The ability to control the motion of mechanical systems through interaction with light has opened the door to a plethora of applications in fundamental and applied physics. With experiments routinely reaching the quantum regime, the focus has now turned towards creating and exploiting interesting non-classical states of motion and entanglement in optomechanical systems. Quantumness has also shifted from being the very reason why experiments are constructed to becoming a resource for the investigation of fundamental physics and the creation of quantum technologies. Here, by focusing on opto- and electromechanical platforms we review recent progress in quantum state preparation and entanglement of mechanical systems, together with applications to signal processing and transduction, quantum sensing and topological physics, as well as small-scale thermodynamics.
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Ashkin, A. The pressure of laser light. Sci. Am. 226, 62–71 (1972).
Einstein, A. Zur Quantentheorie der Strahlung. Phys. Z. 18, 121–128 (1917).
Kepler, J. De Cometis Libelli Tres I. Astronomicus, Theoremata Continens de Novam… III. Astrologicus, de Significationibus Cometarum Annorum Motu Cometarum… II. Physicus, Continens Physiologiam Cometarum 1607 et 1618 (Mylii, 1619).
Aspelmeyer, M., Kippenberg, T. J. & Marquardt, F. Cavity optomechanics. Rev. Mod. Phys. 86, 1391–1452 (2014).
Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).
Verhagen, E., Deléglise, S., Weis, S., Schliesser, A. & Kippenberg, T. J. Quantum-coherent coupling of a mechanical oscillator to an optical cavity mode. Nature 482, 63–67 (2012).
Wollman, E. E. et al. Quantum squeezing of motion in a mechanical resonator. Science 349, 952–955 (2015).
Pirkkalainen, J. M., Damskägg, E., Brandt, M., Massel, F. & Sillanpää, M. A. Squeezing of quantum noise of motion in a micromechanical resonator. Phys. Rev. Lett. 115, 243601 (2015).
Barzanjeh, S. et al. Stationary entangled radiation from micromechanical motion. Nature 570, 480–483 (2019).
Dowling, J. P. & Milburn, G. J. Quantum technology: the second quantum revolution. Philos. Trans. R. Soc. A 361, 1655–1674 (2003).
Rogers, B., Lo Gullo, N., De Chiara, G., Palma, G. M. & Paternostro, M. Hybrid optomechanics for quantum technologies. Quantum Meas. Quantum Metrol. 2, 11–43 (2014).
Kurizki, G. et al. Quantum technologies with hybrid systems. Proc. Natl Acad. Sci. USA 112, 3866–3873 (2015).
Braginskii, V. B. & Manukin, A. B. Measurement of Weak Forces in Physics Experiments (Univ. Chicago Press, 1977).
Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).
Hanbury Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light. Nature 177, 27–29 (1956).
Horodecki, R., Horodecki, P., Horodecki, M. & Horodecki, K. Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009).
Brunner, N., Cavalcanti, D., Pironio, S., Scarani, V. & Wehner, S. Bell nonlocality. Rev. Mod. Phys. 86, 419–478 (2014).
Lauk, N. et al. Perspectives on quantum transduction. Quantum Sci. Technol. 5, 020501 (2020).
Lambert, N. J., Rueda, A., Sedlmeir, F. & Schwefel, H. G. L. Coherent conversion between microwave and optical photons—an overview of physical implementations. Adv. Quantum Technol. 3, 1900077 (2020).
Gemmer, J., Michel, M. & Mahler, G. Quantum Thermodynamics Vol. 784 (Springer, 2009).
Vinjanampathy, S. & Anders, J. Quantum thermodynamics. Contemp. Phys. 57, 545–579 (2016).
Bohr Brask, J., Haack, G., Brunner, N. & Huber, M. Autonomous quantum thermal machine for generating steady-state entanglement. New J. Phys. 17, 113029 (2015).
Karrai, K., Favero, I. & Metzger, C. Doppler optomechanics of a photonic crystal. Phys. Rev. Lett. 100, 240801 (2008).
Xuereb, A., Domokos, P., Asbóth, J., Horak, P. & Freegarde, T. Scattering theory of cooling and heating in optomechanical systems. Phys. Rev. A 79, 053810 (2009).
O’Connell, A. D. et al. Quantum ground state and single-phonon control of a mechanical resonator. Nature 464, 697–703 (2010).
Chu, Y. et al. Quantum acoustics with superconducting qubits. Science 358, 199–202 (2017).
