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Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics


Mechanical resonators are emerging as an important new platform for quantum science and technologies. A large number of proposals for using them to store, process and transduce quantum information motivates the development of increasingly sophisticated techniques for controlling mechanical motion in the quantum regime. By interfacing mechanical resonators with superconducting circuits, circuit quantum acoustodynamics can make a variety of important tools available for manipulating and measuring motional quantum states. Here we demonstrate the direct measurements of phonon number distribution and parity of non-classical mechanical states. We do this by operating our system in the strong dispersive regime, where a superconducting qubit can be used to spectroscopically resolve the phonon Fock states. These measurements are some of the basic building blocks for constructing acoustic quantum memories and processors. Furthermore, our results open the door for performing even more complex quantum algorithms using mechanical systems, such as quantum error correction and multimode operations.

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Fig. 1: Characterization of the BAR device.
Fig. 2: Dispersive measurement of phonon coherent states.
Fig. 3: Dispersive measurement of phonon Fock states.
Fig. 4: Wigner tomography of non-classical phonon states.

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Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Code availability

Analysis and simulation codes that support the findings of this study are available from the corresponding authors upon reasonable request.


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We thank X. Cao and A. deMello for help with the flip-chip-bonding process and J.-C. Besse for help with the qubit fabrication. We thank B. Li for providing support with the QuTiP simulations. The fabrication of devices was performed at the FIRST cleanroom of ETH Zürich and the BRNC cleanroom of IBM Zürich. M.F. acknowledge The Branco Weiss Fellowship—Society in Science, administered by the ETH Zürich.

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Authors and Affiliations



U.v.L. and L.M. designed and fabricated the device. U.v.L. and M.B. constructed the parametric amplifier used for the qubit readout. M.B. wrote the experiment control software. Y.Y., U.v.L. and M.B. performed the experiment and analysed the data. Y.Y. performed the QuTiP simulations of the experiment. M.F., M.B. and Y.C. performed the theoretical calculations. Y.C. supervised the work. U.v.L., Y.Y., M.B., M.F. and Y.C. wrote the manuscript.

Corresponding authors

Correspondence to Uwe von Lüpke or Yiwen Chu.

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Nature Physics thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Table 1, Figs. 1–6 and Sections A–G.

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Source Data Fig. 1

Source data for Fig. 1d.

Source Data Fig. 2

Source data for Fig. 2 (one tab for each subfigure).

Source Data Fig. 3

Source ata for Fig. 3 (one tab for each subfigure).

Source Data Fig. 4

Source ata for Fig. 4d.

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von Lüpke, U., Yang, Y., Bild, M. et al. Parity measurement in the strong dispersive regime of circuit quantum acoustodynamics. Nat. Phys. 18, 794–799 (2022).

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