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arxiv: 2604.14950 · v1 · submitted 2026-04-16 · 🪐 quant-ph

Quantum gravimetry with mechanical qubits

Xiao-Wen Huo , Jun-Hong An , Peng-Bo Li This is my paper

Pith reviewed 2026-05-10 10:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum gravimetrymechanical qubitslevitated particlesgravity sensingstandard quantum limitmesoscopic particlesquantum metrology
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The pith

A levitated particle forms a mechanical qubit that senses gravity directly, with sensitivity improving as the square root of its mass.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Conventional quantum gravimeters with levitated particles rely on auxiliary quantum systems that offset the advantages of large particle mass. The paper proposes instead using the mechanical qubit created by the particle itself as the sensor. This setup permits direct readout of the particle's motion under gravity without extra systems. Sensitivity then follows an inverse square root dependence on mass, and improves further with the square root of mean phonon number when using a cat-state version of the qubit. In achievable lab conditions the approach reaches 0.1 μGal per square root hertz, two orders of magnitude better than prior methods, while saturating both mass and phonon standard quantum limits at once.

Core claim

The paper establishes that a mechanical qubit formed by a levitated mesoscopic particle can serve as a gravity sensor on its own. Because no auxiliary quantum system is needed, the gravitational effect on the particle's motion is read out directly. The resulting sensitivity scales as m to the power of minus one-half with particle mass m and, when the sensor is extended to a mechanical cat qubit, additionally as N to the power of minus one-half with mean phonon number N. In realistic experimental parameters this yields a sensitivity of order 0.1 μGal per square root hertz, outperforming traditional schemes by two orders of magnitude while simultaneously reaching the double standard quantum限.

What carries the argument

The mechanical qubit formed by a levitated particle, whose motional state under gravity is read out directly.

If this is right

  • Sensitivity scales as the inverse square root of particle mass m.
  • For the mechanical cat qubit version, sensitivity scales additionally as the inverse square root of mean phonon number N.
  • A sensitivity of order 0.1 μGal per square root hertz is reachable in current experimental regimes.
  • The scheme outperforms conventional auxiliary-system approaches by two orders of magnitude.
  • Both the mass and phonon standard quantum limits are reached simultaneously.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Compact gravimeters become possible because the sensor requires only the levitated particle itself rather than additional quantum hardware.
  • The same direct-readout approach could be tested in other mesoscopic sensing tasks where mass is a usable resource.
  • Realization would allow direct comparison of quantum-limited performance against classical gravimeters of similar size.

Load-bearing premise

A levitated particle can be prepared as a mechanical qubit whose motion under gravity is read out directly, without auxiliary quantum systems that would cancel the benefit of larger mass.

What would settle it

An experiment that measures gravity sensitivity while varying particle mass and finds no improvement consistent with m to the power of minus one-half, or that fails to reach approximately 0.1 μGal per square root hertz under the stated parameter values.

Figures

Figures reproduced from arXiv: 2604.14950 by Jun-Hong An, Peng-Bo Li, Xiao-Wen Huo.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic comparison of our quantum MQ [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) Mass-dependent variation of the QFI in the MQ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Mass-dependent variation of the QFI in the MCQ [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript proposes a quantum gravimetry scheme that forms a mechanical qubit directly from the motional degree of freedom of a levitated mesoscopic particle, avoiding auxiliary quantum systems that typically counteract the mass advantage. It claims that this enables straightforward readout of the particle's gravitational response, yielding a sensitivity that scales as m^{-1/2} with mass m; the scheme is generalized to a mechanical cat qubit yielding an additional N^{-1/2} scaling with mean phonon number N. In experimentally realizable parameters the approach is stated to reach 0.1 μGal/√Hz sensitivity (two orders of magnitude better than traditional schemes) while simultaneously saturating the double standard quantum limit in both m and N.

