[1] Schleier-Smith M. Editorial: hybridizing quantum physics and engineering[J]. Physical Review Letters, 117, 100001(2016).

[6] Abbott B P, Abbott R, Abbott T D et al. GW150914: the advanced LIGO detectors in the era of first discoveries[J]. Physical Review Letters, 116, 131103(2016).

[7] Vahala K J. Optical microcavities[J]. Nature, 424, 839-846(2003).

[8] Gröblacher S, Hammerer K, Vanner M R et al. Observation of strong coupling between a micromechanical resonator and an optical cavity field[J]. Nature, 460, 724-727(2009).

[9] Dobrindt J M, Wilson-Rae I, Kippenberg T J. Parametric normal-mode splitting in cavity optomechanics[J]. Physical Review Letters, 101, 263602(2008).

[10] Safavi-Naeini A H, Alegre T P M, Chan J et al. Electromagnetically induced transparency and slow light with optomechanics[J]. Nature, 472, 69-73(2011).

[11] Weis S, Rivière R, Deléglise S et al. Optomechanically induced transparency[J]. Science, 330, 1520-1523(2010).

[12] Teufel J D, Donner T, Li D L et al. Sideband cooling of micromechanical motion to the quantum ground state[J]. Nature, 475, 359-363(2011).

[13] Clark J B, Lecocq F, Simmonds R W et al. Sideband cooling beyond the quantum backaction limit with squeezed light[J]. Nature, 541, 191-195(2017).

[14] Lei C U, Weinstein A J, Suh J et al. Quantum nondemolition measurement of a quantum squeezed state beyond the 3 dB limit[J]. Physical Review Letters, 117, 100801(2016).

[15] Grudinin I S, Lee H, Painter O et al. Phonon laser action in a tunable two-level system[J]. Physical Review Letters, 104, 083901(2010).

[16] Mahboob I, Nishiguchi K, Fujiwara A et al. Phonon lasing in an electromechanical resonator[J]. Physical Review Letters, 110, 127202(2013).

[17] Wollman E E, Lei C U, Weinstein A J et al. Quantum squeezing of motion in a mechanical resonator[J]. Science, 349, 952-955(2015).

[18] Manley J, Chowdhury M D, Grin D et al. Searching for vector dark matter with an optomechanical accelerometer[J]. Physical Review Letters, 126, 061301(2021).

[19] Baker C G, Bowen W P, Cox P et al. Optomechanical dark matter instrument for direct detection[J]. Physical Review D, 110, 043005(2024).

[20] Aspelmeyer M, Kippenberg T J, Marquardt F. Cavity optomechanics[J]. Reviews of Modern Physics, 86, 1391-1452(2014).

[21] Gil-Santos E, Ruz J J, Malvar O et al. Optomechanical detection of vibration modes of a single bacterium[J]. Nature Nanotechnology, 15, 469-474(2020).

[22] Lai Y H, Suh M G, Lu Y K et al. Earth rotation measured by a chip-scale ring laser gyroscope[J]. Nature Photonics, 14, 345-349(2020).

[23] Abbott B P, Abbott R, Abbott T D et al. Observation of gravitational waves from a binary black hole merger[J]. Physical Review Letters, 116, 061102(2016).

[24] Zhu J G, Ozdemir S K, Xiao Y F et al. On-chip single nanoparticle detection and sizing by mode splitting in an ultrahigh-Q microresonator[J]. Nature Photonics, 4, 46-49(2010).

[27] Mason D, Chen J X, Rossi M et al. Continuous force and displacement measurement below the standard quantum limit[J]. Nature Physics, 15, 745-749(2019).

[28] Schreppler S, Spethmann N, Brahms N et al. Optically measuring force near the standard quantum limit[J]. Science, 344, 1486-1489(2014).

[29] Clerk A A, Devoret M H, Girvin S M et al. Introduction to quantum noise, measurement, and amplification[J]. Reviews of Modern Physics, 82, 1155-1208(2010).

[30] Burd S C, Srinivas R, Bollinger J J et al. Quantum amplification of mechanical oscillator motion[J]. Science, 364, 1163-1165(2019).

[31] Blūms V, Piotrowski M, Hussain M I et al. A single-atom 3D sub-attonewton force sensor[J]. Science Advances, 4, eaao4453(2018).

[32] Moser J, Güttinger J, Eichler A et al. Ultrasensitive force detection with a nanotube mechanical resonator[J]. Nature Nanotechnology, 8, 493-496(2013).

[33] Pooser R C, Lawrie B. Ultrasensitive measurement of microcantilever displacement below the shot-noise limit[J]. Optica, 2, 393-399(2015).

