RE S EAR CH | R E P O R T S
RE FE RENCES AND N OT ES
1. Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48, 1687–1690 (1993).
SCIENCE sciencemag.org
2. E. Farhi, S. Gutmann, Phys. Rev. A 58, 915–928 (1998). 3. S. E. Venegas-Andraca, Quantum Inf. Process. 11, 1015–1106 (2012). 4. K. Manouchehri, J. Wang, Physical Implementation of Quantum Walks (Springer-Verlag, Berlin, 2014). 5. H. Schmitz et al., Phys. Rev. Lett. 103, 090504 (2009). 6. F. Zähringer et al., Phys. Rev. Lett. 104, 100503 (2010). 7. M. Karski et al., Science 325, 174–177 (2009). 8. C. Weitenberg et al., Nature 471, 319–324 (2011). 9. T. Fukuhara et al., Nature 502, 76–79 (2013). 10. Y. Bromberg, Y. Lahini, R. Morandotti, Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009). 11. S. Aaronson, A. Arkhipov, Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (ACM Press, New York, 2011), pp. 333–342. 12. A. Peruzzo et al., Science 329, 1500–1503 (2010). 13. L. Sansoni et al., Phys. Rev. Lett. 108, 010502 (2012). 14. M. A. Broome et al., Science 339, 794–798 (2013). 15. J. B. Spring et al., Science 339, 798–801 (2013). 16. M. Tillmann et al., Nat. Photonics 7, 540–544 (2013). 17. A. Crespi et al., Nat. Photonics 7, 545–549 (2013). 18. E. Knill, R. Laflamme, G. J. Milburn, Nature 409, 46–52 (2001). 19. Y. Lahini et al., Phys. Rev. A 86, 011603 (2012). 20. A. Ahlbrecht et al., New J. Phys. 14, 073050 (2012). 21. D. L. Shepelyansky, Phys. Rev. Lett. 73, 2607–2610 (1994). 22. A. M. Childs, D. Gosset, Z. Webb, Science 339, 791–794 (2013). 23. A. Schreiber et al., Science 336, 55–58 (2012). 24. G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, Nat. Commun. 4, 1555 (2013). 25. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, M. Greiner, Nature 462, 74–77 (2009). 26. See supplementary materials on Science Online. 27. T. Hartmann, F. Keck, H. J. Korsch, S. Mossmann, New J. Phys. 6, 2 (2004). 28. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, C. Salomon, Phys. Rev. Lett. 76, 4508–4511 (1996). 29. A. Alberti, V. V. Ivanov, G. M. Tino, G. Ferrari, Nat. Phys. 5, 547–550 (2009). 30. E. Haller et al., Phys. Rev. Lett. 104, 200403 (2010).
31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.
M. Genske et al., Phys. Rev. Lett. 110, 190601 (2013). T. Jeltes et al., Nature 445, 402–405 (2007). A. M. Kaufman et al., Science 345, 306–309 (2014). S. Fölling et al., Nature 434, 481–484 (2005). M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, Rev. Mod. Phys. 83, 1405–1466 (2011). B. Paredes et al., Nature 429, 277–281 (2004). T. Kinoshita, T. Wenger, D. S. Weiss, Science 305, 1125–1128 (2004). K. Winkler et al., Nature 441, 853–856 (2006). S. Fölling et al., Nature 448, 1029–1032 (2007). R. Khomeriki, D. O. Krimer, M. Haque, S. Flach, Phys. Rev. A 81, 065601 (2010). F. Meinert et al., Science 344, 1259–1262 (2014). W. S. Dias, E. M. Nascimento, M. L. Lyra, F. A. B. F. de Moura, Phys. Rev. B 76, 155124 (2007). J. P. Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013).