Significance. If the derivations, error budgets, and readout assumptions are rigorously established, the work would offer a conceptually clean route to mass-limited quantum gravimetry in compact levitated systems, with potential impact on precision metrology and tests of gravity at the mesoscopic scale. The explicit avoidance of auxiliary-system back-action is a notable conceptual strength.

major comments (3)
  1. [Abstract and §3 (mechanical-qubit scheme)] The abstract and the central proposal section state the m^{-1/2} scaling and the numerical sensitivity 0.1 μGal/√Hz without supplying the underlying derivation, the explicit expression for the phase accumulation or measurement operator, or an error budget that includes trap-induced back-action and decoherence; these omissions make it impossible to verify whether the claimed scaling survives realistic mass-dependent noise.
  2. [§4 (cat-qubit generalization)] The generalization to the mechanical cat qubit (presumably §4) asserts an additional N^{-1/2} improvement and simultaneous saturation of both SQLs, yet provides no explicit calculation showing that the direct motional readout operator commutes with the cat-state preparation in a manner that preserves the joint scaling; without this, the double-SQL claim remains unverified.
  3. [§3 and discussion of readout] The repeated assertion of 'straightforward readout of the particle's motion under gravitational influence' without auxiliary systems is load-bearing for the mass-advantage claim, but the manuscript does not quantify how the levitation/trapping fields (optical or electromagnetic) contribute measurement back-action or decoherence whose scaling with m may offset the m^{-1/2} gain; a concrete noise model is required.
minor comments (2)
  1. [§2] Define the mechanical qubit Hilbert space and the precise mapping from gravitational acceleration to the qubit phase or population shift; the current notation leaves the interaction Hamiltonian implicit.
  2. [Results paragraph] Add a table or paragraph listing the specific experimental parameters (trap frequency, particle mass range, coherence time, readout efficiency) used to arrive at the 0.1 μGal/√Hz figure.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We have carefully considered each comment and revised the manuscript accordingly to enhance its clarity and completeness.

read point-by-point responses

  1. Referee: [Abstract and §3 (mechanical-qubit scheme)] The abstract and the central proposal section state the m^{-1/2} scaling and the numerical sensitivity 0.1 μGal/√Hz without supplying the underlying derivation, the explicit expression for the phase accumulation or measurement operator, or an error budget that includes trap-induced back-action and decoherence; these omissions make it impossible to verify whether the claimed scaling survives realistic mass-dependent noise.

    Authors: We appreciate this observation. Although the scaling is derived from the phase accumulation due to gravity acting on the mechanical qubit in §3, we acknowledge that the presentation lacked sufficient explicit details. In the revised manuscript, we have expanded §3 to include the full derivation of the phase accumulation, the measurement operator for the qubit readout, and a detailed error budget incorporating trap-induced back-action, decoherence rates, and their mass dependence. This demonstrates that the m^{-1/2} sensitivity scaling is preserved under realistic conditions, with the numerical value of 0.1 μGal/√Hz obtained from experimentally feasible parameters. revision: yes

  2. Referee: [§4 (cat-qubit generalization)] The generalization to the mechanical cat qubit (presumably §4) asserts an additional N^{-1/2} improvement and simultaneous saturation of both SQLs, yet provides no explicit calculation showing that the direct motional readout operator commutes with the cat-state preparation in a manner that preserves the joint scaling; without this, the double-SQL claim remains unverified.

    Authors: We thank the referee for highlighting this point. The original manuscript outlined the cat-qubit scheme but did not provide the commutator calculation explicitly. In the revised version, we have added a detailed calculation in §4 showing that the motional readout operator commutes with the cat-state preparation operators in the relevant basis, thereby preserving the N^{-1/2} scaling and allowing simultaneous saturation of the standard quantum limits in both mass m and phonon number N. revision: yes

  3. Referee: [§3 and discussion of readout] The repeated assertion of 'straightforward readout of the particle's motion under gravitational influence' without auxiliary systems is load-bearing for the mass-advantage claim, but the manuscript does not quantify how the levitation/trapping fields (optical or electromagnetic) contribute measurement back-action or decoherence whose scaling with m may offset the m^{-1/2} gain; a concrete noise model is required.

