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arXiv:2605.28289 · Quantum Science and Technology

Mechanical Squeezed-Fock Gravimeter

Rozhin Yousefjani, Saif Al-Kuwari

quant-phSubmitted May 27, 2026• Announced May 28, 2026• 0 citations• Revised Jul 30, 2026 (v2)
v1 · May 27, 2026v2 · Jul 30, 2026
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Abstract

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.

Journal reference
Quantum Science and Technology,2026
DOI
10.1088/2058-9565/ae9186
Comments
Comments are welcome!

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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.
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 $0.1~ \text{\textmu}\text{Gal}/\sqrt{\text{Hz}}$ can be achieved, which outperforms the traditional schemes by two orders of magnitude. Reaching the \textit{double standard quantum limits} with mmm and NNN simultaneously, our scheme provides a feasible route toward compact high-sensitivity quantum gravimetry.
Mechanical qubits offer unique advantages over other qubit platforms, primarily in terms of coherence time and possibilities for enhanced sensing applications, but their potential is constrained by the inherently weak nonlinearities and small anharmonicity of nanomechanical resonators. We propose overcoming this shortcoming by using squeezed-Fock states of phonons in a parametrically driven nonlinear mechanical oscillator. We find that, under two-phonon driving, squeezed-Fock states become eigenstates of a Kerr-nonlinear mechanical oscillator, featuring an energy spectrum with exponentially enhanced and tunable anharmonicity, such that the transitions to higher energy states are exponentially suppressed. This enables us to encode the mechanical qubit within the ground and first excited squeezed-Fock states of the driven mechanical oscillator. This kind of mechanical qubit is termed mechanical squeezed-Fock qubit. We also show that our mechanical qubit can serve as a quantum sensor for weak forces, with its resulting sensitivity increased by at least one order of magnitude over that of traditional mechanical qubits. The proposed mechanical squeezed-Fock qubit provides a powerful quantum phonon platform for quantum sensing and information processing.
Ultra-precise measurements of various parameters such as the mass of nano-particles, magnetic fields or gravity can be attained by probing the phononic modes of a micro-mechanical oscillator with light. The sensitivity of such measurements is in part governed by the noise of the phononic mode as well as the noise of the probing light mode, so by decreasing the noise of the probe beam an enhanced sensitivity can be expected. We demonstrate this effect by using squeezed states of light where the quantum uncertainty of the relevant quadrature is reduced below the shot noise level. Using this squeezing-enhanced sensitivity effect, we demonstrate 1) improved feedback cooling of a phononic mode in a microtoroidal cavity and 2) improved sensing of a magnetic field using the coupling to a microtoroidal phononic mode via a magnetorestrictive material. We present our recent experimental results and discuss future directions.
Mechanical oscillators based on levitated particles are a promising experimental platform for testing fundamental physics and detecting weak forces [1]. Quantum experiments with such systems require a low damping rate and quantum control of their motion. Here we demonstrate a levitated mechanical oscillator with an ultra-low damping rate and, as a result, an ultra-high quality factor [2]. Moreover, we introduce a qubit into the system. Coupling qubits to such oscillators could allow quantum control of their motion, similar to the control that has been achieved with systems based on solid-state oscillators [3].
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.
Mechanical degrees of freedom are natural candidates for continuous-variable quantum information processing and bosonic quantum simulations. These applications, however, require the engineering of squeezing and nonlinearities in the quantum regime. Here we demonstrate ground state squeezing of a gigahertz-frequency mechanical resonator coupled to a superconducting qubit. This is achieved by parametrically driving the qubit, which results in an effective two-phonon drive. In addition, we show that the resonator mode inherits a nonlinearity from the off-resonant coupling with the qubit, which can be tuned by controlling the detuning. We thus realize a mechanical squeezed Kerr oscillator, where we demonstrate the preparation of non-Gaussian quantum states of motion with Wigner function negativities and high quantum Fisher information. This shows that our results also have applications in quantum metrology and sensing.