Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.
Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.
Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with a Fock state |6⟩, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state |5⟩ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state |3⟩. Our results have immediate applications in quantum sensing and simulations with high-overtone bulk acoustic wave resonator devices.
Distributed quantum sensing leverages quantum correlations among multiple sensors to enhance the precision of parameter estimation beyond classical limits. Most existing approaches target phase estimation and rely on a shared phase reference between the signal and the probe, yet many relevant scenarios deal with regimes where such a reference is absent, making the estimation of force or field amplitudes the main task. We study this phase-insensitive regime for bosonic sensors that undergo identical displacements with common phases randomly varying between experimental runs. We derive analytical bounds on the achievable precision and show that it is determined by first-order normal correlations between modes in the probe state, constrained by their average excitations. These correlations yield a collective sensitivity enhancement over the standard quantum limit, with a gain that grows linearly in the total excitation number, revealing a distributed quantum advantage even without a global phase reference. We identify families of multimode states with definite joint parity that saturate this limit and can be probed efficiently via local parity measurements already demonstrated or emerging in several quantum platforms. We further demonstrate that experimentally relevant decoherence channels favor two distinct sensing strategies: splitting of a single-mode nonclassical state among the modes, which is robust to loss and heating, and separable probes, which are instead resilient to dephasing and phase jitter. Our results are relevant to multimode continuous platforms, including trapped-ion, solid-state mechanical, optomechanical, superconducting, and photonic systems.
Quantum metrology enables sensitivity to approach the limits set by fundamental physical laws. Even a single continuous mode offers enhanced precision, with the improvement scaling with its occupation number. Due to their high information capacity, continuous modes allow for the engineering of quantum non-Gaussian states, which not only improve metrological performance but can also be tailored to specific experimental platforms and conditions. Recent advancements in control over continuous platforms operating in the quantum regime have renewed interest in sensing weak forces, also coupling to massive macroscopic objects. In this work, we investigate a force-sensing scheme where a physical process completely randomizes the direction of the induced phase-space displacement, and the unknown force strength is inferred through excitation-number-resolving measurements. We find that N-spaced states, where only every N^{th} Fock state occupation is nonzero, approach the achievable sensing bound. Additionally, non-Gaussian states are shown to be more resilient against decoherence than their Gaussian counterparts with the same occupation number. While Fock states typically offer the best protection against decoherence, we uncover a transition in the metrological landscape-revealed through a tailored decoherence-aware Fisher-information-based reward functional-where experimental constraints favor a family of number-squeezed Schrödinger cat states. Specifically, by implementing quantum optimal control in a minimal spin-boson system, we identify these states as maximizing force sensitivity under lossy dynamics and finite system controllability. Our results provide a pathway for enhancing force sensing in a variety of continuous quantum systems, ranging from massive systems like mechanical oscillators to massless systems such as quantum light and microwave resonators.
Abstract One of the hallmarks of quantum physics is the generation of non-classical quantum states and superpositions, which has been demonstrated in several quantum systems, including ions, solid-state qubits and photons. However, only indirect demonstrations of non-classical states have been achieved in mechanical systems, despite the scientific appeal and technical utility of such a capability1, 2, including in quantum sensing, computation and communication applications. This is due in part to the highly linear response of most mechanical systems, which makes quantum operations difficult, as well as their characteristically low frequencies, which hinder access to the quantum ground state3–7. Here we demonstrate full quantum control of the mechanical state of a macroscale mechanical resonator. We strongly couple a surface acoustic-wave8 resonator to a superconducting qubit, using the qubit to control and measure quantum states in the mechanical resonator. We generate a non-classical superposition of the zero- and one-phonon Fock states and map this and other states using Wigner tomography9–14. Such precise, programmable quantum control is essential to a range of applications of surface acoustic waves in the quantum limit, including the coupling of disparate quantum systems15, 16.
High-frequency mechanical oscillators with long coherence times are essential to realizing a variety of high-fidelity quantum sensors, transducers, and memories. However, the unprecedented coherence times needed for quantum applications require exquisitely sensitive new techniques to probe the material origins of phonon decoherence and new strategies to mitigate decoherence in mechanical oscillators. Here, we combine non-invasive laser spectroscopy techniques with materials analysis to identify key sources of phonon decoherence in crystalline media. Using micro-fabricated high-overtone bulk acoustic-wave resonators (μHBARs) as an experimental testbed, we identify phonon-surface interactions as the dominant source of phonon decoherence in crystalline quartz; lattice distortion, subsurface damage, and high concentration of elemental impurities near the crystal surface are identified as the likely causes. Removal of this compromised surface layer using an optimized polishing process is seen to greatly enhance coherence times, enabling μHBARs with Q-factors of > 240 million at 12 GHz frequencies, corresponding to > 6 ms phonon coherence times and record-level f-Q products. Complementary phonon linewidth and time-domain ringdown measurements, performed using a new Brillouin-based pump-probe spectroscopy technique, reveal negligible dephasing within these oscillators. Building on these results, we identify a path to > 100 ms coherence times as the basis for high-frequency quantum memories. These findings clearly demonstrate that, with enhanced control over surfaces, dissipation and noise can be significantly reduced in a wide range of quantum systems.
Abstract Recent advances in quantum sensing—optical clocks at 5.5 × 10 − 19 systematic uncertainty, frequency-dependent squeezing below the standard quantum limit, quantum magnetometers approaching fundamental sensitivity limits—raise a natural question: can these technologies detect gravitational waves directly, or enhance existing detectors beyond current capabilities? We show that the answer is primarily determined by the coupling mechanism between the gravitational wave and the sensor. Starting from the tidal Hamiltonian in Fermi normal coordinates, we identify three physically distinct mechanisms by which a gravitational wave couples directly to a quantum system, and derive their transducer gains within linearized general relativity and non-relativistic quantum mechanics. Internal atomic coupling (tidal distortion of electronic wavefunctions) yields a transducer gain G A = 2.4 × 10 − 20 , with vanishing first-order energy shifts for all J = 0 clock states—a ∼ 10 35 deficit relative to laser interferometry that exceeds any projected quantum enhancement. Center-of-mass coupling (Doppler shifts from geodesic motion) reaches strain sensitivities of ∼ 10 − 18 , still 10 4 above LISA requirements. Light propagation coupling (phase accumulation over macroscopic baselines) provides the enormous transducer gain that makes laser interferometry—and atom interferometry—viable. For detectors exploiting this third mechanism, we quantify how much improvement quantum sensors can provide through the detector’s noise architecture: LISA’s noise budget is predominantly classical, limiting combined quantum enhancement to E ≈ 1.04 , while ground-based detectors in the shot-noise-dominated regime achieve E = 1.6 – 2.1 . Atom interferometers exploit the same light-propagation mechanism to target the 0.01–10 Hz band between the LISA and LIGO ranges.