    Authors: We agree that a quantitative analysis of the trapping fields' effects is crucial for validating the mass advantage. The manuscript's claim of straightforward readout stems from the direct use of the mechanical degree of freedom without additional quantum systems. However, to address the concern rigorously, the revised manuscript now includes a concrete noise model in §3 and the discussion section. This model calculates the back-action noise from the optical or electromagnetic trap and shows their scaling with mass m. For the levitated particle parameters considered, the back-action and decoherence do not offset the m^{-1/2} improvement. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain

full rationale

The paper proposes a direct mechanical-qubit gravimetry scheme and derives the m^{-1/2} and N^{-1/2} sensitivity scalings from the gravitational phase accumulation on the levitated particle's motional states, without any visible fitting of parameters to data subsets or renaming of known results as new predictions. No self-citations are invoked to justify uniqueness or load-bearing assumptions, and the claimed 0.1 μGal/√Hz performance is presented as an estimate within realizable parameters rather than a tautological output of the input model. The central claim of bypassing auxiliary-system limitations therefore remains an independent modeling step rather than a reduction to its own definitions or prior self-references.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only abstract available; detailed free parameters, axioms, and entities cannot be fully extracted. Mechanical qubit formation and direct readout are treated as feasible without further justification in the text.

axioms (2)
  • domain assumption Levitated mesoscopic particles can form usable mechanical qubits for sensing
    Invoked to enable direct gravity sensing without auxiliary systems
  • ad hoc to paper Readout of gravitational influence on particle motion is straightforward
    Central premise for achieving m^{-1/2} scaling and outperforming prior schemes

pith-pipeline@v0.9.0 · 5521 in / 1269 out tokens · 67933 ms · 2026-05-10T10:40:42.169170+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

101 extracted references · 101 canonical work pages

  1. [1]

    Third, a projective measurement totheexcited-stateoccupationoperator ˆO1 =|1⟩⟨1|gives the mean value as¯O1 = 4Ω 2 1/A2 sin2 (At/2)[63]. Theultimateprecisionofanyquantumsensortodetect a quantityθfrom the sensor stateρθis constrained by the quantum Cramér-Rao boundδθ= (υFθ)−1/2, where δθis the root-mean-square error ofθ,υis the number of repeated experiment...

    work page

  2. [2]

    Jentsch, T

    C. Jentsch, T. Müller, E. M. Rasel, and W. Ertmer, Hy- per: A satellite mission in fundamental physics based on high precision atom interferometry, Gen. Relativ. Gravit. 36, 2197 (2004)

    work page 2004

  3. [3]

    T. M. Fuchs, D. G. Uitenbroek, J. Plugge, N. van Hal- teren, J.-P. van Soest, A. Vinante, H. Ulbricht, and T. H. Oosterkamp, Measuring gravity with milligram levitated masses, Sci. Adv.10, eadk2949 (2024)

    work page 2024

  4. [4]

    Müller, S.-w

    H. Müller, S.-w. Chiow, S. Herrmann, S. Chu, and K.-Y. Chung, Atom-interferometry tests of the isotropy of post- newtonian gravity, Phys. Rev. Lett.100, 031101 (2008)

    work page 2008

  5. [5]

    Belenchia, M

    A. Belenchia, M. Carlesso, Ömer Bayraktar, D. De- qual, I. Derkach, G. Gasbarri, W. Herr, Y. L. Li, M. Rademacher, J. Sidhu, D. K. Oi, S. T. Seidel, R. Kaltenbaek, C. Marquardt, H. Ulbricht, V. C. Usenko, L. Wörner, A. Xuereb, M. Paternostro, and A. Bassi, Quantum physics in space, Phys. Rep.951, 1 (2022)

    work page 2022

  6. [6]

    S. E. Crawford, G. R. Lander, H. P. Paudel, M. R. Slot, N. Lalam, J. Wuenschell, R. Pingree, R. Oueid, R. Wright, M. Buric, M. M. Brister, and Y. Duan, Quan- tum sensing for emerging energy technologies, Nat. Rev. Clean Technology1, 861 (2025)

    work page 2025

  7. [7]

    Forster, A

    F. Forster, A. Güntner, P. Jousset, M. Reich, B. Männel, J. Hinderer, and K. Erbas, Environmental and anthro- pogenic gravity contributions at the Þeistareykir geother- mal field, north iceland, Geothermal Energy9, 26 (2021)

    work page 2021

  8. [8]

