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Ion Coulomb crystals: An exotic form of condensed matter
Rev. Mod. Phys. 98, 035001 – Published 5 August, 2026
DOI: https://doi.org/10.1103/tn8k-r4w8
Abstract
Ion Coulomb crystals are ordered structures formed by laser-cooled ions in traps that are characterized by interparticle distances of several micrometers and energy scales on the order of . Their crystalline structure emerges from the interplay between Coulomb repulsion and the external confining potential, which can be readily tuned. Moreover, individual ions can be precisely manipulated with lasers and imaged via resonance fluorescence. These unusual and unique properties make ion crystals a powerful platform for studying phases of matter in the strongly correlated regime and at low temperatures where their dynamics is manifestly quantum mechanical. This review examines the theoretical framework and experimental characterization of ion Coulomb crystals from a condensed-matter perspective. Their dynamical and thermodynamic properties are discussed in one, two, and three dimensions, and recent investigations into their out-of-equilibrium behavior are reviewed. An outlook on future directions for exploring novel condensed-matter phenomena with trapped-ion crystals, as well as for exploiting these features for scientific and technical applications, is provided.
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References (377)
- Abdelrahman, A., et al., 2017, Nat. Commun. 8, 15712.
- Abutbul, D., and D. Podolsky, 2022, Phys. Rev. Lett. 128, 255501.
- Anderegg, F., C. F. Driscoll, D. H. E. Dubin, and T. M. O’Neil, 2010, Phys. Plasmas 17, 055702.
- Anderegg, F., D. H. E. Dubin, T. M. O’Neil, and C. F. Driscoll, 2009, Phys. Rev. Lett. 102, 185001.
- Andrei, E. Y., G. Deville, D. C. Glattli, F. I. B. Williams, E. Paris, and B. Etienne, 1988, Phys. Rev. Lett. 60, 2765.
- Andresen, G. B., et al. (ALPHA Collaboration), 2011, Nat. Phys. 7, 558.
- Arias Espinoza, J. D., M. Mazzanti, K. Fouka, R. X. Schüssler, Z. Wu, P. Corboz, R. Gerritsma, and A. Safavi-Naini, 2021, Phys. Rev. A 104, 013302.
- Ashcroft, N. W., and N. D. Mermin, 1976, Solid State Physics (Saunders, Philadelphia).
- Baiko, D. A., 2009, Phys. Rev. E 80, 046405.
- Baiko, D. A., A. Y. Potekhin, and D. G. Yakovlev, 2001, Phys. Rev. E 64, 057402.
- Ball, H., C. D. Marciniak, R. N. Wolf, A. T.-H. Hung, K. Pyka, and M. J. Biercuk, 2019, Rev. Sci. Instrum. 90, 053103.
- Baltrusch, J. D., C. Cormick, G. De Chiara, T. Calarco, and G. Morigi, 2011, Phys. Rev. A 84, 063821.
- Baltrusch, J. D., C. Cormick, and G. Morigi, 2012, Phys. Rev. A 86, 032104.
- Baltrusch, J. D., C. Cormick, and G. Morigi, 2013, Phys. Rev. A 87, 032116.
- Baltrusch, J. D., A. Negretti, J. M. Taylor, and T. Calarco, 2011, Phys. Rev. A 83, 042319.
- Bauer, C. W., et al., 2023, PRX Quantum 4, 027001.
- Baughman, R. H., S. O. Dantas, S. Stafström, A. A. Zakhidov, T. B. Mitchell, and D. H. E. Dubin, 2000, Science 288, 2018.
- Baus, M., and J.-P. Hansen, 1980, Phys. Rep. 59, 1.
- Băzăvan, O., S. Saner, E. Tirrito, G. Araneda, R. Srinivas, and A. Bermudez, 2024, Commun. Phys. 7, 229.
- Bechinger, C., M. Brunner, and P. Leiderer, 2001, Phys. Rev. Lett. 86, 930.
- Benassi, A., A. Vanossi, and E. Tosatti, 2011, Nat. Commun. 2, 236.
- Bergeson, S. D., S. D. Baalrud, C. L. Ellison, E. Grant, F. R. Graziani, T. C. Killian, M. S. Murillo, J. L. Roberts, and L. G. Stanton, 2019, Phys. Plasmas 26, 100501.
- Bermudez, A., J. Almeida, K. Ott, H. Kaufmann, S. Ulm, U. Poschinger, F. Schmidt-Kaler, A. Retzker, and M. B. Plenio, 2012, New J. Phys. 14, 093042.
- Bermudez, A., M. Bruderer, and M. B. Plenio, 2013, Phys. Rev. Lett. 111, 040601.
- Birkl, G., S. Kassner, and H. Walther, 1992, Nature (London) 357, 310.
- Birkl, G., J. A. Yeazell, R. RÃŒckerl, and H. Walther, 1994, Europhys. Lett. 27, 197.
- Blatt, R., and C. F. Roos, 2012, Nat. Phys. 8, 277.
- Block, M., A. Drakoudis, H. Leuthner, P. Seibert, G. Werth, M. Block, A. Drakoudis, H. Leuthner, and P. Seibert, 2000, J. Phys. B 33, L375.
- Blümel, R., C. Kappler, W. Quint, and H. Walther, 1989, Phys. Rev. A 40, 808.
- Bohnet, J. G., B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, 2016, Science 352, 1297.
- Bollinger, J. J., D. J. Heinzen, F. L. Moore, W. M. Itano, D. J. Wineland, and D. H. E. Dubin, 1993, Phys. Rev. A 48, 525.
- Bollinger, J. J., T. B. Mitchell, X.-P. Huang, W. M. Itano, J. N. Tan, B. M. Jelenković, and D. J. Wineland, 2000, Phys. Plasmas 7, 7.
- Bonetti, P. M., A. Rucci, M. L. Chiofalo, and V. Vuletić, 2021, Phys. Rev. Res. 3, 013031.
- Braiman, Y., J. Baumgarten, J. Jortner, and J. Klafter, 1990, Phys. Rev. Lett. 65, 2398.
- Braun, O., and Y. Kivshar, 2004, The Frenkel-Kontorova Model: Concepts, Methods, and Applications (Springer, New York).
- Braun, O. M., Y. S. Kivshar, and I. I. Zelenskaya, 1990, Phys. Rev. B 41, 7118.
- Brewer, L. R., J. D. Prestage, J. J. Bollinger, W. M. Itano, D. J. Larson, and D. J. Wineland, 1988, Phys. Rev. A 38, 859.
- Brillouin, L., 1945, Phys. Rev. 67, 260.
- Britton, J. W., B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, 2012, Nature (London) 484, 489.
