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arXiv:2604.14950

Quantum gravimetry with mechanical qubits

Xiao-Wen Huo, Jun-Hong An, Peng-Bo Li

quant-phSubmitted Apr 16, 2026• Announced Apr 17, 2026• 0 citations
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Abstract

Levitated mesoscopic particles hold the promise of revolutionizing gravity sensing by using quantum effects. However, conventional quantum gravimeters based on such systems fail to harness the intrinsic large-mass advantage of the particles, because their commonly utilized auxiliary quantum systems counteract the role of mass as a resource. To overcome this limitation, we propose a quantum gravimetry by directly using the mechanical qubit (QM) formed by a levitated particle as the gravity sensor. Without resorting to the auxiliary quantum system, our scheme enables a straightforward readout of the particle's motion under gravitational influence. The obtained sensitivity behaves as a $m^{-1/2}$-scaling with the mass $m$. We also generalize our scheme to the \textit{mechanical cat qubit} as the gravity sensor. The sensitivity further scales as $N^{-1/2}$ with the mean phonon number $N$. In the experimentally realizable parameter regime, a sensitivity on the order of $0.1~ \text{\textmu}\text{Gal}/\sqrt{\text{Hz}}$ can be achieved, which outperforms the traditional schemes by two orders of magnitude. Reaching the \textit{double standard quantum limits} with $m$ and $N$ simultaneously, our scheme provides a feasible route toward compact high-sensitivity quantum gravimetry.