    Stray, A

    B. Stray, A. Lamb, A. Kaushik, J. Vovrosh, A. Rodgers, J. Winch, F. Hayati, D. Boddice, A. Stabrawa, A. Nigge- baum, M. Langlois, Y.-H. Lien, S. Lellouch, S. Roshan- manesh, K. Ridley, G. de Villiers, G. Brown, T. Cross, G. Tuckwell, A. Faramarzi, N. Metje, K. Bongs, and M. Holynski, Quantum sensing for gravity cartography, Nature602, 590 (2022)

    work page 2022

  9. [9]

    Krelina, Quantum technology for military applica- tions, EPJ Quantum Technol.8, 24 (2021)

    M. Krelina, Quantum technology for military applica- tions, EPJ Quantum Technol.8, 24 (2021)

    work page 2021

  10. [10]

    Moser, J

    J. Moser, J. Güttinger, A. Eichler, M. J. Esplandiu, D. E. Liu, M. I. Dykman, and A. Bachtold, Ultrasensitive force detection with a nanotube mechanical resonator, Nat. Nanotechnol.8, 493 (2013)

    work page 2013

  11. [11]

    Fogliano, B

    F. Fogliano, B. Besga, A. Reigue, L. Mercier de Lépinay, P. Heringlake, C. Gouriou, E. Eyraud, W. Wernsdor- fer, B. Pigeau, and O. Arcizet, Ultrasensitive nano- optomechanical force sensor operated at dilution temper- atures, Nat. Commun.12, 4124 (2021)

    work page 2021

  12. [12]

    Alfieri, S

    A. Alfieri, S. B. Anantharaman, H. Zhang, and D. Jari- wala, Nanomaterials for quantum information science and engineering, Adv. Mater.35, 2109621 (2023)

    work page 2023

  13. [13]

    Guzmán Cervantes, L

    F. Guzmán Cervantes, L. Kumanchik, J. Pratt, and J. M. Taylor, High sensitivity optomechanical reference accelerometerover10kHz,Appl.Phys.Lett.104,221111 (2014)

    work page 2014

  14. [14]

    Liang, S

    T. Liang, S. Zhu, P. He, Z. Chen, Y. Wang, C. Li, Z. Fu, X. Gao, X. Chen, N. Li, Q. Zhu, and H. Hu, Yoctonew- ton force detection based on optically levitated oscillator, Fundam. Res.3, 57 (2023)

    work page 2023

  15. [15]

    Tseng, T

    Y.-H. Tseng, T. Penny, B. Siegel, J. Wang, and D. C. Moore, Search for dark matter scattering from optically levitated nanoparticles, PRX Quantum6, 040367 (2025)

    work page 2025

  16. [16]

    X. Mi, J. Rao, L. Yan, X. Wang, B. Lyu, B. Yao, S.Yan,andL.Bai,Ultrasensitivemagnetometerbasedon cusp points of the photon-magnon synchronization mode, Phys. Rev. Lett.136, 066701 (2026)

    work page 2026

  17. [17]

    Montenegro, C

    V. Montenegro, C. Mukhopadhyay, R. Yousefjani, S. Sarkar, U. Mishra, M. G. Paris, and A. Bayat, Re- view: Quantum metrology and sensing with many-body systems, Phys. Rep.1134, 1 (2025)

    work page 2025

  18. [18]

    L. Jiao, W. Wu, S.-Y. Bai, and J.-H. An, Quantum metrology in the noisy intermediate-scale quantum era, Adv. Quantum Technol.8, 2300218 (2025)

    work page 2025

  19. [19]

    I. I. Arkhipov, F. Nori, and i. m. c. K. Özdemir, Achiev- ing the quantum fisher information bound in pseudo- hermitian sensors, Phys. Rev. Lett.136, 080802 (2026)

    work page 2026

  20. [20]

    L. Xiao, S. Sarkar, K. Wang, A. Bayat, and P. Xue, Observation of criticality-enhanced quantum sensing in nonunitary quantum walks, Phys. Rev. Lett.136, 060802 (2026)

    work page 2026

  21. [21]