- Brown, K. R., C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, and D. J. Wineland, 2011, Nature (London) 471, 196.
- Brown, L. S., and G. Gabrielse, 1986, Rev. Mod. Phys. 58, 233.
- Brox, J., P. Kiefer, M. Bujak, T. Schaetz, and H. Landa, 2017, Phys. Rev. Lett. 119, 153602.
- Brush, S. G., H. L. Sahlin, and E. Teller, 1966, J. Chem. Phys. 45, 2102.
- Bruzewicz, C. D., J. Chiaverini, R. McConnell, and J. M. Sage, 2019, Appl. Phys. Rev. 6, 021314.
- Bubeck, R., C. Bechinger, S. Neser, and P. Leiderer, 1999, Phys. Rev. Lett. 82, 3364.
- Bylinskii, A., D. Gangloff, I. Counts, and V. Vuletić, 2016, Nat. Mater. 15, 717.
- Bylinskii, A., D. Gangloff, and V. Vuletić, 2015, Science 348, 1115.
- Calvo, F., E. Yurtsever, and D. J. Wales, 2012, J. Chem. Phys. 136, 024303.
- Campa, A., T. Dauxois, and S. Ruffo, 2009, Phys. Rep. 480, 57.
- Cartarius, F., C. Cormick, and G. Morigi, 2013, Phys. Rev. A 87, 013425.
- Casabone, B., K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, and T. E. Northup, 2015, Phys. Rev. Lett. 114, 023602.
- Cetina, M., A. Bylinskii, L. Karpa, D. Gangloff, K. M. Beck, Y. Ge, M. Scholz, A. T. Grier, I. Chuang, and V. Vuletić, 2013, New J. Phys. 15, 053001.
- Chabrier, G., N. W. Ashcroft, and H. E. DeWitt, 1992, Nature (London) 360, 48.
- Champenois, C., 2009, J. Phys. B 42, 154002.
- Champenois, C., M. Marciante, J. Pedregosa-Gutierrez, M. Houssin, M. Knoop, and M. Kajita, 2010, Phys. Rev. A 81, 043410.
- Chelpanova, O., S. P. Kelly, G. Morigi, F. Schmidt-Kaler, and J. Marino, 2023, Europhys. Lett. 143, 25002.
- Chelpanova, O., S. P. Kelly, F. Schmidt-Kaler, G. Morigi, and J. Marino, 2024, Phys. Rev. B 109, 214107.
- Chen, J.-S., S. M. Brewer, C. W. Chou, D. J. Wineland, D. R. Leibrandt, and D. B. Hume, 2017, Phys. Rev. Lett. 118, 053002.
- Chen, S.-J., and D. H. E. Dubin, 1993, Phys. Rev. Lett. 71, 2721.
- Chou, C. W., A. L. Collopy, C. Kurz, Y. Lin, M. E. Harding, P. N. Plessow, T. Fortier, S. Diddams, D. Leibfried, and D. R. Leibrandt, 2020, Science 367, 1458.
- Chu, S., 1998, Rev. Mod. Phys. 70, 685.
- Cirac, J. I., and P. Zoller, 1995, Phys. Rev. Lett. 74, 4091.
- Clark, C. B., 1958, Phys. Rev. 109, 1133.
- Cohen-Tannoudji, C. N., 1998, Rev. Mod. Phys. 70, 707.
- Cormick, C., and G. Morigi, 2012, Phys. Rev. Lett. 109, 053003.
- Cormick, C., and G. Morigi, 2013, Phys. Rev. A 87, 013829.
- Cormick, C., T. Schaetz, and G. Morigi, 2011, New J. Phys. 13, 043019.
- Cosco, F., M. Borrelli, P. Silvi, S. Maniscalco, and G. De Chiara, 2017, Phys. Rev. A 95, 063615.
- Counts, I., J. Hur, D. P. L. Aude Craik, H. Jeon, C. Leung, J. C. Berengut, A. Geddes, A. Kawasaki, W. Jhe, and V. Vuletić, 2020, Phys. Rev. Lett. 125, 123002.
- Dantan, A., J. P. Marler, M. Albert, D. Guénot, and M. Drewsen, 2010, Phys. Rev. Lett. 105, 103001.
- Davidson, R. C., 2001, Physics of Nonneutral Plasmas, 2nd ed. (Imperial College Press, London).
- Debnath, S., N. M. Linke, S.-T. Wang, C. Figgatt, K. A. Landsman, L.-M. Duan, and C. Monroe, 2018, Phys. Rev. Lett. 120, 073001.
- De Chiara, G., T. Calarco, S. Fishman, and G. Morigi, 2008, Phys. Rev. A 78, 043414.
- De Chiara, G., A. del Campo, G. Morigi, M. B. Plenio, and A. Retzker, 2010, New J. Phys. 12, 115003.
- Defenu, N., T. Donner, T. Macrì, G. Pagano, S. Ruffo, and A. Trombettoni, 2023, Rev. Mod. Phys. 95, 035002.
- Defenu, N., A. Lerose, and S. Pappalardi, 2024, Phys. Rep. 1074, 1.
- deGrassie, J. S., and J. H. Malmberg, 1977, Phys. Rev. Lett. 39, 1077.
- deGrassie, J. S., and J. H. Malmberg, 1980, Phys. Fluids 23, 63.
- del Campo, A., G. De Chiara, G. Morigi, M. B. Plenio, and A. Retzker, 2010, Phys. Rev. Lett. 105, 075701.
- del Campo, A., T. W. B. Kibble, and W. H. Zurek, 2013, J. Phys. Condens. Matter 25, 404210.
- Delfau, J.-B., C. Coste, and M. Saint Jean, 2013, Phys. Rev. E 87, 062135.
- DeWitt, H., and W. Slattery, 1999, Contrib. Plasma Phys. 39, 97.
- Diedrich, F., J. C. Bergquist, W. M. Itano, and D. J. Wineland, 1989, Phys. Rev. Lett. 62, 403.
- Diedrich, F., E. Peik, J. M. Chen, W. Quint, and H. Walther, 1987, Phys. Rev. Lett. 59, 2931.
- Ding, S., G. Maslennikov, R. Hablützel, H. Loh, and D. Matsukevich, 2017, Phys. Rev. Lett. 119, 150404.
- D’Onofrio, M., Y. Xie, A. J. Rasmusson, E. Wolanski, J. Cui, and P. Richerme, 2021, Phys. Rev. Lett. 127, 020503.
- Door, M., et al., 2025, Phys. Rev. Lett. 134, 063002.
- Dreissen, L. S., C.-H. Yeh, H. A. Fürst, K. C. Grensemann, and T. E. Mehlstäubler, 2022, Nat. Commun. 13, 7314.