[34] Weber P, Güttinger J, Noury A et al. Force sensitivity of multilayer graphene optomechanical devices[J]. Nature Communications, 7, 12496(2016).

[35] Braginskiĭ V B, Manukin A B. Ponderomotive effects of electromagnetic radiation[J]. Soviet Physics JETP, 25, 653-655(1967).

[36] Yu H C, McCuller L, Tse M et al. Quantum correlations between light and the kilogram-mass mirrors of LIGO[J]. Nature, 583, 43-47(2020).

[37] Chan J, Alegre T P M, Safavi-Naeini A H et al. Laser cooling of a nanomechanical oscillator into its quantum ground state[J]. Nature, 478, 89-92(2011).

[38] Aspelmeyer M, Meystre P, Schwab K. Quantum optomechanics[J]. Physics Today, 65, 29-35(2012).

[39] Braginsky V B, Khalili F Y. Quantum nondemolition measurements: the route from toys to tools[J]. Reviews of Modern Physics, 68, 1-11(1996).

[40] Yap M J, Cripe J, Mansell G L et al. Broadband reduction of quantum radiation pressure noise via squeezed light injection[J]. Nature Photonics, 14, 19-23(2020).

[41] McCuller L, Whittle C, Ganapathy D et al. Frequency-dependent squeezing for advanced LIGO[J]. Physical Review Letters, 124, 171102(2020).

[42] Aggarwal N, Cullen T J, Cripe J et al. Room-temperature optomechanical squeezing[J]. Nature Physics, 16, 784-788(2020).

[44] Pedrozo-Peñafiel E, Colombo S, Shu C et al. Entanglement on an optical atomic-clock transition[J]. Nature, 588, 414-418(2020).

[45] Peterson R W, Purdy T P, Kampel N S et al. Laser cooling of a micromechanical membrane to the quantum backaction limit[J]. Physical Review Letters, 116, 063601(2016).

[46] Rossi M, Mason D, Chen J X et al. Measurement-based quantum control of mechanical motion[J]. Nature, 563, 53-58(2018).

[47] Delić U, Reisenbauer M, Dare K H et al. Cooling of a levitated nanoparticle to the motional quantum ground state[J]. Science, 367, 892-895(2020).

[48] Whittle C, Hall E D, Dwyer S et al. Approaching the motional ground state of a 10 kg object[J]. Science, 372, 1333-1336(2021).

[49] Bondurant R S. Reduction of radiation-pressure-induced fluctuations in interferometric gravity-wave detectors[J]. Physical Review A, 34, 3927-3931(1986).

[50] Rehbein H, Harms J, Schnabel R et al. Optical transfer functions of Kerr nonlinear cavities and interferometers[J]. Physical Review Letters, 95, 193001(2005).

[51] Collett M J, Gardiner C W. Squeezing of intracavity and traveling-wave light fields produced in parametric amplification[J]. Physical Review A, 30, 1386-1391(1984).

[52] Nation P D, Blencowe M P, Buks E. Quantum analysis of a nonlinear microwave cavity-embedded dc SQUID displacement detector[J]. Physical Review B, 78, 104516(2008).

[53] Laflamme C, Clerk A A. Quantum-limited amplification with a nonlinear cavity detector[J]. Physical Review A, 83, 033803(2011).

[54] Laflamme C, Clerk A A. Weak qubit measurement with a nonlinear cavity: beyond perturbation theory[J]. Physical Review Letters, 109, 123602(2012).

[55] Elste F, Girvin S M, Clerk A A. Quantum noise interference and backaction cooling in cavity nanomechanics[J]. Physical Review Letters, 102, 207209(2009).

[56] Xuereb A, Schnabel R, Hammerer K. Dissipative optomechanics in a Michelson-Sagnac interferometer[J]. Physical Review Letters, 107, 213604(2011).

[57] Kronwald A, Marquardt F, Clerk A A. Dissipative optomechanical squeezing of light[J]. New Journal of Physics, 16, 063058(2014).

[58] Dobrindt J M, Kippenberg T J. Theoretical analysis of mechanical displacement measurement using a multiple cavity mode transducer[J]. Physical Review Letters, 104, 033901(2010).

[59] Brooks D W C, Botter T, Schreppler S et al. Non-classical light generated by quantum-noise-driven cavity optomechanics[J]. Nature, 488, 476-480(2012).

[60] Safavi-Naeini A H, Gröblacher S, Hill J T et al. Squeezed light from a silicon micromechanical resonator[J]. Nature, 500, 185-189(2013).