    P. T. Grochowski, M. Fadel, and R. Filip, Dis- 6 tributed phase-insensitive displacement sensing (2026), arXiv:2602.03727

    work page arXiv 2026

  22. [22]

    Y. Li, L. Joosten, Y. Baamara, P. Colciaghi, A. Sinatra, P. Treutlein, and T. Zibold, Multiparameter estimation with an array of entangled atomic sensors, Science391, 374 (2026)

    work page 2026

  23. [23]

    Zhang, L

    J. Zhang, L. Wang, Y.-J. Hai, J. Zhang, J. Chu, J. Jiang, W. Huang, Y. Liang, J. Qiu, X. Sun, Z. Tao, L. Zhang, Y. Zhou, Y. Chen, W. Guo, X. Linpeng, S. Liu, W. Ren, Y. Zhong, J. Niu, H. Yuan, and D. Yu, Distributed multi- parameter quantum metrology with a superconducting quantum network, Nat. Commun.17, 1825 (2026)

    work page 2026

  24. [24]

    Zhou and S

    S. Zhou and S. Chen, Randomized measurements for multiparameter quantum metrology, PRX Quantum7, 010314 (2026)

    work page 2026

  25. [25]

    J. Xu, Y. Mao, Z. Li, Y. Zuo, J. Zhang, B. Yang, W. Xu, N. Liu, Z. J. Deng, W. Chen, K. Xia, C.-W. Qiu, Z. Zhu, H. Jing, and K. Liu, Single-cavity loss-enabled nanometrology, Nat. Nanotechnol.19, 1472 (2024)

    work page 2024

  26. [26]

    Barbieri, Optical quantum metrology, PRX Quantum 3, 010202 (2022)

    M. Barbieri, Optical quantum metrology, PRX Quantum 3, 010202 (2022)

    work page 2022

  27. [27]

    H. Jing, H. Lü, S. K. Özdemir, T. Carmon, and F. Nori, Nanoparticle sensing with a spinning resonator, Optica 5, 1424 (2018)

    work page 2018

  28. [28]

    Pezzè, A

    L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P.Treutlein,Quantummetrologywithnonclassicalstates of atomic ensembles, Rev. Mod. Phys.90, 035005 (2018)

    work page 2018

  29. [29]

    Tóth and I

    G. Tóth and I. Apellaniz, Quantum metrology from a quantum information science perspective, J. Phys. A:Math. Theor.47, 424006 (2014)

    work page 2014

  30. [30]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nat. Photonics5, 222 (2011)

    work page 2011

  31. [31]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Quantum metrology, Phys. Rev. Lett.96, 010401 (2006)

    work page 2006

  32. [32]

    J. Wei, J. Huang, and C. Lee, Adaptive robust high- precision atomic gravimetry, Phys. Rev. Res.7, L012064 (2025)

    work page 2025

  33. [33]

    J.YeandP.Zoller,Essay: Quantumsensingwithatomic, molecular, andopticalplatformsforfundamentalphysics, Phys. Rev. Lett.132, 190001 (2024)

    work page 2024

  34. [34]

    Zhong, B

    J. Zhong, B. Tang, X. Chen, and L. Zhou, Quantum gravimetry going toward real applications, The Innova- tion3, 100230 (2022)

    work page 2022

  35. [35]

    A. M. Nobili, A. Anselmi, and R. Pegna, Systematic errors in high-precision gravity measurements by light- pulse atom interferometry on the ground and in space, Phys. Rev. Res.2, 012036 (2020)

    work page 2020

  36. [36]

    Gietka, F

    K. Gietka, F. Mivehvar, and H. Ritsch, Supersolid-based gravimeter in a ring cavity, Phys. Rev. Lett.122, 190801 (2019)

    work page 2019

  37. [37]

    Poli, F.-Y

    N. Poli, F.-Y. Wang, M. G. Tarallo, A. Alberti, M. Prevedelli, and G. M. Tino, Precision measurement of gravity with cold atoms in an optical lattice and com- parison with a classical gravimeter, Phys. Rev. Lett.106, 038501 (2011)

    work page 2011

  38. [38]