Clerk, A. A., Lehnert, K. W., Bertet, P., Petta, J. R. & Nakamura, Y. Hybrid quantum systems with circuit quantum electrodynamics. Nat. Phys. 16, 257–267 (2020).
Teufel, J. D. et al. Sideband cooling of micromechanical motion to the quantum ground state. Nature 475, 359–363 (2011).
Peterson, R. W. et al. Laser cooling of a micromechanical membrane to the quantum backaction limit. Phys. Rev. Lett. 116, 063601 (2016).
Rossi, M., Mason, D., Chen, J., Tsaturyan, Y. & Schliesser, A. Measurement-based quantum control of mechanical motion. Nature 563, 53–58 (2018).
Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Sideband cooling beyond the quantum backaction limit with squeezed light. Nature 541, 191–195 (2017).
Safavi-Naeini, A. H. et al. Observation of quantum motion of a nanomechanical resonator. Phys. Rev. Lett. 108, 033602 (2012).
Millen, J. & Stickler, B. A. Quantum experiments with microscale particles. Contemp. Phys. 61, 155–168 (2020).
Delić, U. et al. Cooling of a levitated nanoparticle to the motional quantum ground state. Science 367, 892–895 (2020).
Magrini, L. et al. Real-time optimal quantum control of mechanical motion at room temperature. Nature 595, 373–377 (2021).
Tebbenjohanns, F., Mattana, M. L., Rossi, M., Frimmer, M. & Novotny, L. Quantum control of a nanoparticle optically levitated in cryogenic free space. Nature 595, 378–382 (2021).
Shkarin, A. B. et al. Quantum optomechanics in a liquid. Phys. Rev. Lett. 122, 153601 (2019).
He, X. et al. Strong optical coupling through superfluid Brillouin lasing. Nat. Phys. 16, 417–421 (2020).
Renninger, W. H., Kharel, P., Behunin, R. O. & Rakich, P. T. Bulk crystalline optomechanics. Nat. Phys. 14, 601–607 (2018).
Ferraro, A., Olivares, S. & Paris, M. Gaussian States in Quantum Information (Napoli Series on Physics and Astrophysics, Bibliopolis, 2005).
Reed, A. P. et al. Faithful conversion of propagating quantum information to mechanical motion. Nat. Phys. 13, 1163–1167 (2017).
Clerk, A. A. in Quantum Optomechanics and Nanomechanics (eds Cohadon, P.-F. et al.) 183–236 (Oxford Univ. Press, 2020).
Vogel, W., Welsch, D.-G. & Wallentowitz, S. Quantum Optics: an Introduction (Wiley-VCH, 2005).
Lecocq, F., Clark, J. B., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Quantum nondemolition measurement of a nonclassical state of a massive object. Phys. Rev. X 5, 041037 (2015).
Barzanjeh, S. et al. Mechanical on-chip microwave circulator. Nat. Commun. 8, 953 (2017).
Delaney, R. D., Reed, A. P., Andrews, R. W. & Lehnert, K. W. Measurement of motion beyond the quantum limit by transient amplification. Phys. Rev. Lett. 123, 183603 (2019).
Chu, Y. et al. Creation and control of multiphonon Fock states in a bulk acoustic-wave resonator. Nature 563, 666–670 (2018).
Manenti, R. et al. Circuit quantum acoustodynamics with surface acoustic waves. Nat. Commun. 8, 975 (2017).
Moores, B. A., Sletten, L. R., Viennot, J. J. & Lehnert, K. W. Cavity quantum acoustic device in the multimode strong coupling regime. Phys. Rev. Lett. 120, 227701 (2018).
Bienfait, A. et al. Quantum erasure using entangled surface acoustic phonons. Phys. Rev. X 10, 021055 (2020).
Viennot, J. J., Ma, X. & Lehnert, K. W. Phonon-number-sensitive electromechanics. Phys. Rev. Lett. 121, 183601 (2018).
Arrangoiz-Arriola, P. et al. Resolving the energy levels of a nanomechanical oscillator. Nature 571, 537–540 (2019).
Sletten, L. R., Moores, B. A., Viennot, J. J. & Lehnert, K. W. Resolving phonon Fock states in a multimode cavity with a double-slit qubit. Phys. Rev. X 9, 021056 (2019).
Palomaki, T. A., Teufel, J. D., Simmonds, R. W. & Lehnert, K. W. Entangling mechanical motion with microwave fields. Science 342, 710–713 (2013).