[61] Purdy T P, Yu P L, Peterson R W et al. Strong optomechanical squeezing of light[J]. Physical Review X, 3, 031012(2013).

[62] Peano V, Schwefel H G L, Marquardt C et al. Intracavity squeezing can enhance quantum-limited optomechanical position detection through deamplification[J]. Physical Review Letters, 115, 243603(2015).

[63] Huang S M, Agarwal G S. Robust force sensing for a free particle in a dissipative optomechanical system with a parametric amplifier[J]. Physical Review A, 95, 023844(2017).

[64] Zhao W, Zhang S D, Miranowicz A et al. Weak-force sensing with squeezed optomechanics[J]. Science China Physics, 63, 224211(2019).

[65] Bhattacharya M, Uys H, Meystre P. Optomechanical trapping and cooling of partially reflective mirrors[J]. Physical Review A, 77, 033819(2008).

[66] Nunnenkamp A, Børkje K, Harris J G E et al. Cooling and squeezing via quadratic optomechanical coupling[J]. Physical Review A, 82, 021806(2010).

[67] Jayich A M, Sankey J C, Zwickl B M et al. Dispersive optomechanics: a membrane inside a cavity[J]. New Journal of Physics, 10, 095008(2008).

[68] Miao H X, Danilishin S, Corbitt T et al. Standard quantum limit for probing mechanical energy quantization[J]. Physical Review Letters, 103, 100402(2009).

[69] Dellantonio L, Kyriienko O, Marquardt F et al. Quantum nondemolition measurement of mechanical motion quanta[J]. Nature Communications, 9, 3621(2018).

[70] Hauer B D, Metelmann A, Davis J P. Phonon quantum nondemolition measurements in nonlinearly coupled optomechanical cavities[J]. Physical Review A, 98, 043804(2018).

[71] Ludwig M, Safavi-Naeini A H, Painter O et al. Enhanced quantum nonlinearities in a two-mode optomechanical system[J]. Physical Review Letters, 109, 063601(2012).

[72] Clerk A A, Marquardt F, Harris J G E. Quantum measurement of phonon shot noise[J]. Physical Review Letters, 104, 213603(2010).

[73] Thompson J D, Zwickl B M, Jayich A M et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane[J]. Nature, 452, 72-75(2008).

[74] Bullier N P, Pontin A, Barker P F. Quadratic optomechanical cooling of a cavity-levitated nanosphere[J]. Physical Review Research, 3, L032022(2021).

[75] Sankey J C, Yang C, Zwickl B M et al. Strong and tunable nonlinear optomechanical coupling in a low-loss system[J]. Nature Physics, 6, 707-712(2010).

[76] Flowers-Jacobs N E, Hoch S W, Sankey J C et al. Fiber-cavity-based optomechanical device[J]. Applied Physics Letters, 101, 221109(2012).

[77] Lee D, Underwood M, Mason D et al. Multimode optomechanical dynamics in a cavity with avoided crossings[J]. Nature Communications, 6, 6232(2015).

[78] Paraïso T K, Kalaee M, Zang L Y et al. Position-squared coupling in a tunable photonic crystal optomechanical cavity[J]. Physical Review X, 5, 041024(2015).

[79] Leijssen R, La Gala G R, Freisem L et al. Nonlinear cavity optomechanics with nanomechanical thermal fluctuations[J]. Nature Communications, 8, ncomms16024(2017).

[80] Purdy T P, Brooks D W C, Botter T et al. Tunable cavity optomechanics with ultracold atoms[J]. Physical Review Letters, 105, 133602(2010).

[81] Vanner M R. Selective linear or quadratic optomechanical coupling via measurement[J]. Physical Review X, 1, 021011(2011).

[82] Brawley G A, Vanner M R, Larsen P E et al. Nonlinear optomechanical measurement of mechanical motion[J]. Nature Communications, 7, 10988(2016).

[83] Yanay Y, Sankey J C, Clerk A A. Quantum backaction and noise interference in asymmetric two-cavity optomechanical systems[J]. Physical Review A, 93, 063809(2016).

[84] Dumont V, Lau H K, Clerk A A et al. Asymmetry-based quantum backaction suppression in quadratic optomechanics[J]. Physical Review Letters, 129, 063604(2022).

[85] Tsaturyan Y, Barg A, Polzik E S et al. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution[J]. Nature Nanotechnology, 12, 776-783(2017).

[86] Thomas R A, Parniak M, Østfeldt C et al. Entanglement between distant macroscopic mechanical and spin systems[J]. Nature Physics, 17, 228-233(2021).

[87] Chen J X, Rossi M, Mason D et al. Entanglement of propagating optical modes via a mechanical interface[J]. Nature Communications, 11, 943(2020).