AC KNOWLED GME NTS
We thank S. Aaronson, M. Endres, and M. Knap for helpful discussions. Supported by grants from NSF through the Center for Ultracold Atoms, the Army Research Office with funding from the DARPA OLE program and a MURI program, an Air Force Office of Scientific Research MURI program, the Gordon and Betty Moore Foundation’s EPiQS Initiative, the U.S. Department of Defense through the NDSEG program (M.E.T.), a NSF Graduate Research Fellowship (M.R.), and the Pappalardo Fellowship in Physics (Y.L.). SUPPLEMENTARY MATERIALS
www.sciencemag.org/content/347/6227/1229/suppl/DC1 Materials and Methods Table S1 References (44, 45) 25 August 2014; accepted 4 February 2015 10.1126/science.1260364
SYMPATHETIC COOLING
Coulomb crystallization of highly charged ions L. Schmöger,1,2 O. O. Versolato,1,2* M. Schwarz,1,2 M. Kohnen,2 A. Windberger,1 B. Piest,1 S. Feuchtenbeiner,1 J. Pedregosa-Gutierrez,3 T. Leopold,2 P. Micke,1,2 A. K. Hansen,4† T. M. Baumann,5 M. Drewsen,4 J. Ullrich,2 P. O. Schmidt,2,6 J. R. Crespo López-Urrutia1‡ Control over the motional degrees of freedom of atoms, ions, and molecules in a field-free environment enables unrivalled measurement accuracies but has yet to be applied to highly charged ions (HCIs), which are of particular interest to future atomic clock designs and searches for physics beyond the Standard Model. Here, we report on the Coulomb crystallization of HCIs (specifically 40Ar13+) produced in an electron beam ion trap and retrapped in a cryogenic linear radiofrequency trap by means of sympathetic motional cooling through Coulomb interaction with a directly laser-cooled ensemble of Be+ ions. We also demonstrate cooling of a single Ar13+ ion by a single Be+ ion—the prerequisite for quantum logic spectroscopy with a potential 10−19 accuracy level. Achieving a seven-orders-of-magnitude decrease in HCI temperature starting at megakelvin down to the millikelvin range removes the major obstacle for HCI investigation with high-precision laser spectroscopy.
M
ethods to simultaneously control both internal electronic and motional degrees of freedom of individual atoms, molecules, and low-charge-state ions in traps (1) have enabled unparalleled measurement accuracies. Prime examples include optical atomic clocks operating at an accuracy level of a few parts per 10−18 (2, 3), which is sufficient to
measure subtle effects of relativity (4), achieve sensitivity to geodesic gravitational potential differences of Earth, and set upper limits on possible temporal or spatial variations of fundamental constants (5, 6). Most laser spectroscopy work on trapped samples has explored a small class of atoms and atomic ions—namely, the hydrogen atom, the alkali/alkaline-earth atoms/ions, and a 13 MARCH 2015 • VOL 347 ISSUE 6227
1233
Downloaded from www.sciencemag.org on March 12, 2015
energetically forbidden. The two atoms preferentially propagate through the lattice together, as reflected in increasing weights on the diagonal of the correlation matrix. For the strongest interactions, the particles form a repulsively bound pair with effective single-particle behavior (38). The two-particle dynamics may be described as a quantum walk of the bound pair (19, 20) at a decreased tunneling rate Jpair , which reduces to the second-order tunneling (39) Jpair = (2J2/U) 300) starts with the formation of ellipsoidal shell structures at G = 20 (33). This gives an upper limit of 35 mK for the temperature of the Be+ plasma in Fig. 1, at which the shell structure is already quite pronounced. At the same time, the co-trapped Ar13+ ions are clearly fully crystallized, giving a value greater than 300 for the plasma coupling parameter (35). Thus, even assuming nonthermalization of the HCI with the Be+ ion ensemble (at 35 mK), the temperature of the Ar13+ ions would be below 235 mK (Eq. 1). Toward our exploration of the application of precision spectroscopy schemes to HCI, we expelled more Be+ ions until a single coolant ion was left in the trap, with its location clearly displaced from the potential minimum by a repelling dark ion that again possessed a charge state of QHCI = +13 e (Fig. 4). This is the prerequisite needed for application of quantum logic spectroscopy (36). Within this framework, a single Be+ ion can serve as the logic ion for sympathetic cooling, state preparation, and internal state detection of a HCI, enabling ultraprecise laser spectroscopy of HCIs. Our demonstration of such a two-ion crystal paves the way for exciting spectroscopic applications of HCIs, ranging from competitive optical clocks working at a projected 10−19 fractional accuracy level (10, 13) to tests of fundamental physics and varying constants, to development of qubit systems for ion trap–based quantum computing. Last, in this configuration, highest-resolution vacuum ultraviolet and x-ray spectroscopy of HCIs should become feasible at latest-generation light sources.