Riedinger, R. et al. Non-classical correlations between single photons and phonons from a mechanical oscillator. Nature 530, 313–316 (2016).
Cohen, J. D. et al. Phonon counting and intensity interferometry of a nanomechanical resonator. Nature 520, 522–525 (2015).
Hong, S. et al. Hanbury Brown and Twiss interferometry of single phonons from an optomechanical resonator. Science 358, 203–206 (2017).
Marinković, I. et al. Optomechanical Bell test. Phys. Rev. Lett. 121, 220404 (2018).
Riedinger, R. et al. Remote quantum entanglement between two micromechanical oscillators. Nature 556, 473–477 (2018).
Ockeloen-Korppi, C. F. et al. Stabilized entanglement of massive mechanical oscillators. Nature 556, 478–482 (2018).
Mercier de Lépinay, L., Ockeloen-Korppi, C. F., Woolley, M. J. & Sillanpää, M. A. Quantum mechanics-free subsystem with mechanical oscillators. Science 372, 625–629 (2021).
Kotler, S. et al. Direct observation of deterministic macroscopic entanglement. Science 372, 622–625 (2021).
Thomas, R. A. et al. Entanglement between distant macroscopic mechanical and spin systems. Nat. Phys. 17, 228–233 (2021).
Fiaschi, N. et al. Optomechanical quantum teleportation. Nat. Photon. 15, 817–821 (2021).
Barzanjeh, S. et al. Microwave quantum illumination. Phys. Rev. Lett. 114, 080503 (2015).
Barzanjeh, S., Pirandola, S., Vitali, D. & Fink, J. M. Microwave quantum illumination using a digital receiver. Sci. Adv. 6, eabb0451 (2020).
Deffner, S. & Campbell, S. Quantum Thermodynamics: an Introduction to the Thermodynamics of Quantum Information (Morgan & Claypool, 2019).
Tian, L. & Wang, H. Optical wavelength conversion of quantum states with optomechanics. Phys. Rev. A 82, 053806 (2010).
Barzanjeh, S., Abdi, M., Milburn, G. J., Tombesi, P. & Vitali, D. Reversible optical-to-microwave quantum interface. Phys. Rev. Lett. 109, 130503 (2012).
Habraken, S. J. M., Stannigel, K., Lukin, M. D., Zoller, P. & Rabl, P. Continuous mode cooling and phonon routers for phononic quantum networks. New J. Phys. 14, 115004 (2012).
Vermersch, B., Guimond, P. O., Pichler, H. & Zoller, P. Quantum state transfer via noisy photonic and phononic waveguides. Phys. Rev. Lett. 118, 133601 (2017).
Patel, R. N. et al. Single-mode phononic wire. Phys. Rev. Lett. 121, 040501 (2018).
Rueda, A. et al. Efficient microwave to optical photon conversion: an electro-optical realization. Optica 3, 597–604 (2016).
Rueda, A., Hease, W., Barzanjeh, S. & Fink, J. M. Electro-optic entanglement source for microwave to telecom quantum state transfer. npj Quantum Inf. 5, 108 (2019).
McKenna, T. P. et al. Cryogenic microwave-to-optical conversion using a triply resonant lithium-niobate-on-sapphire transducer. Optica 7, 1737–1745 (2020).
Hease, W. et al. Bidirectional electro-optic wavelength conversion in the quantum ground state. PRX Quantum 1, 020315 (2020).
Han, X. et al. Cavity piezo-mechanics for superconducting–nanophotonic quantum interface. Nat. Commun. 11, 3237 (2020).
Andrews, R. W. et al. Bidirectional and efficient conversion between microwave and optical light. Nat. Phys. 10, 321–326 (2014).
Forsch, M. et al. Microwave-to-optics conversion using a mechanical oscillator in its quantum ground state. Nat. Phys. 16, 69–74 (2019).
Mirhosseini, M., Sipahigil, A., Kalaee, M. & Painter, O. Superconducting qubit to optical photon transduction. Nature 588, 599–603 (2020).
Bochmann, J., Vainsencher, A., Awschalom, D. D. & Cleland, A. N. Nanomechanical coupling between microwave and optical photons. Nat. Phys. 9, 712–716 (2013).
Higginbotham, A. P. et al. Harnessing electro-optic correlations in an efficient mechanical converter. Nat. Phys. 14, 1038–1042 (2018).