- Drewsen, M., 2015, Physica B (Amsterdam) 460, 105.
- Drewsen, M., C. Brodersen, L. Hornekær, J. S. Hangst, and J. P. Schifffer, 1998, Phys. Rev. Lett. 81, 2878.
- Drewsen, M., and A. Brøner, 2000, Phys. Rev. A 62, 045401.
- Drewsen, M., I. S. Jensen, N. Kjærgaard, J. Lindballe, A. Mortensen, K. Mølhave, and D. Voigt, 2003, J. Phys. B 36, 525.
- Drewsen, M., T. Matthey, A. Mortensen, and J. P. Hansen, 2012, arXiv:1202.2544.
- Driscoll, C. F., J. H. Malmberg, and K. S. Fine, 1988, Phys. Rev. Lett. 60, 1290.
- Duan, L.-M., and C. Monroe, 2010, Rev. Mod. Phys. 82, 1209.
- Dubin, D. H. E., 1989, Phys. Rev. A 40, 1140.
- Dubin, D. H. E., 1990, Phys. Rev. A 42, 4972.
- Dubin, D. H. E., 1991, Phys. Rev. Lett. 66, 2076.
- Dubin, D. H. E., 1993, Phys. Rev. Lett. 71, 2753.
- Dubin, D. H. E., 1997, Phys. Rev. E 55, 4017.
- Dubin, D. H. E., 2013, Phys. Rev. A 88, 013403.
- Dubin, D. H. E., 2020, Phys. Plasmas 27, 102107.
- Dubin, D. H. E., and T. M. O’Neil, 1988, Phys. Rev. Lett. 60, 511.
- Dubin, D. H. E., and T. M. O’Neil, 1999, Rev. Mod. Phys. 71, 87.
- Dubin, D. H. E., and J. P. Schiffer, 1996, Phys. Rev. E 53, 5249.
- Dyson, F. J., 1953, Phys. Rev. 92, 1331.
- Dzuba, V. A., V. V. Flambaum, and A. J. Mansour, 2024, Phys. Rev. D 110, 055022.
- Earnshaw, S., 1842, Trans. Cambridge Philos. Soc. 7, 97, https://archive.org/details/transactionsofca07camb/page/96/mode/2up.
- Ejtemaee, S., and P. C. Haljan, 2013, Phys. Rev. A 87, 051401.
- Enderlein, M., T. Huber, C. Schneider, and T. Schaetz, 2012, Phys. Rev. Lett. 109, 233004.
- Enzer, D. G., et al., 2000, Phys. Rev. Lett. 85, 2466.
- Eschner, J., G. Morigi, F. Schmidt-Kaler, and R. Blatt, 2003, J. Opt. Soc. Am. B 20, 1003.
- Eschner, J., C. Raab, F. Schmidt-Kaler, and R. Blatt, 2001, Nature (London) 413, 495.
- Farouki, R. T., and S. Hamaguchi, 1993, Phys. Rev. E 47, 4330.
- Feldker, T., L. Pelzer, M. Stappel, P. Bachor, R. Steinborn, D. Kolbe, J. Walz, and F. Schmidt-Kaler, 2014, Appl. Phys. B 114, 11.
- Feng, L., W. L. Tan, A. De, A. Menon, A. Chu, G. Pagano, and C. Monroe, 2020, Phys. Rev. Lett. 125, 053001.
- Fishman, S., G. De Chiara, T. Calarco, and G. Morigi, 2008, Phys. Rev. B 77, 064111.
- Fogarty, T., C. Cormick, H. Landa, V. M. Stojanović, E. Demler, and G. Morigi, 2015, Phys. Rev. Lett. 115, 233602.
- Fogarty, T., E. Kajari, B. G. Taketani, A. Wolf, T. Busch, and G. Morigi, 2013, Phys. Rev. A 87, 050304.
- Fogarty, T., H. Landa, C. Cormick, and G. Morigi, 2016, Phys. Rev. A 94, 023844.
- Gabrielse, G., et al. (ATRAP Collaboration), 2012, Phys. Rev. Lett. 108, 113002.
- Gajewski, M., W. Li, S. Wolf, W. Hahn, C. E. Düllmann, D. Budker, G. Morigi, and F. Schmidt-Kaler, 2022, Phys. Rev. A 106, 033108.
- Gangloff, D., A. Bylinskii, I. Counts, W. Jhe, and V. Vuletić, 2015, Nat. Phys. 11, 915.
- Gangloff, D. A., A. Bylinskii, and V. Vuletić, 2020, Phys. Rev. Res. 2, 013380.
- Gann, R. C., S. Chakravarty, and G. V. Chester, 1979, Phys. Rev. B 20, 326.
- Garcia-Mata, I., O. V. Zhirov, and D. L. Shepelyansky, 2007, Eur. Phys. J. D 41, 325.
- Gärttner, M., J. G. Bohnet, A. Safavi-Naini, M. L. Wall, J. J. Bollinger, and A. M. Rey, 2017, Nat. Phys. 13, 781.
- Gebert, F., Y. Wan, F. Wolf, C. N. Angstmann, J. C. Berengut, and P. O. Schmidt, 2015, Phys. Rev. Lett. 115, 053003.
- Gerlich, D., 1992, in Advances in Chemical Physics, edited by C.-Y. Ng, M. Baer, I. Prigogine, and S. A. Rice (John Wiley & Sons, New York), pp. 1–176, 10.1002/9780470141397.ch1.
- Gerlich, D., 1995, Phys. Scr. 256.
- Ghosh, P. K., 1995, Ion Traps (Oxford University Press, New York), https://academic.oup.com/book/0/chapter/422683010/chapter-pdf/52583496/isbn-9780198539957-front-matter-part-1.pdf.
- Gilbert, S. L., J. J. Bollinger, and D. J. Wineland, 1988, Phys. Rev. Lett. 60, 2022.
- Gilmore, K. A., M. Affolter, R. J. Lewis-Swan, D. Barberena, E. Jordan, A. M. Rey, and J. J. Bollinger, 2021, Science 373, 673.
- Gong, Z.-X., G.-D. Lin, and L.-M. Duan, 2010, Phys. Rev. Lett. 105, 265703.
- Gorman, D. J., B. Hemmerling, E. Megidish, S. A. Moeller, P. Schindler, M. Sarovar, and H. Häffner, 2018, Phys. Rev. X 8, 011038.
- Gorman, D. J., P. Schindler, S. Selvarajan, N. Daniilidis, and H. Häffner, 2014, Phys. Rev. A 89, 062332.
- Grimes, C., and G. Adams, 1980, Surf. Sci. 98, 1.