[88] Zhang S D, Wang J, Zhang Q et al. Squeezing-enhanced quantum sensing with quadratic optomechanics[J]. Optica Quantum, 2, 222-229(2024).

[89] Motazedifard A, Dalafi A, Bemani F et al. Force sensing in hybrid Bose-Einstein-condensate optomechanics based on parametric amplification[J]. Physical Review A, 100, 023815(2019).

[90] Levitan B A, Metelmann A, Clerk A A. Optomechanics with two-phonon driving[J]. New Journal of Physics, 18, 093014(2016).

[91] Gavartin E, Verlot P, Kippenberg T J. A hybrid on-chip optomechanical transducer for ultrasensitive force measurements[J]. Nature Nanotechnology, 7, 509-514(2012).

[92] Forstner S, Prams S, Knittel J et al. Cavity optomechanical magnetometer[J]. Physical Review Letters, 108, 120801(2012).

[93] Jiao Y F, Zhang S D, Zhang Y L et al. Nonreciprocal optomechanical entanglement against backscattering losses[J]. Physical Review Letters, 125, 143605(2020).

[94] Wang J, Zhang Q, Jiao Y F et al. Quantum advantage of one-way squeezing in weak-force sensing[J]. Applied Physics Reviews, 11, 031409(2024).

[95] Tabuchi Y, Ishino S, Ishikawa T et al. Hybridizing ferromagnetic magnons and microwave photons in the quantum limit[J]. Physical Review Letters, 113, 083603(2014).

[96] Hisatomi R, Osada A, Tabuchi Y et al. Bidirectional conversion between microwave and light via ferromagnetic magnons[J]. Physical Review B, 93, 174427(2016).

[97] Lachance-Quirion D, Tabuchi Y, Ishino S et al. Resolving quanta of collective spin excitations in a millimeter-sized ferromagnet[J]. Science Advances, 3, e1603150(2017).

[98] Lachance-Quirion D, Tabuchi Y, Gloppe A et al. Hybrid quantum systems based on magnonics[J]. Applied Physics Express, 12, 070101(2019).

[99] Jünger C, Delagrange R, Chevallier D et al. Magnetic-field-independent subgap states in hybrid Rashba nanowires[J]. Physical Review Letters, 125, 017701(2020).

[100] Rameshti B Z, Kusminskiy S V, Haigh J A et al. Cavity magnonics[J]. Physics Reports, 979, 1-61(2022).

[101] Zhang X F, Zou C L, Jiang L et al. Strongly coupled magnons and cavity microwave photons[J]. Physical Review Letters, 113, 156401(2014).

[102] Potts C A, Varga E, Bittencourt V A S V et al. Dynamical backaction magnomechanics[J]. Physical Review X, 11, 031053(2021).

[103] Zuo X, Fan Z Y, Qian H et al. Cavity magnomechanics: from classical to quantum[J]. New Journal of Physics, 26, 031201(2024).

[104] Zhang X F, Zou C L, Jiang L et al. Cavity magnomechanics[J]. Science Advances, 2, e1501286(2016).

[105] Li J, Zhu S Y, Agarwal G S. Magnon-photon-phonon entanglement in cavity magnomechanics[J]. Physical Review Letters, 121, 203601(2018).

[106] Fan Z Y, Qiu L, Gröblacher S et al. Microwave-optics entanglement via cavity optomagnomechanics[J]. Laser & Photonics Reviews, 17, 2200866(2023).

[107] Fan Z Y, Qian H, Zuo X et al. Entangling ferrimagnetic magnons with an atomic ensemble via optomagnomechanics[J]. Physical Review A, 108, 023501(2023).

[108] Xu D, Gu X K, Li H K et al. Quantum control of a single magnon in a macroscopic spin system[J]. Physical Review Letters, 130, 193603(2023).

[109] Wang Y M, Xiong W, Xu Z Y et al. Dissipation-induced nonreciprocal magnon blockade in a magnon-based hybrid system[J]. Science China Physics, 65, 260314(2022).

[110] Li J, Zhu S Y. Entangling two magnon modes via magnetostrictive interaction[J]. New Journal of Physics, 21, 085001(2019).

[111] Li J, Wang Y P, You J Q et al. Squeezing microwaves by magnetostriction[J]. National Science Review, 10, nwac247(2023).

[112] Li J, Gröblacher S. Entangling the vibrational modes of two massive ferromagnetic spheres using cavity magnomechanics[J]. Quantum Science and Technology, 6, 024005(2021).