Arnold, G. et al. Converting microwave and telecom photons with a silicon photonic nanomechanical interface. Nat. Commun. 11, 4460 (2020).
Caves, C. M., Thorne, K. S., Drever, R. W., Sandberg, V. D. & Zimmermann, M. On the measurement of a weak classical force coupled to a quantum-mechanical oscillator. I. Issues of principle. Rev. Mod. Phys. 52, 341 (1980).
Braginsky, V. B., Vorontsov, Y. I. & Thorne, K. S. Quantum nondemolition measurements. Science 209, 547–557 (1980).
Hertzberg, J. et al. Back-action-evading measurements of nanomechanical motion. Nat. Phys. 6, 213–217 (2010).
Ockeloen-Korppi, C. et al. Quantum backaction evading measurement of collective mechanical modes. Phys. Rev. Lett. 117, 140401 (2016).
Tsang, M. & Caves, C. M. Evading quantum mechanics: engineering a classical subsystem within a quantum environment. Phys. Rev. X 2, 031016 (2012).
Aasi, J. et al. Enhanced sensitivity of the LIGO gravitational wave detector by using squeezed states of light. Nat. Photon. 7, 613–619 (2013).
Tse, M. E. et al. Quantum-enhanced advanced LIGO detectors in the era of gravitational-wave astronomy. Phys. Rev. Lett. 123, 231107 (2019).
Purdy, T. P., Peterson, R. W. & Regal, C. A. Observation of radiation pressure shot noise on a macroscopic object. Science 339, 801–804 (2013).
Cripe, J. et al. Measurement of quantum back action in the audio band at room temperature. Nature 568, 364–367 (2019).
Brooks, D. W. et al. Non-classical light generated by quantum-noise-driven cavity optomechanics. Nature 488, 476–480 (2012).
Safavi-Naeini, A. H. et al. Squeezed light from a silicon micromechanical resonator. Nature 500, 185–189 (2013).
Purdy, T. P., Yu, P. L., Peterson, R. W., Kampel, N. S. & Regal, C. A. Strong optomechanical squeezing of light. Phys. Rev. X 3, 031012 (2013).
Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Observation of strong radiation pressure forces from squeezed light on a mechanical oscillator. Nat. Phys. 12, 683–687 (2016).
Vyatchanin, S. & Zubova, E. Quantum variation measurement of a force. Phys. Lett. A 201, 269–274 (1995).
Kampel, N. S. et al. Improving broadband displacement detection with quantum correlations. Phys. Rev. X 7, 021008 (2017).
Mason, D., Chen, J., Rossi, M., Tsaturyan, Y. & Schliesser, A. Continuous force and displacement measurement below the standard quantum limit. Nat. Phys. 15, 745–749 (2019).
Li, Y. L. & Barker, P. F. Characterization and testing of a micro-g whispering gallery mode optomechanical accelerometer. J. Lightwave Technol. 36, 3919–3926 (2018).
Yap, M. J. et al. Broadband reduction of quantum radiation pressure noise via squeezed light injection. Nat. Photon. 14, 19–23 (2020).
McCuller, L. et al. Frequency-dependent squeezing for advanced LIGO. Phys. Rev. Lett. 124, 171102 (2020).
Zhang, K., Bariani, F. & Meystre, P. Quantum optomechanical heat engine. Phys. Rev. Lett. 112, 150602 (2014).
Zhang, K., Bariani, F. & Meystre, P. Theory of an optomechanical quantum heat engine. Phys. Rev. A 90, 023819 (2014).
Dong, Y., Zhang, K., Bariani, F. & Meystre, P. Work measurement in an optomechanical quantum heat engine. Phys. Rev. A 92, 033854 (2015).
Abari, N. E., Angelis, G. V. D., Zippilli, S. & Vitali, D. An optomechanical heat engine with feedback-controlled in-loop light. New J. Phys. 21, 093051 (2019).
Mari, A., Farace, A. & Giovannetti, V. Quantum optomechanical piston engines powered by heat. J. Phys. B 48, 175501 (2015).
Gelbwaser-Klimovsky, D. & Kurizki, G. Work extraction from heat-powered quantized optomechanical setups. Sci. Rep. 5, 7809 (2015).
Dechant, A., Kiesel, N. & Lutz, E. All-optical nanomechanical heat engine. Phys. Rev. Lett. 114, 183602 (2015).
