Optically Hyperpolarized Materials for Levitated Optomechanics
Institut für Theoretische Physik, Albert-Einstein-Allee 11, Universität Ulm, D-89081 Ulm, Germany
Center for Integrated Quantum Science and Technology (IQST), Ulm University, Albert-Einstein-Allee 11, 89081 Ulm, Germany
| Published: | 2025-12-03, volume 9, page 1928 |
| Editor: | Roohollah Ghobadi |
| Eprint: | arXiv:2405.13869v2 |
| Doi: | https://doi.org/10.22331/q-2025-12-03-1928 |
| Citation: | Quantum 9, 1928 (2025). |
Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.
Abstract
We explore the potential of levitating solids embedded with non-permanent, optically controllable electron spins, which can be used to hyperpolarize their nuclear spin environment with exceptionally long lifetimes. For example, pentacene-doped naphthalene, which will also serve as our prime example, can achieve bulk polarization exceeding $80\,\%$ at cryogenic temperatures with polarization lifetimes extending over weeks. These materials make a compelling case for applications such as matter-wave interferometry and novel uses of established NMR techniques. In that spirit, we design a multi-spin Stern-Gerlach-type interferometry protocol which, thanks to the homogeneous spin distribution and the absence of a preferential nuclear-spin quantization axis in such materials, avoids many of the limitations associated with solid state crystals hosting electronic spin defects, such as nanodiamonds containing NV centers. We assess the potential of our interferometer to enhance existing bounds on the free parameters of objective collapse models. Beyond matter-wave interferometry, we analyze the prospects for implementing magic angle spinning at frequencies surpassing the current standard in NMR, capitalizing on the exceptional rotational capabilities offered by levitation. Additionally, we outline a novel protocol for measuring spin ensemble polarization via the position of the nanoparticle and conduct an analysis of dominant noise sources, benchmarking the required isolation levels for various applications.

Featured image: A diamagnetically levitated naphthalene particle follows an oscillatory trajectory in a magnetic field gradient, where the nuclear spin state determines its equilibrium position. By preparing a superposition of different spin states, one can create a spatially delocalized state of a solid containing billions of atoms. The displaced Gaussian wave packets rephase after one full trap period. This constitutes the basis of the spin-dependent matter-wave interferometer. The nuclear spins originate from the hydrogen atoms in naphthalene, the molecular structure of which is shown on the right.
Popular summary
Building on this platform, we propose for the first time to levitate optically hyperpolarized materials that contain electron spins, which can be controlled with laser light and microwaves. These electron spins can be used to polarize the surrounding nuclear spins in the crystal. In materials like pentacene-doped naphthalene, this results in remarkably high nuclear-spin polarization, over 80%, that can remain stable for weeks. This combination of long-lived internal spin degrees of freedom and mechanical isolation creates a unique hybrid system.
In this theoretical work, we investigate both the opportunities and the challenges offered by this hybrid platform, and propose using it as a multi-spin matter-wave interferometer inspired by the Stern–Gerlach effect, in which the particle’s wavefunction is split in space depending on its spin. Such an interferometer could serve as a powerful probe of the foundations of physics, potentially placing much stronger bounds than existing technologies on alternative models that modify quantum mechanics at macroscopic scales, including so-called collapse models.
► BibTeX data
► References
[1] Y. Quan, B. van den Brandt, J. Kohlbrecher, W.Th. Wenckebach and P. Hautle, Nuclear Instruments and Methods in Physics Research Section A, 921 22–26 (2019), 10.1016/j.nima.2018.12.047.
https://doi.org/10.1016/j.nima.2018.12.047
[2] E. R. ANDREW, A. BRADBURY and R. G. EADES, Nature, 182 1659–1659 (1958), 10.1038/1821659a0.
https://doi.org/10.1038/1821659a0
[3] Jacek W. Hennel and Jacek Klinowski, Topics in Current Chemistry (2004), 10.1007/b98646.
https://doi.org/10.1007/b98646
[4] Marcel Schuck, Daniel Steinert, Thomas Nussbaumer and Johann W. Kolar, Science Advances, 4 e170151 (2018), 10.1126/sciadv.1701519.
https://doi.org/10.1126/sciadv.1701519
[5] P. S. Bassi, N. K. Sharma and M. K. Sharma, Crystal Research and Technology, 18 1191–1197 (1983), 10.1002/crat.2170180922.
https://doi.org/10.1002/crat.2170180922
[6] Vadim E. Zorin, Steven P. Brown and Paul Hodgkinson, The Journal of Chemical Physics, 125 144508 (2006), 10.1063/1.2357602.
https://doi.org/10.1063/1.2357602
[7] K. Tennakone and M. G. C. Peiris, American Journal of Physics, 46 418–419 (1978), 10.1119/1.11338.
https://doi.org/10.1119/1.11338
[8] William M. Haynes, CRC Handbook of Chemistry and Physics, (2014), 10.1201/b17118.
https://doi.org/10.1201/b17118
[9] Yoshihiko Arita, Andrew W. McKinley, Michael Mazilu, Halina Rubinsztein-Dunlop and Kishan Dholakia, Analytical Chemistry, 83 8855–8858 (2011), 10.1021/ac2024365.
https://doi.org/10.1021/ac2024365
[10] Yoshihiko Arita, Michael Mazilu and Kishan Dholakia, Nature Communications, 4 2374 (2013), 10.1038/ncomms3374.
https://doi.org/10.1038/ncomms3374
[11] S. Bhagavantam, Proceedings of the Royal Society of London. Series A, 124 545–554 (1929), 10.1098/rspa.1929.0137.
https://doi.org/10.1098/rspa.1929.0137
[12] Nimmrichter, Stefan, Hornberger, Klaus and Hammerer, Klemens, Physical Review Letters, 113 020405 (2014), 10.1103/physrevlett.113.020405.