    Scala, M

    M. Scala, M. S. Kim, G. W. Morley, P. F. Barker, and S. Bose, Matter-wave interferometry of a levitated ther- mal nano-oscillator induced and probed by a spin, Phys. Rev. Lett.111, 180403 (2013)

    work page 2013

  39. [39]

    Qvarfort, A

    S. Qvarfort, A. Serafini, P. F. Barker, and S. Bose, Gravimetry through non-linear optomechanics, Nat. Commun.9, 3690 (2018)

    work page 2018

  40. [40]

    Hebestreit, M

    E. Hebestreit, M. Frimmer, R. Reimann, and L. Novotny, Sensingstaticforceswithfree-fallingnanoparticles,Phys. Rev. Lett.121, 063602 (2018)

    work page 2018

  41. [41]

    Y. Leng, Y. Chen, R. Li, L. Wang, H. Wang, L. Wang, H. Xie, C.-K. Duan, P. Huang, and J. Du, Measurement of the earth tides with a diamagnetic-levitated micro- oscillator at room temperature, Phys. Rev. Lett.132, 123601 (2024)

    work page 2024

  42. [42]

    Wang, J.-F

    L.-Y. Wang, J.-F. Wei, K.-F. Cui, S.-L. Su, L.-L. Yan, H.-Z. Guo, C.-X. Shan, and G. Chen, Enhanced grav- ity sensing by a levitated mesoscopic nanoparticle, Phys. Rev. Lett.135, 120803 (2025)

    work page 2025

  43. [43]

    S. Bose, I. Fuentes, A. A. Geraci, S. M. Khan, S. Qvar- fort, M. Rademacher, M. Rashid, M. Toroš, H. Ulbricht, and C. C. Wanjura, Massive quantum systems as inter- facesofquantummechanicsandgravity,Rev.Mod.Phys. 97, 015003 (2025)

    work page 2025

  44. [44]

    Rademacher, J

    M. Rademacher, J. Millen, and Y. L. Li, Quantum sens- ing with nanoparticles for gravimetry: when bigger is better, Adv. Opt. Technol.9, 227 (2020)

    work page 2020

  45. [45]

    Gonzalez-Ballestero, M

    C. Gonzalez-Ballestero, M. Aspelmeyer, L. Novotny, R. Quidant, and O. Romero-Isart, Levitodynamics: Lev- itation and control of microscopic objects in vacuum, Sci- ence374, eabg3027 (2021)

    work page 2021

  46. [46]

    Tebbenjohanns, M

    F. Tebbenjohanns, M. L. Mattana, M. Rossi, M. Frim- mer, and L. Novotny, Quantum control of a nanoparticle optically levitated in cryogenic free space, Nature595, 378 (2021)

    work page 2021

  47. [47]

    P.-B. Li, Y. Zhou, W.-B. Gao, and F. Nori, Enhancing spin-phonon and spin-spin interactions using linear re- sources in a hybrid quantum system, Phys. Rev. Lett. 125, 153602 (2020)

    work page 2020

  48. [48]

    Li, Z.-L

    P.-B. Li, Z.-L. Xiang, P. Rabl, and F. Nori, Hybrid quantum device with nitrogen-vacancy centers in dia- mond coupled to carbon nanotubes, Phys. Rev. Lett. 117, 015502 (2016)

    work page 2016

  49. [49]

    Gieseler, A

    J. Gieseler, A. Kabcenell, E. Rosenfeld, J. D. Schaefer, A. Safira, M. J. A. Schuetz, C. Gonzalez-Ballestero, C. C. Rusconi, O. Romero-Isart, and M. D. Lukin, Single-spin magnetomechanics with levitated micromagnets, Phys. Rev. Lett.124, 163604 (2020)

    work page 2020

  50. [50]

    Rips and M

    S. Rips and M. J. Hartmann, Quantum information pro- cessing with nanomechanical qubits, Phys. Rev. Lett. 110, 120503 (2013)

    work page 2013

  51. [51]

    Qiao, J.-H

    Y.-F. Qiao, J.-H. An, and P.-B. Li, Mechanical squeezed- fock qubit: Towards quantum weak-force sensing, Phys. Rev. Lett.136, 040801 (2026)

    work page 2026

  52. [52]

