# Parametric Control of Phonon Mode Coupling in Double-Drum Resonators

Xin Zhou, Bahram Djafari-Rouhani, Yan Pennec, Eddy Collin

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Xin Zhou, Bahram Djafari-Rouhani, Yan Pennec, Eddy Collin. Parametric Control of Phonon Mode Coupling in Double-Drum Resonators. QuaLiCo 2025 - French-Brazilian Workshop on "Quantum transport of light and cold matter", Jul 2025, Peyresq, France. hal-05231386

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Submitted on 22 Sep 2025

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Distributed under a Creative Commons Attribution 4.0 International License
Parametric Control of Phonon Mode Coupling in Double-Drum Resonators

Xin Zhou¹, Eddy Collin², Bahram Djafari-Rouhani¹, Yan Pennec¹

¹CNRS, Univ. Lille, UMR 8520 IEMN, F-59000 Lille, France

²Grenoble Alpes, Institut NEEL - CNRS UPR2940, 38042 Grenoble Cedex 9, France

Parametrically coupled micro- and nano-electromechanical resonators serve as ideal model systems for the study of coherent multimode energy transfer and conversion, offering diverse interaction mechanisms and flexible control of mode coupling [1-3]. This work presents experimental and theoretical studies of two-mode coupling, the control of multimode coupling, and unconventional thermal noise squeezing in double-drum resonator systems. The results reveal the rich dynamics of coupled double-drum resonators and present potential for advancing phononic applications in the fields of quantum engineering and quantum sensing.

The double-drum resonator used in this study consists of a silicon nitride drum and an aluminium drum configured as parallel vibrating plates coupled by electrostatic forces [1-2]. Its special design provides unique access to exploring the phonon-cavity electromechanics through analogies with microwave optomechanical systems [4-5]. First, we will present sideband cooling of the phonon mode and the creation of constructive and destructive interferences in this double-drum system [2-3]. Then, we introduce the squeezing of the thermal noise carried by both drum resonators by simultaneously pumping the silicon nitride resonator at its blue and red sidebands with frequency detuning around the aluminium drum resonance frequency. The unconventional squeezing phenomenon was observed, beyond the standard 2Ω parametric pumping with the 3dB limit. These observations are modelled by the parametrically coupled equations of motion in the linear regime and can be understood by considering the destructive interference produced by the two pump tones in this parametrically coupled system.

We also demonstrate the control of 3-mode coupling by introducing multi-tone techniques. In a single double-drum resonator device, we select two modes of the silicon nitride drum as two 'phonon cavities' to couple coherently with the fundamental mode of the aluminium drum. Two pump tones are used to pump the phonon cavities, and the third tone is used to probe one of these three modes. By tuning the phonon coupling rates between the coupled low frequency drum and two cavities, one of the mechanical modes can be brought into or out of the coupled system by controlling the mechanical dark mode and the bright mode. The relative phases between the different modes can be well defined, although they correspond to different frequencies. A similar method has been used to guide phonons between four drum resonators.

References

[1] A. Pokharel, et al., Nano Letters, **22**, 7351 (2022)

[2] X. Zhou, et al., Nano Letters, **21**, 5738 (2021)

[3] H. Xu, et al., Nano Letters, **24**, 8550-8557 (2024)

[4] X. Zhou, et al., Physical Review Applied 12.4 (2019): 044066.

[5] D Cattiaux, et al., Nature Communications 12, 6182 (2021)