https://doi.org/10.1103/physrevlett.113.020405
[13] Ghirardi, G. C., Rimini, A. and Weber, T., Physical Review D, 34 470–491 (1986), 10.1103/physrevd.34.470.
https://doi.org/10.1103/physrevd.34.470
[14] Romero-Isart, Oriol, Physical Review A, 84 052121 (2011), 10.1103/physreva.84.052121.
https://doi.org/10.1103/physreva.84.052121
[15] Schlosshauer, Maximilian A., Springer Berlin Heidelberg, (2010), https://doi.org/10.1007/978-3-540-35775-9.
https://doi.org/10.1007/978-3-540-35775-9
[16] THOMSON, G. P. and REID, A., Nature, 119 890–890 (1927), 10.1038/119890a0.
https://doi.org/10.1038/119890a0
[17] Rauch, Helmut and Werner, Samuel A., Oxford University Press, (2015), 10.1093/acprof:oso/9780198712510.001.0001.
https://doi.org/10.1093/acprof:oso/9780198712510.001.0001
[18] Rasel, Ernst M., Oberthaler, Markus K., Batelaan, Herman, Schmiedmayer, Jörg and Zeilinger, Anton, Physical Review Letters, 75 2633–2637 (1995), 10.1103/physrevlett.75.2633.
https://doi.org/10.1103/physrevlett.75.2633
[19] Hall, D. S., Matthews, M. R., Wieman, C. E. and Cornell, E. A., Physical Review Letters, 81 1543–1546 (1998), 10.1103/physrevlett.81.1543.
https://doi.org/10.1103/physrevlett.81.1543
[20] Arndt, Markus, Nairz, Olaf, Vos-Andreae, Julian, Keller, Claudia, van der Zouw, Gerbrand and Zeilinger, Anton, Nature, 401 680–682 (1999), 10.1038/44348.
https://doi.org/10.1038/44348
[21] Eibenberger, Sandra, Gerlich, Stefan, Arndt, Markus, Mayor, Marcel and Tüxen, Jens, Physical Chemistry Chemical Physics, 15 14696 (2013), 10.1039/c3cp51500a.
https://doi.org/10.1039/c3cp51500a
[22] Fein, Yaakov Y., Geyer, Philipp, Zwick, Patrick, KiaÅ‚ka, Filip, Pedalino, Sebastian, Mayor, Marcel, Gerlich, Stefan and Arndt, Markus, Nature Physics, 15 1242–1245 (2019), 10.1038/s41567-019-0663-9.
https://doi.org/10.1038/s41567-019-0663-9
[23] Delić, UroÅ¡, Reisenbauer, Manuel, Dare, Kahan, Grass, David, Vuletić, Vladan, Kiesel, Nikolai and Aspelmeyer, Markus, Science, 367 892–895 (2020), 10.1126/science.aba3993.
https://doi.org/10.1126/science.aba3993
[24] Millen, James, Monteiro, Tania S, Pettit, Robert and Vamivakas, A Nick, Reports on Progress in Physics, 83 026401 (2020), 10.1088/1361-6633/ab6100.
https://doi.org/10.1088/1361-6633/ab6100
[25] Gonzalez-Ballestero, Carlos, Aspelmeyer, Markus, Novotny, Lucas, Quidant, Roman and Romero-Isart, Oriol, Science, 374 168 (2021), 10.1126/science.abg3027.
https://doi.org/10.1126/science.abg3027
[26] Rademacher, Markus, Millen, James and Li, Ying Lia, Advanced Optical Technologies, 9 227–239 (2019), 10.1515/aot-2020-0019.
https://doi.org/10.1515/aot-2020-0019
[27] Qvarfort, Sofia, Serafini, Alessio, Barker, P. F. and Bose, Sougato, Nature Communications, 9 (2018), 10.1038/s41467-018-06037-z.
https://doi.org/10.1038/s41467-018-06037-z
[28] Mancini, S., Man’ko, V. I. and Tombesi, P., Physical Review A, 55 3042–3050 (1997), 10.1103/physreva.55.3042.
https://doi.org/10.1103/physreva.55.3042
[29] Bose, S., Jacobs, K. and Knight, P. L., Physical Review A, 59 3204–3210 (1999), 10.1103/physreva.59.3204.
https://doi.org/10.1103/physreva.59.3204
[30] Marshall, William, Simon, Christoph, Penrose, Roger and Bouwmeester, Dik, Physical Review Letters, 91 130401 (2003), 10.1103/physrevlett.91.130401.
https://doi.org/10.1103/physrevlett.91.130401
[31] Arndt, Markus and Hornberger, Klaus, Nature Physics, 10 271–277 (2014), 10.1038/nphys2863.
https://doi.org/10.1038/nphys2863
[32] Bonvin, Eric, Devaud, Louisiane, Rossi, Massimiliano, Militaru, Andrei, Dania, Lorenzo, Bykov, Dmitry S., Romero-Isart, Oriol, Northup, Tracy E., Novotny, Lukas and Frimmer, Martin, arXiv:2312.13111.
arXiv:2312.13111
[33] Weiss, T., Roda-Llordes, M., Torrontegui, E., Aspelmeyer, M. and Romero-Isart, O., Physical Review Letters, 127 023601 (2021), 10.1103/physrevlett.127.023601.
https://doi.org/10.1103/physrevlett.127.023601
[34] Cosco, F., Pedernales, J. S. and Plenio, M. B., Physical Review A, 103 l061501 (2021), 10.1103/physreva.103.l061501.
https://doi.org/10.1103/physreva.103.l061501
[35] Marshman, Ryan J., Mazumdar, Anupam, Folman, Ron and Bose, Sougato, Physical Review Research, 4 023087 (2022), 10.1103/physrevresearch.4.023087.