5. T. Rosenband et al., Science 319, 1808–1812 (2008). 6. N. Huntemann et al., arXiv:1407.4408 [physics.atom-ph] (2014). 7. D. J. Larson, J. C. Bergquist, J. J. Bollinger, W. M. Itano, D. J. Wineland, Phys. Rev. Lett. 57, 70–73 (1986). 8. M. Drewsen et al., Int. J. Mass Spectrom. 229, 83–91 (2003). 9. J. R. Crespo López-Urrutia, Z. Harman, in Fundamental Physics in Particle Traps, W. Quint, M. Vogel, Eds. (Springer, Heidelberg, Germany, 2014), pp. 315–373. 10. A. Derevianko, V. A. Dzuba, V. V. Flambaum, Phys. Rev. Lett. 109, 180801 (2012). 11. S. Bernitt et al., Nature 492, 225–228 (2012). 12. K. Schnorr et al., Astrophys. J. 776, 121 (2013). 13. M. S. Safronova et al., Phys. Rev. Lett. 113, 030801 (2014). 14. M. Zolotorev, D. Budker, Phys. Rev. Lett. 78, 4717–4720 (1997). 15. S. Sturm et al., Phys. Rev. Lett. 107, 023002 (2011). 16. J. C. Berengut, V. A. Dzuba, V. V. Flambaum, Phys. Rev. Lett. 105, 120801 (2010). 17. J. C. Berengut, V. A. Dzuba, V. V. Flambaum, A. Ong, Phys. Rev. Lett. 106, 210802 (2011). 18. L. Gruber et al., Phys. Rev. Lett. 86, 636–639 (2001). 19. Z. Andelkovic et al., Phys. Rev. A 87, 033423 (2013). 20. S. Brewer, N. Guise, J. Tan, Phys. Rev. A 88, 063403 (2013). 21. P. Blythe, B. Roth, U. Fröhlich, H. Wenz, S. Schiller, Phys. Rev. Lett. 95, 183002 (2005). 22. L. Hornekaer, N. Kjaergaard, A. M. Thommesen, M. Drewsen, Phys. Rev. Lett. 86, 1994–1997 (2001). 23. V. Mäckel, R. Klawitter, G. Brenner, J. R. Crespo López-Urrutia, J. Ullrich, Phys. Rev. Lett. 107, 143002 (2011). 24. A. Lapierre et al., Phys. Rev. Lett. 95, 183001 (2005). 25. R. S. Orts et al., Phys. Rev. Lett. 97, 103002 (2006). 26. M. Schwarz et al., Rev. Sci. Instrum. 83, 083115 (2012). 27. A. K. Hansen et al., Nature 508, 76–79 (2014). 28. L. Schmöger, thesis, Heidelberg University (2013). 29. M. Drewsen, A. Mortensen, R. Martinussen, P. Staanum, J. L. Sørensen, Phys. Rev. Lett. 93, 243201 (2004). 30. H. C. Nägerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, R. Blatt, Appl. Phys. B 66, 603–608 (1998). 31. T. P. Meyrath, D. F. V. James, Phys. Lett. A 240, 37–42 (1998). 32. S. Knünz et al., Phys. Rev. A 85, 023427 (2012). 33. D. H. Dubin, T. M. O’Neil, Phys. Rev. Lett. 60, 511–514 (1988). 34. H. Thomas et al., Phys. Rev. Lett. 73, 652–655 (1994). 35. L. Hornekær, M. Drewsen, Phys. Rev. A 66, 013412 (2002). 36. P. O. Schmidt et al., Science 309, 749–752 (2005). AC KNOWLED GME NTS
The project was supported by the Max-Planck Society and the Physikalisch-Technische Bundesanstalt. P.O.S. acknowledges the support of Deutsche Forschungsgemeinschaft through the Cluster of Excellence Quantum Engineering and Space-Time Research (QUEST). M.D. appreciates generous support through the Danish National Research Foundation Center for Quantum Optics (QUANTOP); The Danish Agency for Science, Technology and Innovation; the Carlsberg Foundation; the Lundbeck Foundation; and the European Commission under the Seventh Framework Programme FP7 GA 607491 COMIQ. J.P.-G., O.O.V., and M.S. acknowledge funding from Short-Term Scientific Missions travel grants from COST-Action IOTA. Last, the Max-Planck-Institut für Kernphysik mechanical workshops have been of crucial importance for the construction of the cryogenic traps.
