Macroscopic Quantum Test with Bulk Acoustic Wave Resonators

Recently, solid-state mechanical resonators have become a platform for demonstrating nonclassical behavior of systems involving a truly macroscopic number of particles. Here, we perform the most macroscopic quantum test in a mechanical resonator to date, which probes the validity of quantum mechanics by ruling out a classical description at the microgram mass scale. This is done by a direct measurement of the Wigner function of a high-overtone bulk acoustic wave resonator mode, monitoring the gradual decay of negativities over tens of microseconds. While the obtained macroscopicity of $\mu =11.3$ is on par with state-of-the-art atom interferometers, future improvements of mode geometry and coherence times could test the quantum superposition principle at unprecedented scales and also place more stringent bounds on spontaneous collapse models.

Figure 1

Illustration of the HBAR device used in this work (not to scale, see Ref. [14] for details). A superconducting qubit couples to a mechanical acoustic mode localized in the bulk of a sapphire crystal through a piezoelectric material. This allows the preparation and measurement of the quantum state of the phonon mode.

Figure 2

Measured Wigner functions of a bulk acoustic mode initially prepared in the Fock state $|1⟩$ (top row) and in the superposition state $(|0⟩+|1⟩)/\sqrt{2}$ (bottom row). Both states are initially nonclassical, as indicated by the phase space regions with negative quasiprobability (blue). As time evolves (left to right), both states approach the ground state $|0⟩$ due to relaxation. Comparing the measured data to the theoretical model Eq. (7) allows us to extract the maximal compatible diffusion rate $\mathrm{\Gamma }$ through Bayesian inference, yielding the macroscopicity $\mu$ for the considered experiment.