{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T01:05:27Z","timestamp":1775869527898,"version":"3.50.1"},"reference-count":71,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,11,11]],"date-time":"2022-11-11T00:00:00Z","timestamp":1668124800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018703","name":"European Innovation Council","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/100018703","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000266","name":"Engineering and Physical Sciences Research Council","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["766900"],"award-info":[{"award-number":["766900"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["10032223"],"award-info":[{"award-number":["10032223"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["EP\/W007444\/1"],"award-info":[{"award-number":["EP\/W007444\/1"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["EP\/V035975\/1"],"award-info":[{"award-number":["EP\/V035975\/1"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["EP\/V000624\/1"],"award-info":[{"award-number":["EP\/V000624\/1"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100000275","name":"Leverhulme Trust","doi-asserted-by":"publisher","award":["RPG-2022-57"],"award-info":[{"award-number":["RPG-2022-57"]}],"id":[{"id":"10.13039\/501100000275","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Magnetically levitated microparticles have been proposed as mechanical sensors with extreme sensitivity. In particular, micromagnets levitated above a superconductor can achieve very low levels of dissipation and thermal noise. In this paper, we review recent initial experiments and discuss the potential for using these systems as sensors of magnetic fields and rotational motion, as well as possible applications to fundamental physics.<\/jats:p>","DOI":"10.3390\/e24111642","type":"journal-article","created":{"date-parts":[[2022,11,14]],"date-time":"2022-11-14T02:32:01Z","timestamp":1668393121000},"page":"1642","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Levitated Micromagnets in Superconducting Traps: A New Platform for Tabletop Fundamental Physics Experiments"],"prefix":"10.3390","volume":"24","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9385-2127","authenticated-orcid":false,"given":"Andrea","family":"Vinante","sequence":"first","affiliation":[{"name":"CNR-Istituto di Fotonica e Nanotecnologie and Fondazione Bruno Kessler, Via Alla Cascata 56\/C, 38123 Trento, Italy"}]},{"given":"Chris","family":"Timberlake","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK"}]},{"given":"Hendrik","family":"Ulbricht","sequence":"additional","affiliation":[{"name":"School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, UK"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,11]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gonzalez-Ballestero, C., Aspelmeyer, M., Novotny, L., Quidant, R., and Romero-Isart, O. (2021). Levitodynamics: Levitation and control of microscopic objects in vacuum. Science, 374.","DOI":"10.1126\/science.abg3027"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Jain, V., Gieseler, J., Moritz, C., Dellago, C., Quidant, R., and Novotny, L. (2016). Direct Measurement of Photon Recoil from a Levitated Nanoparticle. Phys. Rev. Lett., 116.","DOI":"10.1103\/PhysRevLett.116.243601"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Timberlake, C., Gasbarri, G., Vinante, A., Setter, A., and Ulbricht, H. (2019). Acceleration sensing with magnetically levitated oscillators above a superconductor. Appl. Phys. Lett., 115.","DOI":"10.1063\/1.5129145"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Prat-Camps, J., Teo, C., Rusconi, C., Wieczorek, W., and Romero-Isart, O. (2017). Ultrasensitive Inertial and Force Sensors with Diamagnetically Levitated Magnets. Phys. Rev. Appl., 9.","DOI":"10.1103\/PhysRevApplied.8.034002"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Jackson Kimball, D.F., Sushkov, A.O., and Budker, D. (2016). Precessing Ferromagnetic Needle Magnetometer. Phys. Rev. Lett., 116.","DOI":"10.1103\/PhysRevLett.116.190801"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Vinante, A., Timberlake, C., Budker, D., Jackson Kimball, D.F., Sushkov, A.O., and