- Grimm, R., M. Weidemüller, and Y. B. Ovchinnikov, 2000, Adv. At. Mol. Opt. Phys., 42, 95.
- Guo, S.-A., et al., 2024, Nature (London) 630, 613.
- Guthöhrlein, G. R., M. Keller, K. Hayasaka, W. Lange, and H. Walther, 2001, Nature (London) 414, 49.
- Häffner, H., C. Roos, and R. Blatt, 2008, Phys. Rep. 469, 155.
- Hakelberg, F., P. Kiefer, M. Wittemer, U. Warring, and T. Schaetz, 2019, Phys. Rev. Lett. 123, 100504.
- Harlander, M., R. Lechner, M. Brownnutt, R. Blatt, and W. Hänsel, 2011, Nature (London) 471, 200.
- Hasse, R. W., 1992, Phys. Rev. A 46, 5189.
- Hasse, R. W., 2003, J. Phys. B 36, 1011.
- Hasse, R. W., and V. V. Avilov, 1991, Phys. Rev. A 44, 4506.
- Hasse, R. W., and J. P. Schiffer, 1990, Ann. Phys. (N.Y.) 203, 419.
- Hausser, H. N., et al., 2025, Phys. Rev. Lett. 134, 023201.
- Hawaldar, S., P. Shahi, A. L. Carter, A. M. Rey, J. J. Bollinger, and A. Shankar, 2024, Phys. Rev. X 14, 031030.
- Haze, S., Y. Tateishi, A. Noguchi, K. Toyoda, and S. Urabe, 2012, Phys. Rev. A 85, 031401.
- Heinzen, D. J., J. J. Bollinger, F. L. Moore, W. M. Itano, and D. J. Wineland, 1991, Phys. Rev. Lett. 66, 2080.
- Hoenig, D., F. Thielemann, L. Karpa, T. Walker, A. Mohammadi, and T. Schaetz, 2023, arXiv:2306.12518.
- Hohenberg, P. C., 1967, Phys. Rev. 158, 383.
- Home, J. P., 2013, in Advances in Atomic, Molecular, and Optical Physics, Vol. 62, edited by E. Arimondo, P. R. Berman, and C. C. Lin (Academic Press, New York), pp. 231–277.
- Home, J. P., D. Hanneke, J. D. Jost, D. Leibfried, and D. J. Wineland, 2011, New J. Phys. 13, 073026.
- Horak, P., A. Dantan, and M. Drewsen, 2012, Phys. Rev. A 86, 043435.
- Hornekær, L., and M. Drewsen, 2002, Phys. Rev. A 66, 013412.
- Hornekær, L., N. Kjærgaard, A. M. Thommesen, and M. Drewsen, 2001, Phys. Rev. Lett. 86, 1994.
- Hou, P.-Y., J. J. Wu, S. D. Erickson, G. Zarantonello, A. D. Brandt, D. C. Cole, A. C. Wilson, D. H. Slichter, and D. Leibfried, 2024, Phys. Rev. X 14, 021003.
- Huang, X.-P., F. Anderegg, E. M. Hollmann, C. F. Driscoll, and T. M. O’Neil, 1997, Phys. Rev. Lett. 78, 875.
- Huang, X.-P., J. J. Bollinger, T. B. Mitchell, and W. M. Itano, 1998, Phys. Rev. Lett. 80, 73.
- Huang, X.-P., J. J. Bollinger, T. B. Mitchell, W. M. Itano, and D. H. E. Dubin, 1998, Phys. Plasmas 5, 1656.
- Huntemann, N., M. Okhapkin, B. Lipphardt, S. Weyers, C. Tamm, and E. Peik, 2012, Phys. Rev. Lett. 108, 090801.
- Ichimaru, S., 1982, Rev. Mod. Phys. 54, 1017.
- Ichimaru, S., H. Iyetomi, and S. Tanaka, 1987, Phys. Rep. 149, 91.
- Imajo, H., K. Hayasaka, R. Ohmukai, U. Tanaka, M. Watanabe, and S. Urabe, 1997, Phys. Rev. A 55, 1276.
- Itano, W. M., J. J. Bollinger, J. N. Tan, B. Jelenković, X.-P. Huang, and D. J. Wineland, 1998, Science 279, 686.
- Jain, S., J. Alonso, M. Grau, and J. P. Home, 2020, Phys. Rev. X 10, 031027.
- Jain, S., et al., 2024, Nature (London) 627, 510.
- James, D. F. V., 1998, Appl. Phys. B 66, 181.
- Jensen, M. J., T. Hasegawa, and J. J. Bollinger, 2004, Phys. Rev. A 70, 033401.
- Johanning, M., A. F. Varón, and C. Wunderlich, 2009, J. Phys. B 42, 154009.
- Johnson, W., A. Shankar, J. Zaris, J. J. Bollinger, and S. E. Parker, 2024, Phys. Rev. A 109, L021102.
- Jordan, E., K. A. Gilmore, A. Shankar, A. Safavi-Naini, J. G. Bohnet, M. J. Holland, and J. J. Bollinger, 2019, Phys. Rev. Lett. 122, 053603.
- José, J. V., L. P. Kadanoff, S. Kirkpatrick, and D. R. Nelson, 1977, Phys. Rev. B 16, 1217.
- Joshi, M. K., A. Fabre, C. Maier, T. Brydges, D. Kiesenhofer, H. Hainzer, R. Blatt, and C. F. Roos, 2020, New J. Phys. 22, 103013.
- Kahan, A., and C. Cormick, 2024, Phys. Rev. A 110, 012461.
- Kahan, A., P. Vinas, T. V. Zache, and A. Bermudez, 2025, arXiv:2512.07748.
- Kamsap, M. R., C. Champenois, J. Pedregosa-Gutierrez, S. Mahler, M. Houssin, and M. Knoop, 2017, Phys. Rev. A 95, 013413.
- Kato, A., A. Goel, R. Lee, Z. Ye, S. Karki, J. J. Liu, A. Nomerotski, and B. B. Blinov, 2022, Phys. Rev. A 105, 023101.
- Kaufmann, H., S. Ulm, G. Jacob, U. Poschinger, H. Landa, A. Retzker, M. B. Plenio, and F. Schmidt-Kaler, 2012, Phys. Rev. Lett. 109, 263003.
- Keller, J., et al., 2024, J. Phys. Conf. Ser. 2889, 012050.
- Keller, M., B. Lange, K. Hayasaka, W. Lange, and H. Walther, 2004, Nature (London) 431, 1075.
- Kibble, T., 1980, Phys. Rep. 67, 183.