Landi, G. T. & Paternostro, M. Irreversible entropy production, from quantum to classical. Rev. Mod. Phys. 93, 035008 (2021).
Brunelli, M. et al. Experimental determination of irreversible entropy production in out-of-equilibrium mesoscopic quantum systems. Phys. Rev. Lett. 121, 160604 (2018).
Belenchia, A., Mancino, L., Landi, G. T. & Paternostro, M. Entropy production in continuously measured quantum systems. npj Quant. Inf. 6, 97 (2020).
Millen, J., Deesuwan, T., Barker, P. & Anders, J. Nanoscale temperature measurements using non-equilibrium Brownian dynamics of a levitated nanosphere. Nat. Nanotechnol. 9, 425–429 (2014).
Hafezi, M. & Rabl, P. Optomechanically induced non-reciprocity in microring resonators. Opt. Express 20, 7672 (2012).
Metelmann, A. & Clerk, A. A. Nonreciprocal photon transmission and amplification via reservoir engineering. Phys. Rev. X 5, 021025 (2015).
Miri, M.-A., Ruesink, F., Verhagen, E. & Alù, A. Optical nonreciprocity based on optomechanical coupling. Phys. Rev. Appl. 7, 064014 (2017).
Bernier, N. R. et al. Nonreciprocal reconfigurable microwave optomechanical circuit. Nat. Commun. 8, 604 (2017).
Barzanjeh, S., Aquilina, M. & Xuereb, A. Manipulating the flow of thermal noise in quantum devices. Phys. Rev. Lett. 120, 060601 (2018).
Peterson, G. A. et al. Demonstration of efficient nonreciprocity in a microwave optomechanical circuit. Phys. Rev. X 7, 031001 (2017).
Fang, K. et al. Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering. Nat. Phys. 13, 465–471 (2017).
Ruesink, F., Miri, M.-A., Alù, A. & Verhagen, E. Nonreciprocity and magnetic-free isolation based on optomechanical interactions. Nat. Commun. 7, 13662 (2016).
Xu, X.-W. & Li, Y. Optical nonreciprocity and optomechanical circulator in three-mode optomechanical systems. Phys. Rev. A 91, 053854 (2015).
Brendel, C., Peano, V., Painter, O. J. & Marquardt, F. Pseudomagnetic fields for sound at the nanoscale. Proc. Natl Acad. Sci. USA 114, E3390–E3395 (2017).
Peano, V., Brendel, C., Schmidt, M. & Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 (2015).
Cha, J., Kim, K. W. & Daraio, C. Experimental realization of on-chip topological nanoelectromechanical metamaterials. Nature 564, 229–233 (2018).
Ren, H. et al. Topological phonon transport in an optomechanical system. Preprint at https://arxiv.org/abs/2009.06174 (2020).
Heinrich, G., Ludwig, M., Qian, J., Kubala, B. & Marquardt, F. Collective dynamics in optomechanical arrays. Phys. Rev. Lett. 107, 043603 (2011).
Schmidt, M., Peano, V. & Marquardt, F. Optomechanical Dirac physics. New J. Phys. 17, 023025 (2015).
Sanavio, C., Peano, V. & Xuereb, A. Nonreciprocal topological phononics in optomechanical arrays. Phys. Rev. B 101, 085108 (2020).
Gan, J.-H., Xiong, H., Si, L.-G., Lü, X.-Y. & Wu, Y. Solitons in optomechanical arrays. Opt. Lett. 41, 2676 (2016).
Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).
Mousavi, S. H., Khanikaev, A. B. & Wang, Z. Topologically protected elastic waves in phononic metamaterials. Nat. Commun. 6, 8682 (2015).
Brendel, C., Peano, V., Painter, O. & Marquardt, F. Snowflake phononic topological insulator at the nanoscale. Phys. Rev. B 97, 020102 (2018).
Bassi, A., Lochan, K., Satin, S., Singh, T. P. & Ulbricht, H. Models of wave-function collapse, underlying theories, and experimental tests. Rev. Mod. Phys. 85, 471–527 (2013).
Schlosshauer, M. Decoherence, the measurement problem, and interpretations of quantum mechanics. Rev. Mod. Phys. 76, 1267–1305 (2004).
Bassi, A., Großardt, A. & Ulbricht, H. Gravitational decoherence. Class. Quantum Gravity 34, 193002 (2017).