https://doi.org/10.1103/physrevresearch.4.023087
[36] Scala, M., Kim, M. S., Morley, G. W., Barker, P. F. and Bose, S., Physical Review Letters, 111 180403 (2013), 10.1103/physrevlett.111.180403.
https://doi.org/10.1103/physrevlett.111.180403
[37] Yin, Zhang-qi, Li, Tongcang, Zhang, Xiang and Duan, L. M., Physical Review A, 88 033614 (2013), 10.1103/physreva.88.033614.
https://doi.org/10.1103/physreva.88.033614
[38] Eichhorn, T. R., Haag, M., van den Brandt, B., Hautle, P. and Wenckebach, W.Th., Chemical Physics Letters, 555 296–299 (2013), 10.1016/j.cplett.2012.11.007.
https://doi.org/10.1016/j.cplett.2012.11.007
[39] Can, T.V., Ni, Q.Z. and Griffin, R.G., Journal of Magnetic Resonance, 253 23–35 (2015), 10.1016/j.jmr.2015.02.005.
https://doi.org/10.1016/j.jmr.2015.02.005
[40] Eichhorn, T. R., Brandt, B. van den, Hautle, P., Henstra, A. and Wenckebach, W. Th., Molecular Physics, 112 1773–1782 (2013), 10.1080/00268976.2013.863405.
https://doi.org/10.1080/00268976.2013.863405
[41] Henstra, A., Lin, T.-S., Schmidt, J. and Wenckebach, W.Th., Chemical Physics Letters, 165 6–10 (1990), 10.1016/0009-2614(90)87002-9.
https://doi.org/10.1016/0009-2614(90)87002-9
[42] Rudolph, Henning, Schäfer, Jonas, Stickler, Benjamin A. and Hornberger, Klaus, Physical Review A, 103 043514 (2021), 10.1103/physreva.103.043514.
https://doi.org/10.1103/physreva.103.043514
[43] Komatsu, Koichi, Murata, Yasujiro, Sugita, Nobuyuki, Takeuchi, Ken’ichi and Wan, Terence S.M., Tetrahedron Letters, 34 8473–8476 (1993), 10.1016/s0040-4039(00)61362-x.
https://doi.org/10.1016/s0040-4039(00)61362-x
[44] Downs, C. R., Industrial and Engineering Chemistry, 32 1294–1298 (1940), 10.1021/ie50370a004.
https://doi.org/10.1021/ie50370a004
[45] Wang, Zerong, John Wiley & Sons, Inc, (2010), 10.1002/9780470638859.
https://doi.org/10.1002/9780470638859
[46] Dash, Smruti Rekha, Sarkar, Ritwik and Bhattacharyya, Santanu, Ceramics International, 41 3775–3790 (2015), 10.1016/j.ceramint.2014.11.053.
https://doi.org/10.1016/j.ceramint.2014.11.053
[47] B. D. Wood, S. Bose and G. W. Morley, Physical Review A, 105 012824 (2021), 10.1103/PhysRevA.105.012824.
https://doi.org/10.1103/PhysRevA.105.012824
[48] Berry, Michael Victor, Proceedings of the Royal Society of London. Series A, 452 1207–1220 (1996), 10.1098/rspa.1996.0062.
https://doi.org/10.1098/rspa.1996.0062
[49] Gov, S., Shtrikman, S. and Thomas, H., Physica D: Nonlinear Phenomena, 126 214–224 (1999), 10.1016/s0167-2789(98)00282-6.
https://doi.org/10.1016/s0167-2789(98)00282-6
[50] Marti, Lea, Şahin Solmaz, Nergiz, Kern, Michal, Chu, Anh, Farsi, Reza, Hengel, Philipp, Gao, Jialiang, Alaniva, Nicholas, Urban, Michael A., Gunzenhauser, Ronny, Däpp, Alexander, Klose, Daniel, Anders, Jens, Boero, Giovanni, Novotny, Lukas, Frimmer, Martin and Barnes, Alexander B., Journal of Magnetic Resonance Open, 18 100145 (2024), 10.1016/j.jmro.2023.100145.
https://doi.org/10.1016/j.jmro.2023.100145
[51] Lea Marti and Nergiz Åžahin Solmaz, Journal of Magnetic Resonance Open, 18 100145 (2024), https://doi.org/10.1016/j.jmro.2023.100145.
https://doi.org/10.1016/j.jmro.2023.100145
[52] Reimann, René, Doderer, Michael, Hebestreit, Erik, Diehl, Rozenn, Frimmer, Martin, Windey, Dominik, Tebbenjohanns, Felix and Novotny, Lukas, Physical Review Letters, 121 033602 (2018), 10.1103/physrevlett.121.033602.
https://doi.org/10.1103/physrevlett.121.033602
[53] Yuanbin Jin, Jiangwei Yan, Shah Jee Rahman, Jie Li, Xudong Yu and Jing Zhang, Photon. Res., 9 1344–1350 (2021), 10.1364/PRJ.422975.
https://doi.org/10.1364/PRJ.422975
[54] Monteiro, Fernando, Ghosh, Sumita, van Assendelft, Elizabeth C. and Moore, David C., Phys. Rev. A, 97 051802 (2018), 10.1103/PhysRevA.97.051802.
https://doi.org/10.1103/PhysRevA.97.051802
[55] Nishiyama, Yusuke, Hou, Guangjin, Agarwal, Vipin, Su, Yongchao and Ramamoorthy, Ayyalusamy, Chemical Reviews, 123 918-988 (2023), 10.1021/acs.chemrev.2c00197.
https://doi.org/10.1021/acs.chemrev.2c00197
[56] RůžiÄka, KvÄ›toslav, Fulem, Michal and RůžiÄka, Vlastimil, Journal of Chemical & Engineering Data, 50 1956-1970 (2005), 10.1021/je050216m.