- Kiesenhofer, D., H. Hainzer, A. Zhdanov, P. C. Holz, M. Bock, T. Ollikainen, and C. F. Roos, 2023, PRX Quantum 4, 020317.
- Kiethe, J., R. Nigmatullin, D. Kalincev, T. Schmirander, and T. E. Mehlstäubler, 2017, Nat. Commun. 8, 15364.
- Kiethe, J., R. Nigmatullin, T. Schmirander, D. Kalincev, and T. E. Mehlstäubler, 2018, New J. Phys. 20, 123017.
- Kiethe, J., L. Timm, H. Landa, D. Kalincev, G. Morigi, and T. E. Mehlstäubler, 2021, Phys. Rev. B 103, 104106.
- Kittel, C., 1991, Quantum Theory of Solids, 2nd ed. (Wiley, New York).
- Kjærgaard, N., and M. Drewsen, 2003, Phys. Rev. Lett. 91, 095002.
- Kortunov, I. V., S. Alighanbari, M. G. Hansen, G. S. Giri, V. I. Korobov, and S. Schiller, 2021, Nat. Phys. 17, 569.
- Kotler, S., N. Akerman, Y. Glickman, A. Keselman, and R. Ozeri, 2011, Nature (London) 473, 61.
- Koulakov, A. A., and B. I. Shklovskii, 1998, Phys. Rev. B 57, 2352.
- Krajewski, F. R., and M. H. Müser, 2004, Phys. Rev. Lett. 92, 030601.
- Kriesel, J. M., J. J. Bollinger, T. B. Mitchell, L. B. King, and D. H. E. Dubin, 2002, Phys. Rev. Lett. 88, 125003.
- Landa, H., C. Cormick, and G. Morigi, 2020, Condens. Matter 5, 35.
- Landa, H., M. Drewsen, B. Reznik, and A. Retzker, 2012a, J. Phys. A 45, 455305.
- Landa, H., M. Drewsen, B. Reznik, and A. Retzker, 2012b, New J. Phys. 14, 093023.
- Landa, H., S. Marcovitch, A. Retzker, M. B. Plenio, and B. Reznik, 2010, Phys. Rev. Lett. 104, 043004.
- Landa, H., A. Retzker, T. Schaetz, and B. Reznik, 2014, Phys. Rev. Lett. 113, 053001.
- Landa, H., B. Reznik, J. Brox, M. Mielenz, and T. Schaetz, 2013, New J. Phys. 15, 093003.
- Langin, T. K., G. M. Gorman, and T. C. Killian, 2019, Science 363, 61.
- Larson, D. J., J. C. Bergquist, J. J. Bollinger, W. M. Itano, and D. J. Wineland, 1986, Phys. Rev. Lett. 57, 70.
- Lauprêtre, T., R. B. Linnet, I. D. Leroux, H. Landa, A. Dantan, and M. Drewsen, 2019, Phys. Rev. A 99, 031401.
- Lechner, R., C. Maier, C. Hempel, P. Jurcevic, B. P. Lanyon, T. Monz, M. Brownnutt, R. Blatt, and C. F. Roos, 2016, Phys. Rev. A 93, 053401.
- Lenler-Eriksen, E., M. Drewsen, and M. Carlesso, 2024, New J. Phys. 26, 113008.
- Li, H., et al., 2024, Science 385, 86.
- Li, H.-K., et al., 2017, Phys. Rev. Lett. 118, 053001.
- Li, J., L. L. Yan, L. Chen, Z. C. Liu, F. Zhou, J. Q. Zhang, W. L. Yang, and M. Feng, 2019, Phys. Rev. A 99, 063402.
- Li, W., and I. Lesanovsky, 2012, Phys. Rev. Lett. 108, 023003.
- Li, W., S. Wolf, L. Klein, D. Budker, C. E. Dullmann, and F. Schmidt-Kaler, 2022, New J. Phys. 24, 043028.
- Lin, G.-D., and L.-M. Duan, 2011, New J. Phys. 13, 075015.
- Lin, G.-D., S.-L. Zhu, R. Islam, K. Kim, M.-S. Chang, S. Korenblit, C. Monroe, and L.-M. Duan, 2009, Europhys. Lett. 86, 60004.
- Lin, Y., J. P. Gaebler, T. R. Tan, R. Bowler, J. D. Jost, D. Leibfried, and D. J. Wineland, 2013, Phys. Rev. Lett. 110, 153002.
- Linnet, R. B., I. D. Leroux, M. Marciante, A. Dantan, and M. Drewsen, 2012, Phys. Rev. Lett. 109, 233005.
- Liu, B., and J. Goree, 2005, Phys. Rev. E 71, 046410.
- Lou, J., A. W. Sandvik, and L. Balents, 2007, Phys. Rev. Lett. 99, 207203.
- Lysne, N. K., J. F. Niedermeyer, A. C. Wilson, D. H. Slichter, and D. Leibfried, 2024, Phys. Rev. Lett. 133, 033201.
- Mallweger, M., N. Kuk, V. Shankar, R. Thomm, H. Parke, I. Straka, W. Li, I. Lesanovsky, and M. Hennrich, 2025, arXiv:2507.23631.
- Malmberg, J. H., and T. M. O’Neil, 1977, Phys. Rev. Lett. 39, 1333.
- Marshall, M. C., et al., 2025, Phys. Rev. Lett. 135, 033201.
- Martins, W. S., M. Hennrich, F. Schmidt-Kaler, and I. Lesanovsky, 2026, arXiv:2601.01626.
- Maslennikov, G., S. Ding, R. Hablützel, J. Gan, A. Roulet, S. Nimmrichter, J. Dai, V. Scarani, and D. Matsukevich, 2019, Nat. Commun. 10, 202.
- Matthey, T., J. P. Hansen, and M. Drewsen, 2003, Phys. Rev. Lett. 91, 165001.
- Mavadia, S., J. F. Goodwin, G. Stutter, S. Bharadia, D. R. Crick, D. M. Segal, and R. C. Thompson, 2013, Nat. Commun. 4, 2571.
- Mazzanti, M., R. X. Schüssler, J. D. Arias Espinoza, Z. Wu, R. Gerritsma, and A. Safavi-Naini, 2021, Phys. Rev. Lett. 127, 260502.
- McKay, K. S., D. A. Hite, P. D. Kent, S. Kotler, D. Leibfried, D. H. Slichter, A. C. Wilson, and D. P. Pappas, 2021, Phys. Rev. A 104, 052610.
- McMahon, B. J., K. R. Brown, C. D. Herold, and B. C. Sawyer, 2024, Phys. Rev. Lett. 133, 173201.
- Megidish, E., J. Broz, N. Greene, and H. Häffner, 2019, Phys. Rev. Lett. 122, 123605.
