increases at lower temperatures. As mechanical losses are driven down in systems such as microfabricated bulk acoustic wave resonators, tunneling states are expected to emerge as the dominant mechanism for phonon decoherence. A quantitative description of these mesoscopic systems therefore requires a framework that captures interactions between a selected phonon mode and a large ensemble of TLS. Here, we derive a quantum master equation for this coupled system, permitting the phonon decoherence produced by two-level tunneling states to be calculated. As an example, we estimate the lifetime of several quantum states within quartz microresonators hosting a thin surface layer of tunneling states. We find that the phonon coherence time is maximized at low temperatures, in spite of increased mechanical dissipation, and that phonon-TLS coupling can be reduced for modes with strain nodes at the surfaces.

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Phys. Rev. Applied 26, 034047– Published 22 September, 2026
  • Received 24 February 2026
  • Revised 5 June 2026
  • Accepted 17 August 2026
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