https://doi.org/10.1021/je050216m
[57] Oddershede, Jette and Larsen, Sine, The Journal of Physical Chemistry A, 108 1057–1063 (2004), 10.1021/jp036186g.
https://doi.org/10.1021/jp036186g
[58] Bateman, James, Nimmrichter, Stefan, Hornberger, Klaus and Ulbricht, Hendrik, Nature Communications, 5 4788 (2014), 10.1038/ncomms5788.
https://doi.org/10.1038/ncomms5788
[59] Hicks, J. F. G., Journal of the American Chemical Society, 60 1000–1004 (1938), 10.1021/ja01272a005.
https://doi.org/10.1021/ja01272a005
[60] Chirico, R.D, Knipmeyer, S.E and Steele, W.V, The Journal of Chemical Thermodynamics, 34 1873–1884 (2002), 10.1016/s0021-9614(02)00262-8.
https://doi.org/10.1016/s0021-9614(02)00262-8
[61] Schwoerer, Markus and Wolf, Hans Christoph, The Journal of Chemical Thermodynamics, 34 1873–1884 (2002), 10.1016/s0021-9614(02)00262-8.
https://doi.org/10.1016/s0021-9614(02)00262-8
[62] Schwoerer, Markus and Wolf, Hans Christoph, Wiley-VCH, Berlin, (2006), 10.1002/9783527618651.
https://doi.org/10.1002/9783527618651
[63] Port, H. and Rund, D., Journal of Molecular Structure, 45 455–464 (1978), 10.1016/0022-2860(78)87089-6.
https://doi.org/10.1016/0022-2860(78)87089-6
[64] Bohren, Craig F. and Huffman, Donald R., Wiley, (1998), 10.1002/9783527618156.
https://doi.org/10.1002/9783527618156
[65] Haag, M., van den Brandt, B., Eichhorn, T. R., Hautle, P. and Wenckebach, W.Th., Nuclear Instruments and Methods in Physics Research Section A, 678 91–97 (2012), 10.1016/j.nima.2012.03.014.
https://doi.org/10.1016/j.nima.2012.03.014
[66] Eichhorn, Tim R., Parker, Anna J., Josten, Felix, Müller, Christoph, Scheuer, Jochen, Steiner, Jakob M., Gierse, Martin, Handwerker, Jonas, Keim, Michael, Lucas, Sebastian, Qureshi, Mohammad Usman, Marshall, Alastair, Salhov, Alon, Quan, Yifan, Binder, Jan, Jahnke, Kay D., Neumann, Philipp, Knecht, Stephan, Blanchard, John W., Plenio, Martin B., Jelezko, Fedor, Emsley, Lyndon, Vassiliou, Christophoros C., Hautle, Patrick and Schwartz, Ilai, Journal of the American Chemical Society, 144 2511–2519 (2022), 10.1021/jacs.1c09119.
https://doi.org/10.1021/jacs.1c09119
[67] Eills, James, Budker, Dmitry, Cavagnero, Silvia, Chekmenev, Eduard Y., Elliott, Stuart J., Jannin, Sami, Lesage, Anne, Matysik, Jörg, Meersmann, Thomas, Prisner, Thomas, Reimer, Jeffrey A., Yang, Hanming and Koptyug, Igor V., Chemical Reviews, 123 1417–1551 (2023), 10.1021/acs.chemrev.2c00534.
https://doi.org/10.1021/acs.chemrev.2c00534
[68] Schwartz, Ilai, Scheuer, Jochen, Tratzmiller, Benedikt, Müller, Samuel, Chen, Qiong, Dhand, Ish, Wang, Zhen-Yu, Müller, Christoph, Naydenov, Boris, Jelezko, Fedor and Plenio, Martin B., Science Advances, 4 eaat8978 (2018), 10.1126/sciadv.aat8978.
https://doi.org/10.1126/sciadv.aat8978
[69] Sangtawesin, S, McLellan, C A, Myers, B A, Jayich, A C Bleszynski, Awschalom, D D and Petta, J R, New Journal of Physics, 18 083016 (2016), 10.1088/1367-2630/18/8/083016.
https://doi.org/10.1088/1367-2630/18/8/083016
[70] Sarkar, Sambeda, Purusottam, Rudra N., Kumar, Ashutosh and Khaneja, Navin, Journal of Magnetic Resonance, 328 107002 (2021), 10.1016/j.jmr.2021.107002.
https://doi.org/10.1016/j.jmr.2021.107002
[71] Vershovskii, A. K. and Dmitriev, A. K., Technical Physics, 65 1301–1306 (2020), 10.1134/s1063784220080216.
https://doi.org/10.1134/s1063784220080216
[72] Martinetz, Lukas, Hornberger, Klaus, Millen, James, Kim, M. S. and Stickler, Benjamin A., npj Quantum Information, 6 101 (2020), 10.1038/s41534-020-00333-7.
https://doi.org/10.1038/s41534-020-00333-7
[73] Vinante, A., Carlesso, M., Bassi, A., Chiasera, A., Varas, S., Falferi, P., Margesin, B., Mezzena, R. and Ulbricht, H., Physical Review Letters, 125 100404 (2020), 10.1103/physrevlett.125.100404.
https://doi.org/10.1103/physrevlett.125.100404
[74] Carlesso, Matteo, Paternostro, Mauro, Ulbricht, Hendrik, Vinante, Andrea and Bassi, Angelo, New Journal of Physics, 20 083022 (2018), 10.1088/1367-2630/aad863.
https://doi.org/10.1088/1367-2630/aad863
[75] Helou, Bassam, Slagmolen, B. J. J., McClelland, David E. and Chen, Yanbei, Physical Review D, 95 084054 (2017), 10.1103/physrevd.95.084054.
https://doi.org/10.1103/physrevd.95.084054
[76] Donadi, Sandro, Piscicchia, Kristian, Del Grande, Raffaele, Curceanu, Catalina, Laubenstein, Matthias and Bassi, Angelo, The European Physical Journal C, 81 773 (2021), 10.1140/epjc/s10052-021-09556-0.