- Mehlstäubler, T. E., G. Grosche, C. Lisdat, P. O. Schmidt, and H. Denker, 2018, Rep. Prog. Phys. 81, 064401.
- Menu, R., J. Y. Malo, V. Vuletić, M. L. Chiofalo, and G. Morigi, 2024a, Phys. Rev. B 110, 155121.
- Menu, R., J. Yago Malo, V. Vuletić, M. L. Chiofalo, and G. Morigi, 2024b, Phys. Rev. B 110, 224103.
- Mermin, N. D., and H. Wagner, 1966, Phys. Rev. Lett. 17, 1133.
- Mielenz, M., J. Brox, S. Kahra, G. Leschhorn, M. Albert, T. Schaetz, H. Landa, and B. Reznik, 2013, Phys. Rev. Lett. 110, 133004.
- Mielenz, M., et al., 2016, Nat. Commun. 7, ncomms11839.
- Mihalcea, B. M., V. S. Filinov, R. A. Syrovatka, and L. M. Vasilyak, 2023, Phys. Rep. 1016, 1.
- Mitchell, T. B., J. J. Bollinger, D. H. E. Dubin, X.-P. Huang, W. M. Itano, and R. H. Baughman, 1998, Science 282.
- Mitchell, T. B., J. J. Bollinger, X.-P. Huang, and W. M. Itano, 1998, Opt. Express 2, 314.
- Mitchell, T. B., J. J. Bollinger, W. M. Itano, and D. H. E. Dubin, 2001, Phys. Rev. Lett. 87, 183001.
- Moehring, D. L., P. Maunz, S. Olmschenk, K. C. Younge, D. N. Matsukevich, L. M. Duan, and C. Monroe, 2007, Nature (London) 449, 68.
- Mølhave, K., and M. Drewsen, 2000, Phys. Rev. A 62, 011401.
- Monroe, C., D. M. Meekhof, B. E. King, S. R. Jefferts, W. M. Itano, D. J. Wineland, and P. Gould, 1995, Phys. Rev. Lett. 75, 4011.
- Monroe, C., et al., 2021, Rev. Mod. Phys. 93, 025001.
- Morigi, G., 2003, Phys. Rev. A 67, 033402.
- Morigi, G., and J. Eschner, 2001, Phys. Rev. A 64, 063407.
- Morigi, G., and J. Eschner, 2003, J. Phys. B 36, 1041.
- Morigi, G., J. Eschner, and C. H. Keitel, 2000, Phys. Rev. Lett. 85, 4458.
- Morigi, G., and S. Fishman, 2004a, Phys. Rev. E 70, 066141.
- Morigi, G., and S. Fishman, 2004b, Phys. Rev. Lett. 93, 170602.
- Morigi, G., and S. Fishman, 2006, J. Phys. B 39, S221.
- Morigi, G., and H. Walther, 2001, Eur. Phys. J. D 13, 261.
- Mortensen, A., E. Nielsen, T. Matthey, and M. Drewsen, 2006, Phys. Rev. Lett. 96, 103001.
- Mortensen, A., E. Nielsen, T. Matthey, and M. Drewsen, 2007, J. Phys. B 40, F223.
- Moses, S. A., et al., 2023, Phys. Rev. X 13, 041052.
- Murphy, T. J., and C. M. Surko, 1992, Phys. Rev. A 46, 5696.
- Nagai, T., and H. Fukuyama, 1982, J. Phys. Soc. Jpn. 51, 3431.
- Nam, Y. S., E. B. Jones, and R. Blümel, 2014, Phys. Rev. A 90, 013402.
- Nath, R., M. Dalmonte, A. W. Glaetzle, P. Zoller, F. Schmidt-Kaler, and R. Gerritsma, 2015, New J. Phys. 17, 065018.
- Niedermeyer, J. F., et al., 2025, arXiv:2512.08037.
- Nigmatullin, R., A. del Campo, G. De Chiara, G. Morigi, M. B. Plenio, and A. Retzker, 2016, Phys. Rev. B 93, 014106.
- Noguchi, A., Y. Shikano, K. Toyoda, and S. Urabe, 2014, Nat. Commun. 5, 3868.
- Ogata, S., and S. Ichimaru, 1987, Phys. Rev. A 36, 5451.
- Ohira, R., S. Kume, K. Takayama, S. Muralidharan, H. Takahashi, and K. Toyoda, 2021, Phys. Rev. A 103, 012612.
- Okada, K., T. Takayanagi, M. Wada, S. Ohtani, and H. A. Schuessler, 2009, Phys. Rev. A 80, 043405.
- Okada, K., M. Wada, T. Takayanagi, S. Ohtani, and H. A. Schuessler, 2010, Phys. Rev. A 81, 013420.
- Oshikawa, M., 2000, Phys. Rev. B 61, 3430.
- Ostendorf, A., C. B. Zhang, M. A. Wilson, D. Offenberg, B. Roth, and S. Schiller, 2006, Phys. Rev. Lett. 97, 243005.
- Pagano, G., et al., 2018, Quantum Sci. Technol. 4, 014004.
- Partner, H. L., R. Nigmatullin, T. Burgermeister, K. Pyka, J. Keller, A. Retzker, M. B. Plenio, and T. E. Mehlstäubler, 2013, New J. Phys. 15, 103013.
- Paul, W., and H. Steinwedel, 1953, Z. Naturforsch. A 8, 448.
- Pedregosa-Gutierrez, J., C. Champenois, M. R. Kamsap, G. Hagel, M. Houssin, and M. Knoop, 2018, J. Mod. Opt. 65, 529.
- Pham, J. H., J. Y. Z. Jee, A. Rischka, M. J. Biercuk, and R. N. Wolf, 2024, Adv. Quantum Technol. 7, 2400086.
- Phillips, E. S., R. J. Hendricks, A. M. Abdulla, H. Ohadi, D. R. Crick, K. Koo, D. M. Segal, and R. C. Thompson, 2008, Phys. Rev. A 78, 032307.
- Phillips, W. D., 1998, Rev. Mod. Phys. 70, 721.
- Piacente, G., F. M. Peeters, and J. J. Betouras, 2004, Phys. Rev. E 70, 036406.
- Piacente, G., I. V. Schweigert, J. J. Betouras, and F. M. Peeters, 2004, Phys. Rev. B 69, 045324.
- Podolsky, D., E. Shimshoni, G. Morigi, and S. Fishman, 2016, Phys. Rev. X 6, 031025.
- Podolsky, D., E. Shimshoni, P. Silvi, S. Montangero, T. Calarco, G. Morigi, and S. Fishman, 2014, Phys. Rev. B 89, 214408.