[113] Xu G T, Zhang M, Wang Y et al. Magnonic frequency comb in the magnomechanical resonator[J]. Physical Review Letters, 131, 243601(2023).

[114] Wang Y, Zhang H L, Wu J L et al. Quantum parametric amplification of phonon-mediated magnon-spin interaction[J]. Science China Physics, 66, 110311(2023).

[115] Kani A, Sarma B, Twamley J. Intensive cavity-magnomechanical cooling of a levitated macromagnet[J]. Physical Review Letters, 128, 013602(2022).

[116] Nair J M P, Zhang Z, Scully M O et al. Nonlinear spin currents[J]. Physical Review B, 102, 104415(2020).

[117] Yang Z B, Wu W J, Li J et al. Steady-entangled-state generation via the cross-Kerr effect in a ferrimagnetic crystal[J]. Physical Review A, 106, 012419(2022).

[118] Zhang G Q, Wang Y P, You J Q. Theory of the magnon Kerr effect in cavity magnonics[J]. Science China Physics, 62, 987511(2019).

[119] Wang Y P, Zhang G Q, Zhang D K et al. Bistability of cavity magnon polaritons[J]. Physical Review Letters, 120, 057202(2018).

[120] Shen R C, Wang Y P, Li J et al. Long-time memory and ternary logic gate using a multistable cavity magnonic system[J]. Physical Review Letters, 127, 183202(2021).

[121] Shen R C, Li J, Fan Z Y et al. Mechanical bistability in Kerr-modified cavity magnomechanics[J]. Physical Review Letters, 129, 123601(2022).

[122] Asjad M, Li J, Zhu S Y et al. Magnon squeezing enhanced ground-state cooling in cavity magnomechanics[J]. Fundamental Research, 3, 3-7(2023).

[123] Zoepfl D, Juan M L, Diaz-Naufal N et al. Kerr enhanced backaction cooling in magnetomechanics[J]. Physical Review Letters, 130, 033601(2023).

[124] Zheng Q J, Zhong W X, Cheng G L et al. Nonreciprocal tripartite entanglement based on magnon Kerr effect in a spinning microwave resonator[J]. Optics Communications, 546, 129796(2023).

[125] Kong C, Liu J B, Xiong H. Nonreciprocal microwave transmission under the joint mechanism of phase modulation and magnon Kerr nonlinearity effect[J]. Frontiers of Physics, 18, 12501(2023).

[126] Kong C, Xiong H, Wu Y. Magnon-induced nonreciprocity based on the magnon Kerr effect[J]. Physical Review Applied, 12, 034001(2019).

[127] Gebremariam T, Zeng Y X, Mazaheri M et al. Enhancing optomechanical force sensing via precooling and quantum noise cancellation[J]. Science China Physics, 63, 210311(2019).

[128] Hu Y W, Xiao Y F, Liu Y C et al. Optomechanical sensing with on-chip microcavities[J]. Frontiers of Physics, 8, 475-490(2013).

[129] Zheng Y, Yu J, Chen H K et al. A vector displacement measurement sensing device based on fiber Bragg grating and its experimental study[J]. Acta Photonica Sinica, 53, 0206005(2024).

[130] Gotardo F, Carey B J, Greenall H et al. Waveguide-integrated chip-scale optomechanical magnetometer[J]. Optics Express, 31, 37663-37672(2023).

[131] Guzmán Cervantes F, Kumanchik L, Pratt J et al. High sensitivity optomechanical reference accelerometer over 10 kHz[J]. Applied Physics Letters, 104, 221111(2014).

[132] Koppenhöfer M, Padgett C, Cady J V et al. Single-spin readout and quantum sensing using optomechanically induced transparency[J]. Physical Review Letters, 130, 093603(2023).

[133] Yu W Y, Jiang W C, Lin Q et al. Cavity optomechanical spring sensing of single molecules[J]. Nature Communications, 7, 12311(2016).

[134] Yang H, Wan S, Zou C L et al. Portable temperature sensing device based on on-chip optical microcavities[J]. Acta Optica Sinica, 44, 2313002(2024).

[135] Jie R M, Xiao C, Liu X et al. Distributed temperature sensing: review of technology and applications[J]. Acta Optica Sinica, 44, 0106011(2024).

[136] Zhang Q, Wang J, Lu T X et al. Quantum weak force sensing with squeezed magnomechanics[J]. Science China Physics, 67, 100313(2024).

[137] Liu Q, Gao P F, Cai S Y et al. Highly sensitive magnetic field sensing based on extrinsic fiber Bragg grating Fabry-Perot filter and optoelectronic oscillator[J]. Acta Optica Sinica, 44, 1306005(2024).