https://doi.org/10.1140/epjc/s10052-021-09556-0
[77] Arnquist, I. J., Avignone, F. T., Barabash, A. S., Barton, C. J., Bhimani, K. H., Blalock, E., Bos, B., Busch, M., Buuck, M., Caldwell, T. S., Chan, Y-D., Christofferson, C. D., Chu, P.-H., Clark, M. L., Cuesta, C., Detwiler, J. A., Efremenko, Yu., Ejiri, H., Elliott, S. R., Giovanetti, G. K., Green, M. P., Gruszko, J., Guinn, I. S., Guiseppe, V. E., Haufe, C. R., Henning, R., Hervas Aguilar, D., Hoppe, E. W., Hostiuc, A., Kim, I., Kouzes, R. T., Lannen V., T. E., Li, A., Lopez, A. M., López-Castaño, J. M., Martin, E. L., Martin, R. D., Massarczyk, R., Meijer, S. J., Oli, T. K., Othman, G., Paudel, L. S., Pettus, W., Poon, A. W. P., Radford, D. C., Reine, A. L., Rielage, K., Ruof, N. W., Tedeschi, D., Varner, R. L., Vasilyev, S., Wilkerson, J. F., Wiseman, C., Xu, W., Yu, C.-H. and Zhu, B. X., Physical Review Letters, 129 080401 (2022), 10.1103/physrevlett.129.080401.
https://doi.org/10.1103/physrevlett.129.080401
[78] ToroÅ¡, Marko, Gasbarri, Giulio and Bassi, Angelo, Physics Letters A, 381 3921–3927 (2017), 10.1016/j.physleta.2017.10.002.
https://doi.org/10.1016/j.physleta.2017.10.002
[79] Carlesso, Matteo, Bassi, Angelo, Falferi, Paolo and Vinante, Andrea, Physical Review D, 94 124036 (2016), 10.1103/physrevd.94.124036.
https://doi.org/10.1103/physrevd.94.124036
[80] Adler, Stephen L, Journal of Physics A: Mathematical and Theoretical, 40 13501–13501 (2007), 10.1088/1751-8121/40/44/c01.
https://doi.org/10.1088/1751-8121/40/44/c01
[81] Bassi, Angelo, Lochan, Kinjalk, Satin, Seema, Singh, Tejinder P. and Ulbricht, Hendrik, Reviews of Modern Physics, 85 471–527 (2013), 10.1103/revmodphys.85.471.
https://doi.org/10.1103/revmodphys.85.471
[82] Pearle, Philip, Physical Review A, 39 2277–2289 (1989), 10.1103/physreva.39.2277.
https://doi.org/10.1103/physreva.39.2277
[83] Ghirardi, Gian Carlo, Pearle, Philip and Rimini, Alberto, Physical Review A, 42 78–89 (1990), 10.1103/physreva.42.78.
https://doi.org/10.1103/physreva.42.78
[84] Magrini, Lorenzo, Rosenzweig, Philipp, Bach, Constanze, Deutschmann-Olek, Andreas, Hofer, Sebastian G., Hong, Sungkun, Kiesel, Nikolai, Kugi, Andreas and Aspelmeyer, Markus, Nature, 595 373–377 (2021), 10.1038/s41586-021-03602-3.
https://doi.org/10.1038/s41586-021-03602-3
[85] Dania, Lorenzo, Heidegger, Katharina, Bykov, Dmitry S., Cerchiari, Giovanni, Araneda, Gabriel and Northup, Tracy E., Physical Review Letters, 129 013601 (2022), 10.1103/physrevlett.129.013601.
https://doi.org/10.1103/physrevlett.129.013601
[86] Ashkin, A., Phys. Rev. Lett., 24 156–159 (1970), 10.1103/PhysRevLett.24.156.
https://doi.org/10.1103/PhysRevLett.24.156
[87] Romero-Isart, Oriol, Juan, Mathieu L, Quidant, Romain and Cirac, J Ignacio, New Journal of Physics, 12 033015 (2010), 10.1088/1367-2630/12/3/033015.
https://doi.org/10.1088/1367-2630/12/3/033015
[88] D. E. Chang, C. A. Regal, S. B. Papp, D. J. Wilson, J. Ye, O. Painter, H. J. Kimble and P. Zoller, Proceedings of the National Academy of Sciences, 107 1005-1010 (2010), 10.1073/pnas.0912969107.
https://doi.org/10.1073/pnas.0912969107
[89] Barker, P. F. and Shneider, M. N., Phys. Rev. A, 81 023826 (2010), 10.1103/PhysRevA.81.023826.
https://doi.org/10.1103/PhysRevA.81.023826
[90] Magrini, Lorenzo, Rosenzweig, Philipp, Bach, Constanze, Deutschmann-Olek, Andreas, Hofer, Sebastian G., Hong, Sungkun, Kiesel, Nikolai, Kugi, Andreas and Aspelmeyer, Markus, Nature, 595 373–377 (2021), 10.1038/s41586-021-03602-3.
https://doi.org/10.1038/s41586-021-03602-3
[91] Tebbenjohanns, Felix, Mattana, M. Luisa, Rossi, Massimiliano, Frimmer, Martin and Novotny, Lukas, Nature, 595 378–382 (2021), 10.1038/s41586-021-03617-w.
https://doi.org/10.1038/s41586-021-03617-w
[92] Aspelmeyer, Markus, Kippenberg, Tobias J. and Marquardt, Florian, Rev. Mod. Phys., 86 1391–1452 (2014), 10.1103/RevModPhys.86.1391.