- Poindron, A., J. Pedregosa-Gutierrez, and C. Champenois, 2023, Phys. Rev. A 108, 013109.
- Pollock, E. L., and J. P. Hansen, 1973, Phys. Rev. A 8, 3110.
- Porras, D., and J. I. Cirac, 2004, Phys. Rev. Lett. 93, 263602.
- Potekhin, A. Y., and G. Chabrier, 2000, Phys. Rev. E 62, 8554.
- Poulsen, G., Y. Miroshnychenko, and M. Drewsen, 2012, Phys. Rev. A 86, 051402.
- Prestage, J. D., G. J. Dick, and L. Maleki, 1989, J. Appl. Phys. 66, 1013.
- Prestage, J. D., A. Williams, L. Maleki, M. J. Djomehri, and E. Harabetian, 1991, Phys. Rev. Lett. 66, 2964.
- Pruttivarasin, T., M. Ramm, I. Talukdar, A. Kreuter, and H. Häffner, 2011, New J. Phys. 13, 075012.
- Puebla, R., R. Nigmatullin, T. E. Mehlstäubler, and M. B. Plenio, 2017, Phys. Rev. B 95, 134104.
- Pyka, K., et al., 2013, Nat. Commun. 4, 2291.
- Qiao, M., et al., 2022, arXiv:2204.07283.
- Raizen, M. G., J. M. Gilligan, J. C. Bergquist, W. M. Itano, and D. J. Wineland, 1992, Phys. Rev. A 45, 6493.
- Ramm, M., T. Pruttivarasin, and H. Häffner, 2014, New J. Phys. 16, 063062.
- Retzker, A., R. C. Thompson, D. M. Segal, and M. B. Plenio, 2008, Phys. Rev. Lett. 101, 260504.
- Richerme, P., 2016, Phys. Rev. A 94, 032320.
- Richter, S., S. Wolf, J. von Zanthier, and F. Schmidt-Kaler, 2021, Phys. Rev. Lett. 126, 173602.
- Roos, C. F., A. Alberti, D. Meschede, P. Hauke, and H. Häffner, 2017, Phys. Rev. Lett. 119, 160401.
- Roos, C. F., D. Leibfried, A. Mundt, F. Schmidt-Kaler, J. Eschner, and R. Blatt, 2000, Phys. Rev. Lett. 85, 5547.
- Roos, C. F., T. Monz, K. Kim, M. Riebe, H. Häffner, D. F. V. James, and R. Blatt, 2008, Phys. Rev. A 77, 040302.
- Rosenband, T., et al., 2008, Science 319, 1808.
- Roßnagel, J., K. N. Tolazzi, F. Schmidt-Kaler, and K. Singer, 2015, New J. Phys. 17, 045004.
- Rüffert, L.-A., E. A. Dijck, L. Timm, J. R. C. López-Urrutia, and T. E. Mehlstäubler, 2024, Phys. Rev. A 110, 063110.
- Ruiz, A., D. Alonso, M. B. Plenio, and A. del Campo, 2014, Phys. Rev. B 89, 214305.
- Ruster, T., H. Kaufmann, M. A. Luda, V. Kaushal, C. T. Schmiegelow, F. Schmidt-Kaler, and U. G. Poschinger, 2017, Phys. Rev. X 7, 031050.
- Sachdev, S., 2011, Quantum Phase Transitions, 2nd ed. (Cambridge University Press, Cambridge, England).
- Safavi-Naini, A., R. J. Lewis-Swan, J. G. Bohnet, M. Gärttner, K. A. Gilmore, J. E. Jordan, J. Cohn, J. K. Freericks, A. M. Rey, and J. J. Bollinger, 2018, Phys. Rev. Lett. 121, 040503.
- Saha, S., M. Shalaev, J. O’Reilly, I. Goetting, G. Toh, A. Kalakuntla, Y. Yu, and C. Monroe, 2025, Nat. Commun. 16, 2533.
- Samanta, A., E. Shimshoni, and D. Podolsky, 2022, Phys. Rev. B 106, 035154.
- Sarkar, S., L. Franke, N. Grivas, and M. Garst, 2023, Phys. Rev. B 108, 235126.
- Sawyer, B. C., J. W. Britton, and J. J. Bollinger, 2014, Phys. Rev. A 89, 033408.
- Sawyer, B. C., J. W. Britton, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, 2012, Phys. Rev. Lett. 108, 213003.
- Schiffer, J. P., 1993, Phys. Rev. Lett. 70, 818.
- Schiffer, J. P., 2003, J. Phys. B 36, 511.
- Schiffer, J. P., M. Drewsen, J. S. Hangst, and L. Hornekaer, 2000, Proc. Natl. Acad. Sci. U.S.A. 97, 10697.
- Schindler, P., et al., 2013, New J. Phys. 15, 123012.
- Schmid, F., J. Weitenberg, J. Moreno, T. W. Hänsch, T. Udem, and A. Ozawa, 2022, Phys. Rev. A 106, L041101.
- Schmidt, J., A. Lambrecht, P. Weckesser, M. Debatin, L. Karpa, and T. Schaetz, 2018, Phys. Rev. X 8, 021028.
- Schmidt, P. O., T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, 2005, Science 309, 749.
- Schmidt-Kaler, F., J. Eschner, G. Morigi, C. F. Roos, D. Leibfried, A. Mundt, and R. Blatt, 2001, Appl. Phys. B 73, 807.
- Schmied, R., J. H. Wesenberg, and D. Leibfried, 2009, Phys. Rev. Lett. 102, 233002.
- Schneider, C., D. Porras, and T. Schaetz, 2012, Rep. Prog. Phys. 75, 024401.
- Schulz, H. J., 1993, Phys. Rev. Lett. 71, 1864.
- Schwerdt, D., et al., 2024, Phys. Rev. X 14, 041017.
- Serafini, A., A. Retzker, and M. B. Plenio, 2009, New J. Phys. 11, 023007.
- Shamai, I., and D. Podolsky, 2018, arXiv:1801.08131.
- Shankar, A., E. Jordan, K. A. Gilmore, A. Safavi-Naini, J. J. Bollinger, and M. J. Holland, 2019, Phys. Rev. A 99, 023409.
- Shankar, A., C. Tang, M. Affolter, K. Gilmore, D. H. E. Dubin, S. Parker, M. J. Holland, and J. J. Bollinger, 2020, Phys. Rev. A 102, 053106.
- Shapir, I., A. Hamo, S. Pecker, C. P. Moca, O. Legeza, G. Zarand, and S. Ilani, 2019, Science 364, 870.
- Shimshoni, E., G. Morigi, and S. Fishman, 2011a, Phys. Rev. A 83, 032308.