Ulbricht, H. (2021). Surpassing the Energy Resolution Limit with ferromagnetic torque sensors. Phys. Rev. Lett., 127.","DOI":"10.1103\/PhysRevLett.127.070801"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Fadeev, P., Timberlake, C., Wang, T., Vinante, A., Band, Y.B., Budker, D., Sushkov, A.O., Ulbricht, H., and Jackson Kimball, D.F. (2021). Ferromagnetic gyroscopes for tests of fundamental physics. Quantum Sci. Technol., 6.","DOI":"10.1088\/2058-9565\/abd892"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Pino, H., Prat-Camps, J., Sinha, K., Venkatesh, B.P., and Romero-Isart, O. (2018). On-chip quantum interference of a superconducting microsphere. Quantum Sci. Technol., 3.","DOI":"10.1088\/2058-9565\/aa9d15"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Vinante, A., Pontin, A., Rashid, M., Toro\u0161, M., Barker, P.F., and Ulbricht, H. (2019). Testing collapse models with levitated nanoparticles: Detection challenge. Phys. Rev. A, 100.","DOI":"10.1103\/PhysRevA.100.012119"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Wang, T., Lourette, S., O\u2019Kelley, S.R., Kayci, M., Band, Y., Kimball, D.F.J., Sushkov, A.O., and Budker, D. (2019). Dynamics of a Ferromagnetic Particle Levitated over a Superconductor. Phys. Rev. Appl., 11.","DOI":"10.1103\/PhysRevApplied.11.044041"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Gieseler, J., Kabcenell, A., Rosenfeld, E., Schaefer, J., Safira, A., Schuetz, M.J., Gonzalez-Ballestero, C., Rusconi, C.C., Romero-Isart, O., and Lukin, M.D. (2020). Single-spin magnetomechanics with levitated micromagnets. Phys. Rev. Lett., 124.","DOI":"10.1103\/PhysRevLett.124.163604"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Vinante, A., Falferi, P., Gasbarri, G., Setter, A., Timberlake, C., and Ulbricht, H. (2020). Ultralow Mechanical Damping with Meissner-Levitated Ferromagnetic Microparticles. Phys. Rev. Appl., 13.","DOI":"10.1103\/PhysRevApplied.13.064027"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Landau, L., and Lifshitz, E. (1984). Electrodynamics of Continuous Media, Pergamon Press. [2nd ed.].","DOI":"10.1016\/B978-0-08-030275-1.50007-2"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Lin, Q.G. (2006). Theoretical development of the image method for a general magnetic source in the presence of a superconducting sphere or a long superconducting cylinder. Phys. Rev. B, 74.","DOI":"10.1103\/PhysRevB.74.024510"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Raut, N.K., Miller, J., Pate, J., Chiao, R., and Sharping, J.E. (2021). Meissner levitation of a millimeter-size neodymium magnet within a superconducting radio frequency cavity. arXiv.","DOI":"10.1109\/TASC.2021.3053206"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Nimmrichter, S., and Hornberger, K. (2015). Optomechanical sensing of spontaneous wave-function collapse. Phys. Rev. Lett., 113.","DOI":"10.1103\/PhysRevLett.113.020405"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Mitchell, M.W., and Alvarez, S.P. (2020). Colloquium: Quantum limits to the energy resolution of magnetic field sensors. Rev. Mod. Phys., 92.","DOI":"10.1103\/RevModPhys.92.021001"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Palacios Alvarez, S., Gomez, P., Coop, S., Zamora-Zamora, R., Mazzinghi, C., and Mitchell, M.W. (2022). Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below \u210f. Proc. Natl. Acad. Sci. USA, 119.","DOI":"10.1073\/pnas.2115339119"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Rashid, M., Tufarelli, T., Bateman, J., Vovrosh, J., Hempston, D., Kim, M.S., and Ulbricht, H. (2016). Experimental Realization of a Thermal Squeezed State of Levitated Optomechanics. Phys. Rev. Lett., 117.","DOI":"10.1103\/PhysRevLett.117.273601"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Aspelmeyer, M., Kippenberg, T.J., and Marquardt, F. (2014). Cavity optomechanics. Rev. Mod. Phys., 86.","DOI":"10.1007\/978-3-642-55312-7"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1242","DOI":"10.1038\/s41567-019-0663-9","article-title":"Quantum superposition of molecules beyond 25 kDa","volume":"15","author":"Fein","year":"2019","journal-title":"Nat. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2021.11.004","article-title":"Quantum physics in space","volume":"951","author":"Belenchia","year":"2022","journal-title":"Phys. Rep."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Arvanitaki, A., and Geraci, A.A. (2013). Detecting high-frequency gravitational waves with optically levitated sensors. Phys. Rev. Lett., 110.","DOI":"10.1103\/PhysRevLett.110.071105"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Pontin, A., Mourounas, L.S., Geraci, A.A., and Barker, P.F. (2018). Levitated optomechanics with a fiber Fabry\u2013Perot interferometer. New J. Phys., 20.","DOI":"10.1088\/1367-2630\/aaa71c"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Qvarfort, S., Serafini, A., Barker, P.F., and Bose, S. (2018). Gravimetry through non-linear optomechanics. Nat. Commun., 9.","DOI":"10.1038\/s41467-018-06037-z"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Hebestreit, E., Frimmer, M., Reimann, R., and Novotny, L. (2018). Sensing static forces with free-falling nanoparticles. Phys. Rev. Lett., 121.","DOI":"10.1103\/PhysRevLett.121.063602"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Carney, D., Krnjaic, G., Moore, D.C., Regal, C.A., Afek, G., Bhave, S., Brubaker, B., Corbitt, T., Cripe, J., and Crisosto, N. (2021). Mechanical quantum sensing in the search for dark matter. Quantum Sci. Technol., 6.","DOI":"10.1088\/2058-9565\/abcfcd"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Carney, D., Hook, A., Liu, Z., Taylor, J.M., and Zhao, Y. (2021). Ultralight dark matter detection with mechanical quantum sensors. New J. Phys., 23.","DOI":"10.1088\/1367-2630\/abd9e7"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Rider, A.D., Moore, D.C., Blakemore, C.P., Louis, M., Lu, M., and Gratta, G. (2016). Search for Screened Interactions Associated with Dark Energy Below the 100 \u03bcm Length Scale. Phys. Rev. Lett., 117.","DOI":"10.1103\/PhysRevLett.117.101101"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Carlesso, M., Bassi, A., Paternostro, M., and Ulbricht, H. (2019). Testing the gravitational field generated by a quantum superposition. New J. Phys., 21.","DOI":"10.1088\/1367-2630\/ab41c1"},{"key":"ref_31","unstructured":"Carlesso, M., Paternostro, M., Ulbricht, H., and Bassi, A. (2021). When Cavendish meets Feynman: A quantum torsion balance for testing the quantumness of gravity. Phys. Rev. D, 103."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Fadeev, P., Wang, T., Band, Y., Budker, D., Graham, P.W., Sushkov, A.O., and Kimball, D.F.J. (2021). Gravity Probe Spin: Prospects for measuring general-relativistic precession of intrinsic spin using a ferromagnetic gyroscope. Phys. Rev. D, 103.","DOI":"10.1103\/PhysRevD.103.044056"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Vinante, A., Carlesso, M., Bassi, A., Chiasera, A., Varas, S., Falferi, P., Margesin, B., Mezzena, R., and Ulbricht, H. (2020). Narrowing the Parameter Space of Collapse Models with Ultracold Layered Force Sensors. Phys. Rev. Lett., 125.","DOI":"10.1103\/PhysRevLett.125.100404"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Riedel, C.J. (2013). Direct detection of classically undetectable dark matter through quantum decoherence. Phys. Rev. D, 88.","DOI":"10.1103\/PhysRevD.88.116005"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Bateman, J., McHardy, I., Merle, A., Morris, T.R., and Ulbricht, H. (2015). On the existence of low-mass dark matter and its direct detection. Sci. Rep., 5.","DOI":"10.1038\/srep08058"},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Riedel, C.J., and Yavin, I. (2017). Decoherence as a way to measure extremely soft collisions with dark matter. Phys. Rev. D, 96.","DOI":"10.1103\/PhysRevD.96.023007"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Bateman, J., Nimmrichter, S., Hornberger, K., and Ulbricht, H. (2014). Near-field interferometry of a free-falling nanoparticle from a point-like source. Nat. Commun., 5.","DOI":"10.1038\/ncomms5788"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Belenchia, A., Gasbarri, G., Kaltenbaek, R., Ulbricht, H., and Paternostro, M. (2019). Talbot-Lau effect beyond the point-particle approximation. Phys. Rev. A, 100.","DOI":"10.1103\/PhysRevA.100.033813"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Wan, C., Scala, M., Morley, G., Rahman, A.A., Ulbricht, H., Bateman, J., Barker, P., Bose, S., and Kim, M. (2016). Free nano-object Ramsey interferometry for large quantum superpositions. Phys. Rev. Lett., 117.","DOI":"10.1103\/PhysRevLett.117.143003"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Stickler, B.A., Papendell, B., Kuhn, S., Schrinski, B., Millen, J., Arndt, M., and Hornberger, K. (2018). Probing macroscopic quantum superpositions with nanorotors. New J. Phys., 20.","DOI":"10.1088\/1367-2630\/aaece4"},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Carlesso, M., Paternostro, M., Ulbricht, H., Vinante, A., and Bassi, A. (2018). Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics. New J. Phys., 20.","DOI":"10.1088\/1367-2630\/aad863"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Millen, J., and Stickler, B.A. (2020). Quantum experiments with microscale particles. Contemp. Phys., 61.","DOI":"10.1080\/00107514.2020.1854497"},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Grossardt, A., Bateman, J., Ulbricht, H., and Bassi, A. (2016). Optomechanical test of the Schr\u00f6dinger-Newton equation. Phys. Rev. D, 93.","DOI":"10.1103\/PhysRevD.93.096003"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Bassi, A., Grossardt, A., and Ulbricht, H. (2017). Gravitational decoherence. Class. Quantum Gravity, 34.","DOI":"10.1088\/1361-6382\/aa864f"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Bahrami, M., Smirne, A., and Bassi, A. (2014). Role of gravity in the collapse of a wave function: A probe into the Di\u00f3si-penrose model. Phys. Rev. A, 90.","DOI":"10.1103\/PhysRevA.90.062105"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/BF02105068","article-title":"On Gravity\u2019s role in Quantum State Reduction","volume":"28","author":"Penrose","year":"1996","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"873","DOI":"10.1007\/s10701-013-9763-z","article-title":"On the gravitization of quantum mechanics 2: Conformal cyclic cosmology","volume":"44","author":"Penrose","year":"2014","journal-title":"Found. Phys."},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Di\u00f3si, L. (1989). Models for universal reduction of macroscopic quantum fluctuations. Phys. Rev. A, 40.","DOI":"10.1103\/PhysRevA.40.1165"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Hu, B.L., and Verdaguer, E. (2008). Stochastic gravity: Theory and applications. Living Rev. Relativ., 11.","DOI":"10.12942\/lrr-2008-3"},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Hu, B.L., Roura, A., and Verdaguer, E. (2004). Induced quantum metric fluctuations and the validity of semiclassical gravity. Phys. Rev. D, 70.","DOI":"10.1103\/PhysRevD.70.044002"},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Roura, A., and Verdaguer, E. (2008). Cosmological perturbations from stochastic gravity. Phys. Rev. D, 78.","DOI":"10.1103\/PhysRevD.78.064010"},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Fr\u00f6b, M.B., Roura, A., and Verdaguer, E. (2012). One-loop gravitational wave spectrum in de Sitter spacetime. J. Cosmol. Astropart. Phys., 1208.","DOI":"10.1088\/1475-7516\/2012\/08\/009"},{"key":"ref_53","doi-asserted-by":"crossref","unstructured":"Bose, S., Mazumdar, A., Morley, G.W., Ulbricht, H., Toro\u0161, M., Paternostro, M., Geraci, A.A., Barker, P.F., Kim, M., and Milburn, G. (2017). Spin entanglement witness for quantum gravity. Phys. Rev. Lett., 119.","DOI":"10.1103\/PhysRevLett.119.240401"},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Belenchia, A., Wald, R.M., Giacomini, F., Castro-Ruiz, E., Brukner, \u010c., and Aspelmeyer, M. (2018). Quantum superposition of massive objects and the quantization of gravity. Phys. Rev. D, 98.","DOI":"10.1103\/PhysRevD.98.126009"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Belenchia, A., Benincasa, D.M., Liberati, S., Marin, F., Marino, F., and Ortolan, A. (2016). Testing quantum gravity induced nonlocality via optomechanical quantum oscillators. Phys. Rev. Lett., 116.","DOI":"10.1103\/PhysRevLett.116.161303"},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Belenchia, A., Benincasa, D., Marin, F., Marino, F., Ortolan, A., Paternostro, M., and Liberati, S. (2019). Tests of Quantum Gravity-Induced Non-Locality: Hamiltonian formulation of a non-local harmonic oscillator. Class. Quantum Gravity, 36.","DOI":"10.1088\/1361-6382\/ab2c0a"},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1038\/nphys3366","article-title":"Universal decoherence due to gravitational time dilation","volume":"11","author":"Pikovski","year":"2015","journal-title":"Nat. Phys."