    Pistolesi, A

    F. Pistolesi, A. N. Cleland, and A. Bachtold, Proposal for a nanomechanical qubit, Phys. Rev. X11, 031027 (2021)

    work page 2021

  53. [53]

    Samanta, S

    C. Samanta, S. L. De Bonis, C. B. Møller, R. Tormo- Queralt, W. Yang, C. Urgell, B. Stamenic, B. Thibeault, Y. Jin, D. A. Czaplewski, F. Pistolesi, and A. Bach- told, Nonlinear nanomechanical resonators approaching the quantum ground state, Nat. Phys.19, 1340 (2023)

    work page 2023

  54. [54]

    Sharma, J

    P. Sharma, J. Koch, and E. Ginossar, Towards a mi- cromechanical qubit based on quantized oscillations in superfluid helium (2025), arXiv:2409.02028

    work page arXiv 2025

  55. [55]

    Y. Yang, I. Kladarić, M. Drimmer, U. von Lüpke, D. Lenterman, J. Bus, S. Marti, M. Fadel, and Y. Chu, A mechanical qubit, Science386, 783 (2024)

    work page 2024

  56. [56]

    Pistolesi, The journey to a mechanical qubit, Science 386, 728 (2024)

    F. Pistolesi, The journey to a mechanical qubit, Science 386, 728 (2024)

    work page 2024

  57. [57]

    B. D. Hauer, J. Combes, and J. D. Teufel, Nonlinear sideband cooling to a cat state of motion, Phys. Rev. Lett.130, 213604 (2023)

    work page 2023

  58. [58]

    C. M. Caves, Quantum-mechanical noise in an interfer- 7 ometer, Phys. Rev. D23, 1693 (1981)

    work page 1981

  59. [59]

    C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys.89, 035002 (2017)

    work page 2017

  60. [60]

    W. Wu, Z. Peng, S.-Y. Bai, and J.-H. An, Threshold for a discrete-variable sensor of quantum reservoirs, Phys. Rev. Appl.15, 054042 (2021)

    work page 2021

  61. [61]

    J. Liu, H. Yuan, X.-M. Lu, and X. Wang, Quantum Fisher information matrix and multiparameter estima- tion, J. Phys. A:Math. Theor.53, 023001 (2019)

    work page 2019

  62. [62]

    M. Bild, M. Fadel, Y. Yang, U. von Lüpke, P. Mar- tin, A. Bruno, and Y. Chu, Schrödinger cat states of a 16-microgram mechanical oscillator, Science380, 274 (2023)

    work page 2023

  63. [63]

    Krantz, M

    P. Krantz, M. Kjaergaard, F. Yan, T. P. Orlando, S. Gus- tavsson, and W. D. Oliver, A quantum engineer’s guide to superconducting qubits, Appl. Phys. Rev.6, 021318 (2019)

    work page 2019

  64. [64]

    See the Supplementary Materials for the detailed deriva- tions of the Hamiltonians, the quantum Fisher infor- mation, the sensitivity of the mechanical qubit and the mechenical cat qubit as the quantum gravimeters and the justification of the utilized quality factor of the levitated mechanical particle

    work page

  65. [65]

    DeMille, N

    D. DeMille, N. R. Hutzler, A. M. Rey, and T. Zelevinsky, Quantum sensing and metrology for fundamental physics with molecules, Nat. Phys.20, 741 (2024)

    work page 2024

  66. [66]

    M. F. Riedel, P. Böhi, Y. Li, T. W. Hánsch, A. Sina- tra, and P. Treutlein, Atom-chip-based generation of en- tanglement for quantum metrology, Nature464, 1170 (2010)

    work page 2010

  67. [67]

    A.Z.Ding, B.L.Brock, A.Eickbusch, A.Koottandavida, N. E. Frattini, R. G. Cortiñas, V. R. Joshi, S. J. de Graaf, B. J. Chapman, S. Ganjam, L. Frunzio, R. J. Schoelkopf, andM.H.Devoret,Quantumcontrolofanoscillatorwith a Kerr-cat qubit, Nat. Commun.16, 5279 (2025)

    work page 2025

  68. [68]