Moore, G. T. Quantum theory of the electromagnetic field in a variable-length one-dimensional cavity. J. Math. Phys. 11, 2679–2691 (1970).
Sanz, M., Wieczorek, W., Gröblacher, S. & Solano, E. Electro-mechanical Casimir effect. Quantum 2, 91 (2018).
Macrì, V. et al. Nonperturbative dynamical Casimir effect in optomechanical systems: vacuum Casimir–Rabi splittings. Phys. Rev. X 8, 011031 (2018).
Wallucks, A., Marinković, I., Hensen, B., Stockill, R. & Gröblacher, S. A quantum memory at telecom wavelengths. Nat. Phys. 16, 772–777 (2020).
MacCabe, G. S. et al. Nano-acoustic resonator with ultralong phonon lifetime. Science 370, 840–843 (2020).
Tsaturyan, Y., Barg, A., Polzik, E. S. & Schliesser, A. Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution. Nat. Nanotechnol. 12, 776–783 (2017).
Fang, K., Matheny, M. H., Luan, X. & Painter, O. Optical transduction and routing of microwave phonons in cavity–optomechanical circuits. Nat. Photon. 10, 489–496 (2016).
Zivari, A., Stockill, R., Fiaschi, N. & Gröblacher, S. Non-classical mechanical states guided in a phononic waveguide. Preprint at https://arxiv.org/abs/2108.06248 (2021).
Marquardt, F., Chen, J. P., Clerk, A. A. & Girvin, S. M. Quantum theory of cavity-assisted sideband cooling of mechanical motion. Phys. Rev. Lett. 99, 093902 (2007).
Thompson, J. D. et al. Strong dispersive coupling of a high-finesse cavity to a micromechanical membrane. Nature 452, 72–75 (2008).
Law, C. K. Interaction between a moving mirror and radiation pressure: a Hamiltonian formulation. Phys. Rev. A 51, 2537–2541 (1995).
Nunnenkamp, A., Børkje, K. & Girvin, S. M. Single-photon optomechanics. Phys. Rev. Lett. 107, 063602 (2011).
Rabl, P. Photon blockade effect in optomechanical systems. Phys. Rev. Lett. 107, 063601 (2011).
S.B. acknowledges funding by the Natural Sciences and Engineering Research Council of Canada (NSERC) through its Discovery Grant, funding and advisory support provided by Alberta Innovates through the Accelerating Innovations into CarE (AICE)—Concepts Program, and support from Alberta Innovates and NSERC through an Advance Grant. A.X. acknowledges funding by the European Union’s Horizon 2020 research and innovation programme under grant agreement 732894 (FET Proactive HOT) and by the Julian Schwinger Foundation project grant JSF-16-03-0000 (TOM). S.G. is supported by the European Research Council (ERC Starting Grant Strong-Q, 676842; and ERC Consolidator Grant Q-ECHOS, 101001005) and by the Netherlands Organization for Scientific Research (NWO/OCW) as part of the Frontiers of Nanoscience program, as well as through Vidi (680-47-541/994) and Vrij Programma (680-92-18-04) grants. M.P. is supported by the H2020/FETOPEN/2018/2020 project TEQ (766900), the DfE-SFI Investigator Programme (15/IA/2864), COST Action CA15220, the Royal Society Wolfson Research Fellowship (RSWF\R3\183013), the Royal Society International Exchanges Programme (IEC\R2\192220), the Leverhulme Trust Research Project Grant (RGP/2018/266), the UK EPSRC (project QuamNESS, grant EP/T028106/1) and the CNR/RS (London) project “Testing fundamental theories with ultracold atoms”. C.A.R. acknowledges funding by the US National Science Foundation under grant 1125844 and a Cottrell FRED Award from the Research Corporation for Science Advancement under grant 27321. E.M.W. acknowledges funding by the European Union’s Horizon 2020 research and innovation program under grant agreement 732894 (FET Proactive HOT), the German Federal Ministry of Education and Research (contract 13N14777) within the European QuantERA co-fund project QuaSeRT, and project QT-6 SPOC of the Baden-Württemberg Foundation.
The authors declare no competing interests.
Peer review information Nature Physics thanks James Millen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
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Barzanjeh, S., Xuereb, A., Gröblacher, S. et al. Optomechanics for quantum technologies. Nat. Phys. 18, 15–24 (2022). https://doi.org/10.1038/s41567-021-01402-0
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