- Shimshoni, E., G. Morigi, and S. Fishman, 2011b, Phys. Rev. Lett. 106, 010401.
- Silvi, P., T. Calarco, G. Morigi, and S. Montangero, 2014, Phys. Rev. B 89, 094103.
- Silvi, P., G. De Chiara, T. Calarco, G. Morigi, and S. Montangero, 2013, Ann. Phys. (Berlin) 525, 827.
- Silvi, P., G. Morigi, T. Calarco, and S. Montangero, 2016, Phys. Rev. Lett. 116, 225701.
- Slattery, W. L., G. D. Doolen, and H. E. DeWitt, 1982, Phys. Rev. A 26, 2255.
- Slodička, L., G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, 2013, Phys. Rev. Lett. 110, 083603.
- Solaro, C., S. Meyer, K. Fisher, J. C. Berengut, E. Fuchs, and M. Drewsen, 2020, Phys. Rev. Lett. 125, 123003.
- Sosnova, K., A. Carter, and C. Monroe, 2021, Phys. Rev. A 103, 012610.
- Splatt, F. E., 2009, Ph.D. thesis (University of Innsbruck).
- Stenholm, S., 1986, Rev. Mod. Phys. 58, 699.
- Stern, F., 1967, Phys. Rev. Lett. 18, 546.
- Stutter, G., P. Hrmo, V. Jarlaud, M. K. Joshi, J. F. Goodwin, and R. C. Thompson, 2018, J. Mod. Opt. 65, 549.
- Szymanski, B., R. Dubessy, B. Dubost, S. Guibal, J.-P. Likforman, and L. Guidoni, 2012, Appl. Phys. Lett. 100, 171110.
- Taketani, B. G., T. Fogarty, E. Kajari, T. Busch, and G. Morigi, 2014, Phys. Rev. A 90, 012312.
- Tamura, M., T. Mukaiyama, and K. Toyoda, 2020, Phys. Rev. Lett. 124, 200501.
- Tan, J. N., J. J. Bollinger, B. Jelenkovic, and D. J. Wineland, 1995, Phys. Rev. Lett. 75, 4198.
- Tang, C., A. Shankar, D. Meiser, D. H. E. Dubin, J. J. Bollinger, and S. E. Parker, 2021, Phys. Rev. A 104, 023325.
- Tarnas, J. D., Y. S. Nam, and R. Blümel, 2013, Phys. Rev. A 88, 041401.
- Taylor, J. M., and T. Calarco, 2008, Phys. Rev. A 78, 062331.
- Thomas, H., G. E. Morfill, V. Demmel, J. Goree, B. Feuerbacher, and D. Möhlmann, 1994, Phys. Rev. Lett. 73, 652.
- Thompson, R. C., 2015, Contemp. Phys. 56, 63.
- Timm, L., L. A. Rüffert, H. Weimer, L. Santos, and T. E. Mehlstäubler, 2021, Phys. Rev. Res. 3, 043141.
- Timm, L., H. Weimer, L. Santos, and T. E. Mehlstäubler, 2020, Phys. Rev. Res. 2, 033198.
- Timm, L., H. Weimer, L. Santos, and T. E. Mehlstäubler, 2023, Phys. Rev. B 108, 134302.
- Tofful, A., et al., 2024, Metrologia 61, 045001.
- Torrisi, S. B., J. W. Britton, J. G. Bohnet, and J. J. Bollinger, 2016, Phys. Rev. A 93, 043421.
- Totsuji, H., T. Kishimoto, C. Totsuji, and K. Tsuruta, 2002, Phys. Rev. Lett. 88, 125002.
- Ulm, S., et al., 2013, Nat. Commun. 4, 2290.
- Urban, E., N. Glikin, S. Mouradian, K. Krimmel, B. Hemmerling, and H. Häffner, 2019, Phys. Rev. Lett. 123, 133202.
- [Usov, N. A., Y. B. Grebenschikov, and F. R. Ulinich, 1980, Zh. Eksp. Teor. Fiz. 78, 296 [Sov. Phys. JETP 51, 148 (1980)].
- Van Horn, H. M., 1991, Science 252, 384.
- Vanossi, A., N. Manini, M. Urbakh, S. Zapperi, and E. Tosatti, 2013, Rev. Mod. Phys. 85, 529.
- Van Winkle, D. H., and C. A. Murray, 1986, Phys. Rev. A 34, 562.
- Vogel, M., 2018, Particle Confinement in Penning Traps—An Introduction (Springer, New York).
- Vybornyi, I., L. S. Dreissen, D. Kiesenhofer, H. Hainzer, M. Bock, T. Ollikainen, D. Vadlejch, C. F. Roos, T. E. Mehlstäubler, and K. Hammerer, 2023, PRX Quantum 4, 040346.
- Waki, I., S. Kassner, G. Birkl, and H. Walther, 1992, Phys. Rev. Lett. 68, 2007.
- Wang, C.-C. J., A. C. Keith, and J. K. Freericks, 2013, Phys. Rev. A 87, 013422.
- Wang, Y., et al., 2020, Adv. Quantum Technol. 3, 2000068.
- Wigner, E., 1934, Phys. Rev. 46, 1002.
- Wineland, D. J., J. C. Bergquist, W. M. Itano, J. J. Bollinger, and C. H. Manney, 1987, Phys. Rev. Lett. 59, 2935.
- Wineland, D. J., and W. M. Itano, 1979, Phys. Rev. A 20, 1521.
- Wipfli, O., H. F. Passagem, C. Fischer, M. Grau, and J. P. Home, 2023, Rev. Sci. Instrum. 94, 083204.
- Wolf, R. N., J. H. Pham, J. Y. Z. Jee, A. Rischka, and M. J. Biercuk, 2024, Phys. Rev. Appl. 21, 054067.
- Wu, Q., Y. Shi, and J. Zhang, 2023, Phys. Rev. Res. 5, 023022.
- Wunderlich, C., G. Morigi, and D. Reiß, 2005, Phys. Rev. A 72, 023421.
- Yannouleas, C., and U. Landman, 2007, Rep. Prog. Phys. 70, 2067.
- Yin, J., and J. Javanainen, 1995, Phys. Rev. A 51, 3959.
- Zawierucha, M. J., T. Rehmert, J. Keller, T. E. Mehlstäubler, P. O. Schmidt, and F. Wolf, 2024, Phys. Rev. A 110, 013107.
- Zhang, J., B. T. Chow, S. Ejtemaee, and P. C. Haljan, 2023, npj Quantum Inf. 9, 68.
- Zurek, W. H., 1985, Nature (London) 317, 505.