Probing the quantum motion of a macroscopic mechanical resonator with a resonant rf-fluxonium

Quantum mechanical resonators provide a promising platform for quantum technologies and experimental tests of fundamental physics. For instance, long-lived mechanical drums oscillating at MHz frequencies could provide experimental evidence to settle the debate on whether gravitational fields exist in quantum superposition. Yet, measuring and controlling them remains challenging, in particular owing to the large frequency mismatch with other well-controlled quantum systems. We perform a Gedankenexperiment, where a mechanical resonator is repeatedly interrogated by a resonant ideal two-level system. This artificial atom interacts with the resonator more than 250 times during its 6 ms lifetime. After each interaction, a single-shot state-selective detection is performed, extracting information bit-by-bit about the mechanical state. More specifically, a 4~MHz suspended silicon nitride membrane is resonantly coupled to a heavy-fluxonium qubit. This superconducting circuit features a MHz qubit-manifold which can be prepared (effective qubit temperature of 35 µK), and readout (single-shot fidelity of 85 %) thanks to microwave transitions to higher circuit excited states. These periodic weak measurements are used to reconstruct the noise spectrum of the oscillator’s position under the influence of the thermal environment (occupation n_th) and qubit backaction. By resetting the qubit in either the ground or excited state, we reveal the fundamental imbalance between the emission and absorption spectra, proportional to n_th and n_th + 1 respectively. This clear signature of the non-commutation between creation and annihilation operators confirms the quantum nature of the interaction.