https://doi.org/10.1103/RevModPhys.86.1391
[93] Ahn, Jonghoon, Xu, Zhujing, Bang, Jaehoon, Deng, Yu-Hao, Hoang, Thai M., Han, Qinkai, Ma, Ren-Min and Li, Tongcang, Phys. Rev. Lett., 121 033603 (2018), 10.1103/PhysRevLett.121.033603.
https://doi.org/10.1103/PhysRevLett.121.033603
[94] Ahn, Jonghoon, Xu, Zhujing, Bang, Jaehoon, Ju, Peng, Gao, Xingyu and Li, Tongcang, Nature Nanotechnology, 15 89–93 (2020), 10.1038/s41565-019-0605-9.
https://doi.org/10.1038/s41565-019-0605-9
[95] Stefan Kuhn, Alon Kosloff, Benjamin A. Stickler, Fernando Patolsky, Klaus Hornberger, Markus Arndt and James Millen, Optica, 4 356–360 (2017), 10.1364/OPTICA.4.000356.
https://doi.org/10.1364/OPTICA.4.000356
[96] Stickler, Benjamin A., Hornberger, Klaus and Kim, M. S., Nature Reviews Physics, 3 589–597 (2021), 10.1038/s42254-021-00335-0.
https://doi.org/10.1038/s42254-021-00335-0
[97] Neukirch, Levi P., von Haartman, Eva, Rosenholm, Jessica M. and Nick Vamivakas, A., Nature Photonics, 9 653–657 (2015), 10.1038/nphoton.2015.162.
https://doi.org/10.1038/nphoton.2015.162
[98] Hoang, Thai M., Ahn, Jonghoon, Bang, Jaehoon and Li, Tongcang, Nature Communications, 7 12250 (2016), 10.1038/ncomms12250.
https://doi.org/10.1038/ncomms12250
[99] Conangla, Gerard P., Schell, Andreas W. and Rica, Raú, Nano Letters, 18 3956–3961 (2018), 10.1021/acs.nanolett.8b01414.
https://doi.org/10.1021/acs.nanolett.8b01414
[100] Gieseler, J., Kabcenell, A., Rosenfeld, E., Schaefer, J. D., Safira, A., Schuetz, M. J. A., Gonzalez-Ballestero, C., Rusconi, C. C., Romero-Isart, O. and Lukin, M. D., Phys. Rev. Lett., 124 163604 (2020), 10.1103/PhysRevLett.124.163604.
https://doi.org/10.1103/PhysRevLett.124.163604
[101] Vinante, A., Falferi, P., Gasbarri, G., Setter, A., Timberlake, C. and Ulbricht, H., Phys. Rev. Appl., 13 064027 (2020), 10.1103/PhysRevApplied.13.064027.
https://doi.org/10.1103/PhysRevApplied.13.064027
[102] Wang, Tao, Lourette, Sean, O'Kelley, Sean R., Kayci, Metin, Band, Y.B., Kimball, Derek F. Jackson, Sushkov, Alexander O. and Budker, Dmitry, Phys. Rev. Appl., 11 044041 (2019), 10.1103/PhysRevApplied.11.044041.
https://doi.org/10.1103/PhysRevApplied.11.044041
[103] C. D. Brown, Y. Wang, M. Namazi, G. I. Harris, M. T. Uysal and J. G. E. Harris, Physical Review Letters, 130 216001 (2023), https://doi.org/10.1103/PhysRevLett.130.216001.
https://doi.org/10.1103/PhysRevLett.130.216001
[104] Perdriat, M., Huillery, P., Pellet-Mary, C. and Hétet, G., Phys. Rev. Lett., 128 117203 (2022), 10.1103/PhysRevLett.128.117203.
https://doi.org/10.1103/PhysRevLett.128.117203
[105] Pellet-Mary, C., Huillery, P., Perdriat, M. and Hétet, G., Phys. Rev. B, 104 L100411 (2021), 10.1103/PhysRevB.104.L100411.
https://doi.org/10.1103/PhysRevB.104.L100411
[106] Delord, T., Huillery, P., Nicolas, L. and Hétet, Nature, 580 56–59 (2020), 10.1038/s41586-020-2133-z.
https://doi.org/10.1038/s41586-020-2133-z
[107] Scala, M., Kim, M. S., Morley, G. W., Barker, P. F. and Bose, S., Phys. Rev. Lett., 111 180403 (2013), 10.1103/PhysRevLett.111.180403.
https://doi.org/10.1103/PhysRevLett.111.180403
[108] Wan, C., Scala, M., Morley, G. W., Rahman, ATM. A., Ulbricht, H., Bateman, J., Barker, P. F., Bose, S. and Kim, M. S., Phys. Rev. Lett., 117 143003 (2016), 10.1103/PhysRevLett.117.143003.
https://doi.org/10.1103/PhysRevLett.117.143003
[109] Pedernales, Julen S., Morley, Gavin W. and Plenio, Martin B., Phys. Rev. Lett., 125 023602 (2020), 10.1103/PhysRevLett.125.023602.
https://doi.org/10.1103/PhysRevLett.125.023602
[110] Streltsov, Kirill, Pedernales, Julen S. and Plenio, Martin B., Phys. Rev. Lett., 126 193602 (2021), 10.1103/PhysRevLett.126.193602.
https://doi.org/10.1103/PhysRevLett.126.193602
[111] Pedernales, J. S., Cosco, F. and Plenio, M. B., Phys. Rev. Lett., 125 090501 (2020), 10.1103/PhysRevLett.125.090501.
https://doi.org/10.1103/PhysRevLett.125.090501
[112] Albrecht, Andreas, Retzker, Alex and Plenio, Martin B, Physical Review A, 90 033834 (2014), 10.1103/PhysRevA.90.033834.
https://doi.org/10.1103/PhysRevA.90.033834
[113] March, James E, Wood, Benjamin D, Stephen, Colin J and Fervenza, Laura Durán, Physical Review Applied, 20 044045 (2023), 10.1103/PhysRevApplied.20.044045.