Comments
7+12 pages,4+6 figures

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Levitated mesoscopic particles hold the promise of revolutionizing gravity sensing by using quantum effects. However, conventional quantum gravimeters based on such systems fail to harness the intrinsic large-mass advantage of the particles, because their commonly utilized auxiliary quantum systems counteract the role of mass as a resource. To overcome this limitation, we propose a quantum gravimetry by directly using the mechanical qubit (QM) formed by a levitated particle as the gravity sensor. Without resorting to the auxiliary quantum system, our scheme enables a straightforward readout of the particle's motion under gravitational influence. The obtained sensitivity behaves as a m−1/2m^{-1/2}m−1/2-scaling with the mass mmm. We also generalize our scheme to the \textit{mechanical cat qubit} as the gravity sensor. The sensitivity further scales as N−1/2N^{-1/2}N−1/2 with the mean phonon number NNN. In the experimentally realizable parameter regime, a sensitivity on the order of 0.1 \textmuGal/Hz0.1~ \text{\textmu}\text{Gal}/\sqrt{\text{Hz}}0.1 \textmuGal/Hz​ can be achieved, which outperforms the traditional schemes by two orders of magnitude. Reaching the \textit{double standard quantum limits} with mmm and NNN simultaneously, our scheme provides a feasible route toward compact high-sensitivity quantum gravimetry.
Levitated mechanical systems are promising candidates for quantum gravimetry, as gravity couples directly to their center-of-mass motion, enabling the large mass of a mesoscopic particle to serve as a sensing resource. In this paper, we propose a mechanical squeezed-Fock qubit gravimeter using a Duffing oscillator that is driven by a detuned two-phonon pump. In the squeezed-Fock basis, the gravitational force couples to the anti-squeezed quadrature, which enhances the gravity-induced transition rate while preserving the direct mass scaling of the mechanical force coupling. We show that sensitivity improves with reduced effective qubit splitting that is controlled by the squeezing parameter and the Duffing nonlinearity. We further analyze mechanical damping and show that squeezing converts ordinary dissipation into anisotropic qubit noise, setting a practical trade-off between signal amplification and decoherence rate. These results identify the mechanical squeezed-Fock qubit as a new platform for quantum-enhanced gravimetry.
Precision measurements of gravitational acceleration, or gravimetry, enable the testing of physical theories and find numerous applications in geodesy and space exploration. By harnessing quantum effects, high-precision sensors can achieve sensitivity and accuracy far beyond their classical counterparts when using the same number of sensing resources. Therefore, developing gravimeters with quantum-enhanced sensitivity is essential for advancing theoretical and applied physics. While novel quantum gravimeters have already been proposed for this purpose, the ultimate sensing precision, known as the Heisenberg limit, remains largely elusive. Here, we demonstrate that the gravimetry precision of a conditional displacement spin-mechanical system increases quadratically with the number of spins: a Heisenberg-limited spin-mechanical gravimeter. In general, the gravitational parameter is dynamically encoded into the entire entangled spin-mechanical probe. However, at some specific times, the mechanical degree of freedom disentangles from the spin subsystem, transferring all the information about the gravitational acceleration to the spin subsystem. Hence, we prove that a feasible spin magnetization measurement can reveal the ultimate gravimetry precision at such disentangling times. We predict an absolute gravimetry uncertainty of 10 − 11 m/s 2 to 10 − 6 m/s 2 , without relying on free-fall methodologies, ground-state cooling of the mechanical object, and robust against spin-mechanical coupling anisotropies.
Precise gravitational measurements are vital for geophysics and inertial navigation, but compact gravimeters with high measurement bandwidth remain difficult to realize. We propose and analyze a chip-scale superconducting gravimeter in which a flux-tunable transmon qubit is coupled to a high quality factor (QmQ_mQm​) nanomechanical beam. The beam is embedded in a SQUID loop placed in parallel with the qubit's flux-tunable SQUID; gravity induced beam displacement therefore modulates the qubit frequency through the SQUID flux and is mapped onto the qubit's geometric phase. A stroboscopic readout at mechanical revival times suppresses qubit mechanics dephasing, yielding a projected sensitivity of 10210^2102--103 nGal/Hz10^3\,\mathrm{nGal}/\sqrt{\mathrm{Hz}}103nGal/Hz​ with sub-millisecond interrogation times. Electrical \emph{in situ} tunability and microwave-based calibration make this architecture a practical route toward compact, high-bandwidth on-chip gravimetry.
The ground-state cooling and quantum control of levitated nanoparticles have become attainable, which makes the enhanced quantum sensing based on the large mass advantage of mesoscopic quantum systems accessible. Here, we propose an enhanced gravity-sensing protocol for a nanodiamond levitated in a linear ion trap, which improves the sensing sensitivity and further reduces device size. By introducing gravitational acceleration into the vibrational state through transient free fall, we achieve a square-accelerated relative phase accumulation, yielding higher sensitivity than the linear accumulation process. The sensitivity reaches the standard quantum limit for a nanodiamond containing multiple nitrogen-vacancy (N-V) centers. Besides, by using phonon-mediated one-axis twisting dynamics induced by magnetic field gradient to squeeze the initial spin state, the sensitivity can further surpass the standard quantum limit as a scaling law of N^{-5/6}. To fully assess the protocol performance, we further analyze the effects of decoherence and control errors, which are negligible under experimentally achievable conditions. Specifically, the sensitivity reaches ∼18 μGal/sqrt[Hz] for the nanodiamond containing only one N-V center over a free-fall distance of ∼20 μm, while exceeds 0.4 μGal/sqrt[Hz] for 100 N-V centers. Our results will further facilitate research on compact and high-sensitivity gravimeters.
Due to their exceptional isolation from the environment, magnetically levitated particles are explored as extremely sensitive mechanical sensors. For future gravity experiments on quantum superpositions, such systems need to be cooled close to their ground state. To demonstrate the combination of state of the art vibration isolation, milligram levitated high Q mechanical resonators and position detection with low noise, we present linear feedback cooling of a magnetically levitated gravity sensor to below 2 picometer amplitude and below 10 millikelvin mode temperature for two translational modes (the x- and y-mode) simultaneously. The sensor is a levitating permanent magnet in a type I superconducting trap, where its six resonance frequencies are measured with a superconducting coil coupled to a DC SQUID. This signal is measured with a lock-in amplifier and a feedback signal is sent to a piezoelectric actuator, allowing the cooling of resonant modes at 50.6 and 68.0 Hz simultaneously. These two translational modes have Q factors of 3.8⋅1063.8 \cdot 10^63.8⋅106 and 5.5⋅1065.5 \cdot 10^65.5⋅106 respectively. The experiment is mounted inside a dry dilution refrigerator where it is vibrationally attenuated with 110-130 dB at these frequencies. In this work, we discuss future improvements on the setup which may enable quantum ground state cooling on a magnetically levitated particle, that has previously been shown to be a gravitational sensor.
High-sensitivity accelerometers and gravimeters, achieving the ultimate limits of measurement sensitivity are key tools for advancing both fundamental and applied physics. While numerous platforms have been proposed to achieve this goal, from atom interferometers to optomechanical systems, all of these studies neglect the effects of intrinsic quantum uncertainty in time estimation. Starting from the Hamiltonian of a generic linear quantum sensor, we derive the two-parameter quantum Fisher information matrix and establish the corresponding Cram'er-Rao bound, treating time as an uncertain (nuisance) parameter. Our analysis reveals a fundamental coupling between time and signal estimation that inherently degrades measurement sensitivity, with the standard single-parameter quantum limit recovered only at specific interrogation times or under special decoupling conditions. We then apply these results to an optomechanical gravimeter and explicitly derive an optimal decoupling condition under which the effects of time uncertainty are averaged out in a continuous measurement scheme. Our approach is general and can be readily extended to a broad class of quantum sensors.