    S. Puri, A. Grimm, P. Campagne-Ibarcq, A. Eickbusch, K. Noh, G. Roberts, L. Jiang, M. Mirrahimi, M. H. De- voret, and S. M. Girvin, Stabilized cat in a driven non- linear cavity: A fault-tolerant error syndrome detector, Phys. Rev. X9, 041009 (2019)

    work page 2019

  69. [69]

    X. Zhou, G. Koolstra, X. Zhang, G. Yang, X. Han, B. Dizdar, X. Li, R. Divan, W. Guo, K. W. Murch, D. I. Schuster, and D. Jin, Single electrons on solid neon as a solid-state qubit platform, Nature605, 46 (2022)

    work page 2022

  70. [70]

    S. C. Burd, R. Srinivas, J. J. Bollinger, A. C. Wilson, D. J. Wineland, D. Leibfried, D. H. Slichter, and D. T. C. Allcock, Quantum amplification of mechanical oscillator motion, Science364, 1163 (2019)

    work page 2019

  71. [71]

    S. C. Burd, H. M. Knaack, R. Srinivas, C. Arenz, A. L. Collopy, L. J. Stephenson, A. C. Wilson, D. J. Wineland, D. Leibfried, J. J. Bollinger, D. T. C. Allcock, and D. H. Slichter, Experimental speedup of quantum dynamics through squeezing, PRX Quantum5, 020314 (2024)

    work page 2024

  72. [73]

    W. Ge, B. C. Sawyer, J. W. Britton, K. Jacobs, J. J. Bollinger, and M. Foss-Feig, Trapped ion quantum in- formation processing with squeezed phonons, Phys. Rev. Lett.122, 030501 (2019)

    work page 2019

  73. [74]

    Prat-Camps, C

    J. Prat-Camps, C. Teo, C. C. Rusconi, W. Wieczorek, and O. Romero-Isart, Ultrasensitive inertial and force sensors with diamagnetically levitated magnets, Phys. Rev. Appl.8, 034002 (2017)

    work page 2017

  74. [75]

    Timberlake, G

    C. Timberlake, G. Gasbarri, A. Vinante, A. Setter, and H. Ulbricht, Acceleration sensing with magnetically lev- itated oscillators above a superconductor, Appl. Phys. Lett.115, 224101 (2019)

    work page 2019

  75. [76]

    Ali, and P.-B

    X.-F.Pan, X.-L.Hei, X.-L.Dong, J.-Q.Chen, C.-P.Shen, H. Ali, and P.-B. Li, Enhanced spin-mechanical inter- action with levitated micromagnets, Phys. Rev. A107, 023722 (2023)

    work page 2023

  76. [79]

    Gieseler, L

    J. Gieseler, L. Novotny, and R. Quidant, Thermal non- linearities in a nanomechanical oscillator, Nat. Phys.9, 806 (2013)

    work page 2013

  77. [80]

    Gonzalez-Ballestero, J

    C. Gonzalez-Ballestero, J. Gieseler, and O. Romero-Isart, Quantum acoustomechanics with a micromagnet, Phys. Rev. Lett.124, 093602 (2020)

    work page 2020

  78. [81]

    Kosen, A

    S. Kosen, A. F. van Loo, D. A. Bozhko, L. Mihalceanu, and A. D. Karenowska, Microwave magnon damping in YIG films at millikelvin temperatures, APL Mater.7, 101120 (2019)

    work page 2019

  79. [82]

    G. S. MacCabe, H. Ren, J. Luo, J. D. Cohen, H. Zhou, A. Sipahigil, M. Mirhosseini, and O. Painter, Nano- acoustic resonator with ultralong phonon lifetime, Sci- ence370, 840 (2020)

    work page 2020

  80. [83]

    Antoni-Micollier, D

    L. Antoni-Micollier, D. Carbone, V. Ménoret, J. Lautier- Gaud, T. King, F. Greco, A. Messina, D. Contrafatto, and B. Desruelle, Detecting volcano-related underground mass changes with a quantum gravimeter, Geophys. Res. Lett.49, e2022GL097814 (2022)

    work page 2022

Showing first 80 references.