https://doi.org/10.1103/PhysRevApplied.20.044045
[114] Pedernales, Julen S and Plenio, Martin B, Contemporary Physics, 64 147–163 (2023), https://doi.org/10.1080/00107514.2023.2286074.
https://doi.org/10.1080/00107514.2023.2286074
[115] Kenneth G. Libbrecht and Eric D. Black, Physics Letters A, 321 99-102 (2004), https://doi.org/10.1016/j.physleta.2003.12.022.
https://doi.org/10.1016/j.physleta.2003.12.022
[116] Levitt, Malcolm H., Progress in Nuclear Magnetic Resonance Spectroscopy, 18 61–122 (1986), 10.1016/0079-6565(86)80005-x.
https://doi.org/10.1016/0079-6565(86)80005-x
[117] Levitt, Malcolm H., Encyclopedia of Magnetic Resonance, (2007), 10.1002/9780470034590.emrstm0086.
https://doi.org/10.1002/9780470034590.emrstm0086
[118] Tsuji, Koji and Yamada, Haruka, The Journal of Physical Chemistry, 76 260–269 (1972), 10.1021/j100646a021.
https://doi.org/10.1021/j100646a021
[119] Deimling, M, Brunner, H, Dinse, K.P, Hausser, K.H and Colpa, J.P, Journal of Magnetic Resonance (1969), 39 185–202 (1980), 10.1016/0022-2364(80)90128-6.
https://doi.org/10.1016/0022-2364(80)90128-6
[120] Miyanishi, Koichiro, Segawa, Takuya F., Takeda, Kazuyuki, Ohki, Izuru, Onoda, Shinobu, Ohshima, Takeshi, Abe, Hiroshi, Takashima, Hideaki, Takeuchi, Shigeki, Shames, Alexander I., Morita, Kohki, Wang, Yu, So, Frederick T.-K., Terada, Daiki, Igarashi, Ryuji, Kagawa, Akinori, Kitagawa, Masahiro, Mizuochi, Norikazu, Shirakawa, Masahiro and Negoro, Makoto, Magnetic Resonance, 2 33–48 (2021), 10.5194/mr-2-33-2021.
https://doi.org/10.5194/mr-2-33-2021
[121] Iinuma, M., Takahashi, Y., Shaké, I., Oda, M., Masaike, A., Yabuzaki, T. and Shimizu, H. M., Physical Review Letters, 84 171–174 (2000), 10.1103/physrevlett.84.171.
https://doi.org/10.1103/physrevlett.84.171
[122] Van Strien, A.J. and Schmidt, J., Chemical Physics Letters, 70 513–517 (1980), 10.1016/0009-2614(80)80115-1.
https://doi.org/10.1016/0009-2614(80)80115-1
[123] Sakamoto, Keita, Hamachi, Tomoyuki, Miyokawa, Katsuki, Tateishi, Kenichiro, Uesaka, Tomohiro, Kurashige, Yuki and Yanai, Nobuhiro, Proceedings of the National Academy of Sciences, 120 e2307926120 (2023), 10.1073/pnas.2307926120.
https://doi.org/10.1073/pnas.2307926120
[124] Sellner, S, Besirli, M, Bohman, M, Borchert, M J, Harrington, J, Higuchi, T, Mooser, A, Nagahama, H, Schneider, G, Smorra, C, Tanaka, T, Blaum, K, Matsuda, Y, Ospelkaus, C, Quint, W, Walz, J, Yamazaki, Y and Ulmer, S, New Journal of Physics, 19 083023 (2017), 10.1088/1367-2630/aa7e73.
https://doi.org/10.1088/1367-2630/aa7e73
[125] Wasielewski, Michael R., Forbes, Malcolm D. E., Frank, Natia L., Kowalski, Karol, Scholes, Gregory D., Yuen-Zhou, Joel, Baldo, Marc A., Freedman, Danna E., Goldsmith, Randall H., Goodson, Theodore, Kirk, Martin L., McCusker, James K., Ogilvie, Jennifer P., Shultz, David A., Stoll, Stefan and Whaley, K. Birgitta, Nature Reviews Chemistry, 4 490–504 (2020), 10.1038/s41570-020-0200-5.
https://doi.org/10.1038/s41570-020-0200-5
[126] Pedernales, Julen S. and Plenio, Martin B., Phys. Rev. A, 105 063313 (2022), 10.1103/PhysRevA.105.063313.
https://doi.org/10.1103/PhysRevA.105.063313
[127] Faltermeier, Daniel, Gompf, Bruno, Dressel, Martin, Tripathi, Ashutosh K. and Pflaum, Jens, Physical Review B, 74 125416 (2006), 10.1103/physrevb.74.125416.
https://doi.org/10.1103/physrevb.74.125416
[128] Naito, Tomoya, Suzuki, Tomoaki and Ikezoe, Yasuhiro, Applied Physics Letters, 125 (2024), 10.1063/5.0241203.
https://doi.org/10.1063/5.0241203
[129] Rusconi, C. C., Pöchhacker, V., Cirac, J. I. and Romero-Isart, O., Physical Review B, 96 134419 (2017), 10.1103/physrevb.96.134419.
https://doi.org/10.1103/physrevb.96.134419
[130] Rugar, D., Budakian, R., Mamin, H. J. and Chui, B. W., Nature, 430 329–332 (2004), 10.1038/nature02658.
https://doi.org/10.1038/nature02658
[131] Nicholas, J.V., Chemical Physics Letters, 82 225–228 (1981), 10.1016/0009-2614(81)85144-5.
https://doi.org/10.1016/0009-2614(81)85144-5
Cited by
[1] M. Rademacher, A. Pontin, J.M.H. Gosling, P.F. Barker, and M. Toroš, "Roto-translational levitated optomechanics", Physics Reports 1187, 1 (2026).