SUPPLEMENTARY MATERIALS RE FERENCES AND NOTES
1. D. J. Wineland, Rev. Mod. Phys. 85, 1103–1114 (2013). 2. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, T. Rosenband, Phys. Rev. Lett. 104, 070802 (2010). 3. B. J. Bloom et al., Nature 506, 71–75 (2014). 4. C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland, Science 329, 1630–1633 (2010).
www.sciencemag.org/content/347/6227/1233/suppl/DC1 Materials and Methods Figs. S1 to S3 Reference (37) 13 November 2014; accepted 2 February 2015 10.1126/science.aaa2960
sciencemag.org SCIENCE
Coulomb crystallization of highly charged ions L. Schmöger et al. Science 347, 1233 (2015); DOI: 10.1126/science.aaa2960
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RE FE RENCES AND N OT ES
1. Y. Aharonov, L. Davidovich, N. Zagury, Phys. Rev. A 48, 1687–1690 (1993).
SCIENCE sciencemag.org
2. E. Farhi, S. Gutmann, Phys. Rev. A 58, 915–928 (1998). 3. S. E. Venegas-Andraca, Quantum Inf. Process. 11, 1015–1106 (2012). 4. K. Manouchehri, J. Wang, Physical Implementation of Quantum Walks (Springer-Verlag, Berlin, 2014). 5. H. Schmitz et al., Phys. Rev. Lett. 103, 090504 (2009). 6. F. Zähringer et al., Phys. Rev. Lett. 104, 100503 (2010). 7. M. Karski et al., Science 325, 174–177 (2009). 8. C. Weitenberg et al., Nature 471, 319–324 (2011). 9. T. Fukuhara et al., Nature 502, 76–79 (2013). 10. Y. Bromberg, Y. Lahini, R. Morandotti, Y. Silberberg, Phys. Rev. Lett. 102, 253904 (2009). 11. S. Aaronson, A. Arkhipov, Proceedings of the 43rd Annual ACM Symposium on Theory of Computing (ACM Press, New York, 2011), pp. 333–342. 12. A. Peruzzo et al., Science 329, 1500–1503 (2010). 13. L. Sansoni et al., Phys. Rev. Lett. 108, 010502 (2012). 14. M. A. Broome et al., Science 339, 794–798 (2013). 15. J. B. Spring et al., Science 339, 798–801 (2013). 16. M. Tillmann et al., Nat. Photonics 7, 540–544 (2013). 17. A. Crespi et al., Nat. Photonics 7, 545–549 (2013). 18. E. Knill, R. Laflamme, G. J. Milburn, Nature 409, 46–52 (2001). 19. Y. Lahini et al., Phys. Rev. A 86, 011603 (2012). 20. A. Ahlbrecht et al., New J. Phys. 14, 073050 (2012). 21. D. L. Shepelyansky, Phys. Rev. Lett. 73, 2607–2610 (1994). 22. A. M. Childs, D. Gosset, Z. Webb, Science 339, 791–794 (2013). 23. A. Schreiber et al., Science 336, 55–58 (2012). 24. G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, R. Osellame, Nat. Commun. 4, 1555 (2013). 25. W. S. Bakr, J. I. Gillen, A. Peng, S. Fölling, M. Greiner, Nature 462, 74–77 (2009). 26. See supplementary materials on Science Online. 27. T. Hartmann, F. Keck, H. J. Korsch, S. Mossmann, New J. Phys. 6, 2 (2004). 28. M. Ben Dahan, E. Peik, J. Reichel, Y. Castin, C. Salomon, Phys. Rev. Lett. 76, 4508–4511 (1996). 29. A. Alberti, V. V. Ivanov, G. M. Tino, G. Ferrari, Nat. Phys. 5, 547–550 (2009). 30. E. Haller et al., Phys. Rev. Lett. 104, 200403 (2010).