},{"key":"ref_58","unstructured":"Toro\u0161, M., Grossardt, A., and Bassi, A. (2017). Quantum mechanics for non-inertial observers. arXiv."},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Roura, A. (2020). Gravitational Redshift in Quantum-Clock Interferometry. Phys. Rev. X, 10.","DOI":"10.1103\/PhysRevX.10.021014"},{"key":"ref_60","doi-asserted-by":"crossref","unstructured":"Fink, M., Rodriguez-Aramendia, A., Handsteiner, J., Ziarkash, A., Steinlechner, F., Scheidl, T., Fuentes, I., Pienaar, J., Ralph, T.C., and Ursin, R. (2017). Experimental test of photonic entanglement in accelerated reference frames. Nat. Commun., 8.","DOI":"10.1038\/ncomms15304"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Restuccia, S., Toro\u0161, M., Gibson, G.M., Ulbricht, H., Faccio, D., and Padgett, M.J. (2019). Photon bunching in a rotating reference frame. Phys. Rev. Lett., 123.","DOI":"10.1103\/PhysRevLett.123.110401"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Toro\u0161, M., Restuccia, S., Gibson, G.M., Cromb, M., Ulbricht, H., Padgett, M., and Faccio, D. (2020). Revealing and concealing entanglement with noninertial motion. Phys. Rev. A, 101.","DOI":"10.1103\/PhysRevA.101.043837"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1086\/161130","article-title":"A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis","volume":"270","author":"Milgrom","year":"1983","journal-title":"Astrophys. J."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Zwicky, F. (1937). On the Masses of Nebulae and of Clusters of Nebulae. Astrophys. J., 86.","DOI":"10.1086\/143864"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Brouwer, M.M., Oman, K.A., Valentijn, E.A., Bilicki, M., Heymans, C., Hoekstra, H., Napolitano, N.R., Roy, N., Tortora, C., and Wright, A.H. (2021). The weak lensing radial acceleration relation: Constraining modified gravity and cold dark matter theories with KiDS-1000. Astron. Astrophys., 650.","DOI":"10.1051\/0004-6361\/202040108"},{"key":"ref_66","doi-asserted-by":"crossref","unstructured":"Milgrom, M. (2021). MOND fiducial specific angular momentum of disc galaxies. Phys. Rev. D, 104.","DOI":"10.1103\/PhysRevD.104.064030"},{"key":"ref_67","doi-asserted-by":"crossref","unstructured":"Gundlach, J.H., Schlamminger, S., Spitzer, C.D., Choi, K.Y., Woodahl, B.A., Coy, J.J., and Fischbach, E. (2007). Laboratory test of Newton\u2019s second law for small accelerations. Phys. Rev. Lett., 98.","DOI":"10.1103\/PhysRevLett.98.150801"},{"key":"ref_68","doi-asserted-by":"crossref","unstructured":"Little, S., and Little, M. (2014). Laboratory test of Newtons law of gravity for small accelerations. Class. Quantum Gravity, 31.","DOI":"10.1088\/0264-9381\/31\/19\/195008"},{"key":"ref_69","doi-asserted-by":"crossref","unstructured":"Klein, N. (2020). Evidence for modified Newtonian dynamics from Cavendish-type gravitational constant experiments. Class. Quantum Gravity, 37.","DOI":"10.1088\/1361-6382\/ab6cab"},{"key":"ref_70","doi-asserted-by":"crossref","unstructured":"Timberlake, C., Vinante, A., Shankar, F., Lapi, A., and Ulbricht, H. (2021). Probing modified gravity with magnetically levitated resonators. Phys. Rev. D, 104.","DOI":"10.1103\/PhysRevD.104.L101101"},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Das, S., and Patitsas, S.N. (2013). Can MOND type hypotheses be tested in a free fall laboratory environment?. Phys. Rev. D, 87.","DOI":"10.1103\/PhysRevD.87.107101"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1642\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:16:43Z","timestamp":1760145403000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/24\/11\/1642"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,11]]},"references-count":71,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["e24111642"],"URL":"https:\/\/doi.org\/10.3390\/e24111642","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,11]]}}}