[2] Adrian Mena, Nicholas P. Sloane, Max R. Bonengel, Cameron M. Gould, Scott A. Sulway, and Dane R. McCamey, "Spatially‐Resolved Coherence of Organic Molecular Spins at Room‐Temperature", Advanced Functional Materials 36 62, e76752 (2026).
[3] Robert Smit, Boleslaw Kozankiewicz, and Michel Orrit, "Phosphorescence detection as the first step toward all-optical spin manipulation in single perylene molecules", Physical Review Research 8 2, 023111 (2026).
[4] Sneha Narasimha Moorthy and Anupam Mazumdar, "Magnetic noise in macroscopic quantum spatial superposition induced by an inverted harmonic oscillator potential", Physical Review A 113 1, 012419 (2026).
[5] Trinidad B. Lantaño, Luciano Petruzziello, Susana F. Huelga, and Martin B. Plenio, "Angular Momentum Entanglement Mediated By General Relativistic Frame Dragging", Quantum 10, 2042 (2026).
[6] Vanessa Wachter, Silvia Viola Kusminskiy, Gabriel Hétet, and Benjamin A. Stickler, "Gyroscopically Stabilized Quantum Spin Rotors", Physical Review Letters 136 7, 073604 (2026).
[7] Sougato Bose, Anupam Mazumdar, Roger Penrose, Ivette Fuentes, Marko Toroš, Ron Folman, Gerard J. Milburn, Myungshik Kim, Adrian Kent, A. T. M. Anishur Rahman, Cyril Laplane, Aaron Markowitz, Debarshi Das, Ethan Campos-Méndez, Eva Kilian, David Groswasser, Menachem Givon, Or Dobkowski, Peter Skakunenko, Maria Muretova, Yonathan Japha, Naor Levi, Omer Feldman, Damián Pitalúa-García, Jonathan M. H. Gosling, Ka-Di Zhu, Marco Genovese, Kia Romero-Hojjati, Ryan J. Marshman, Markus Rademacher, Martine Schut, Melanie Bautista-Cruz, Qian Xiang, Stuart M. Graham, James E. March, William J. Fairbairn, Karishma S. Gokani, Joseph Aziz, Richard Howl, Run Zhou, Ryan Rizaldy, Thiago Guerreiro, Tian Zhou, Jason Twamley, Chiara Marletto, Vlatko Vedral, Jonathan Oppenheim, Mauro Paternostro, Hendrik Ulbricht, Peter F. Barker, Thomas P. Purdy, M. V. Gurudev Dutt, Andrew A. Geraci, David C. Moore, and Gavin W. Morley, "A Spin-Based Pathway to Testing the Quantum Nature of Gravity", arXiv:2509.01586, (2025).
[8] Jonas Schäfer, Benjamin A. Stickler, and Klaus Hornberger, "Decoherence of dielectric particles by thermal emission", Physical Review Research 6 4, 043307 (2024).
[9] Stefan Nimmrichter, Dennis Rätzel, Isobel C. Bicket, Michael S. Seifner, and Philipp Haslinger, "Electron-Enabled Nanoparticle Diffraction", Physical Review Letters 135 17, 173601 (2025).
[10] Burak Gurlek, Shubham Sharma, Paolo Lazzaroni, Angel Rubio, and Mariana Rossi, "Accurate machine learning interatomic potentials for polyacene molecular crystals: application to single molecule host-guest systems", npj Computational Mathematics 11 1, 318 (2025).
[11] Lorenzo Braccini, Alessio Serafini, and Sougato Bose, "Exponential Expansion of Massive Schrödinger Cats for Sensing and Entanglement", arXiv:2408.11930, (2024).
[12] Tian Zhou, Ryan Rizaldy, Martine Schut, and Anupam Mazumdar, "Spin contrast, finite temperature, and noise in matter-wave interferometers", Physical Review A 112 1, 012613 (2025).
[13] J. Voisin, A. Durand, T. Copie, M. Perdriat, and G. Hétet, "Nuclear Magnetic Resonance with a Levitating Microparticle", Physical Review Letters 133 21, 213602 (2024).
[14] Tian Zhou, Sougato Bose, and Anupam Mazumdar, "Gyroscopic stability for nanoparticles in Stern-Gerlach Interferometry and spin contrast", arXiv:2407.15813, (2024).
[15] Ryan Rizaldy, Tian Zhou, Sougato Bose, and Anupam Mazumdar, "Rotational stability in nanorotor and spin contrast in one-loop interferometry in the Stern-Gerlach setup", Physical Review Research 7 4, 043095 (2025).
[16] Burak Gurlek and Daqing Wang, "Small but large: Single organic molecules as hybrid platforms for quantum technologies", Physical Review Research 7 2, 021001 (2025).
[17] Tian Zhou, Sougato Bose, and Anupam Mazumdar, "Gyroscopic stability for nanoparticles in Stern-Gerlach interferometry and spin contrast", Physical Review A 112 1, 013315 (2025).
[18] Robert Smit, Boleslaw Kozankiewicz, and Michel Orrit, "Towards all-optical spin manipulation in single molecules: a refined region for locating a dark resonance", arXiv:2508.08835, (2025).
[19] Ryan Rizaldy, Tian Zhou, Run Zhou, and Anupam Mazumdar, "Spatial superposition for a two-dimensional matter-wave interferometer in an inverted harmonic potential with gyroscopic rotational stability", arXiv:2601.20949, (2026).
[20] Sarah K. Mann and Sam L. Bayliss, "Optically addressable molecular spin qubits", MRS Bulletin 51 3, 312 (2026).
The above citations are from Crossref's cited-by service (last updated successfully 2026-08-13 21:37:12) and SAO/NASA ADS (last updated successfully 2026-08-13 21:37:13). The list may be incomplete as not all publishers provide suitable and complete citation data.
This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.