31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.
M. Genske et al., Phys. Rev. Lett. 110, 190601 (2013). T. Jeltes et al., Nature 445, 402–405 (2007). A. M. Kaufman et al., Science 345, 306–309 (2014). S. Fölling et al., Nature 434, 481–484 (2005). M. A. Cazalilla, R. Citro, T. Giamarchi, E. Orignac, M. Rigol, Rev. Mod. Phys. 83, 1405–1466 (2011). B. Paredes et al., Nature 429, 277–281 (2004). T. Kinoshita, T. Wenger, D. S. Weiss, Science 305, 1125–1128 (2004). K. Winkler et al., Nature 441, 853–856 (2006). S. Fölling et al., Nature 448, 1029–1032 (2007). R. Khomeriki, D. O. Krimer, M. Haque, S. Flach, Phys. Rev. A 81, 065601 (2010). F. Meinert et al., Science 344, 1259–1262 (2014). W. S. Dias, E. M. Nascimento, M. L. Lyra, F. A. B. F. de Moura, Phys. Rev. B 76, 155124 (2007). J. P. Ronzheimer et al., Phys. Rev. Lett. 110, 205301 (2013).
AC KNOWLED GME NTS
We thank S. Aaronson, M. Endres, and M. Knap for helpful discussions. Supported by grants from NSF through the Center for Ultracold Atoms, the Army Research Office with funding from the DARPA OLE program and a MURI program, an Air Force Office of Scientific Research MURI program, the Gordon and Betty Moore Foundation’s EPiQS Initiative, the U.S. Department of Defense through the NDSEG program (M.E.T.), a NSF Graduate Research Fellowship (M.R.), and the Pappalardo Fellowship in Physics (Y.L.). SUPPLEMENTARY MATERIALS
www.sciencemag.org/content/347/6227/1229/suppl/DC1 Materials and Methods Table S1 References (44, 45) 25 August 2014; accepted 4 February 2015 10.1126/science.1260364
SYMPATHETIC COOLING
Coulomb crystallization of highly charged ions L. Schmöger,1,2 O. O. Versolato,1,2* M. Schwarz,1,2 M. Kohnen,2 A. Windberger,1 B. Piest,1 S. Feuchtenbeiner,1 J. Pedregosa-Gutierrez,3 T. Leopold,2 P. Micke,1,2 A. K. Hansen,4† T. M. Baumann,5 M. Drewsen,4 J. Ullrich,2 P. O. Schmidt,2,6 J. R. Crespo López-Urrutia1‡ Control over the motional degrees of freedom of atoms, ions, and molecules in a field-free environment enables unrivalled measurement accuracies but has yet to be applied to highly charged ions (HCIs), which are of particular interest to future atomic clock designs and searches for physics beyond the Standard Model. Here, we report on the Coulomb crystallization of HCIs (specifically 40Ar13+) produced in an electron beam ion trap and retrapped in a cryogenic linear radiofrequency trap by means of sympathetic motional cooling through Coulomb interaction with a directly laser-cooled ensemble of Be+ ions. We also demonstrate cooling of a single Ar13+ ion by a single Be+ ion—the prerequisite for quantum logic spectroscopy with a potential 10−19 accuracy level. Achieving a seven-orders-of-magnitude decrease in HCI temperature starting at megakelvin down to the millikelvin range removes the major obstacle for HCI investigation with high-precision laser spectroscopy.
M
ethods to simultaneously control both internal electronic and motional degrees of freedom of individual atoms, molecules, and low-charge-state ions in traps (1) have enabled unparalleled measurement accuracies. Prime examples include optical atomic clocks operating at an accuracy level of a few parts per 10−18 (2, 3), which is sufficient to
measure subtle effects of relativity (4), achieve sensitivity to geodesic gravitational potential differences of Earth, and set upper limits on possible temporal or spatial variations of fundamental constants (5, 6). Most laser spectroscopy work on trapped samples has explored a small class of atoms and atomic ions—namely, the hydrogen atom, the alkali/alkaline-earth atoms/ions, and a 13 MARCH 2015 • VOL 347 ISSUE 6227
1233
Downloaded from www.sciencemag.org on March 12, 2015
energetically forbidden. The two atoms preferentially propagate through the lattice together, as reflected in increasing weights on the diagonal of the correlation matrix. For the strongest interactions, the particles form a repulsively bound pair with effective single-particle behavior (38). The two-particle dynamics may be described as a quantum walk of the bound pair (19, 20) at a decreased tunneling rate Jpair , which reduces to the second-order tunneling (39) Jpair = (2J2/U) 300) starts with the formation of ellipsoidal shell structures at G = 20 (33). This gives an upper limit of 35 mK for the temperature of the Be+ plasma in Fig. 1, at which the shell structure is already quite pronounced. At the same time, the co-trapped Ar13+ ions are clearly fully crystallized, giving a value greater than 300 for the plasma coupling parameter (35). Thus, even assuming nonthermalization of the HCI with the Be+ ion ensemble (at 35 mK), the temperature of the Ar13+ ions would be below 235 mK (Eq. 1). Toward our exploration of the application of precision spectroscopy schemes to HCI, we expelled more Be+ ions until a single coolant ion was left in the trap, with its location clearly displaced from the potential minimum by a repelling dark ion that again possessed a charge state of QHCI = +13 e (Fig. 4). This is the prerequisite needed for application of quantum logic spectroscopy (36). Within this framework, a single Be+ ion can serve as the logic ion for sympathetic cooling, state preparation, and internal state detection of a HCI, enabling ultraprecise laser spectroscopy of HCIs. Our demonstration of such a two-ion crystal paves the way for exciting spectroscopic applications of HCIs, ranging from competitive optical clocks working at a projected 10−19 fractional accuracy level (10, 13) to tests of fundamental physics and varying constants, to development of qubit systems for ion trap–based quantum computing. Last, in this configuration, highest-resolution vacuum ultraviolet and x-ray spectroscopy of HCIs should become feasible at latest-generation light sources.
5. T. Rosenband et al., Science 319, 1808–1812 (2008). 6. N. Huntemann et al., arXiv:1407.4408 [physics.atom-ph] (2014). 7. D. J. Larson, J. C. Bergquist, J. J. Bollinger, W. M. Itano, D. J. Wineland, Phys. Rev. Lett. 57, 70–73 (1986). 8. M. Drewsen et al., Int. J. Mass Spectrom. 229, 83–91 (2003). 9. J. R. Crespo López-Urrutia, Z. Harman, in Fundamental Physics in Particle Traps, W. Quint, M. Vogel, Eds. (Springer, Heidelberg, Germany, 2014), pp. 315–373. 10. A. Derevianko, V. A. Dzuba, V. V. Flambaum, Phys. Rev. Lett. 109, 180801 (2012). 11. S. Bernitt et al., Nature 492, 225–228 (2012). 12. K. Schnorr et al., Astrophys. J. 776, 121 (2013). 13. M. S. Safronova et al., Phys. Rev. Lett. 113, 030801 (2014). 14. M. Zolotorev, D. Budker, Phys. Rev. Lett. 78, 4717–4720 (1997). 15. S. Sturm et al., Phys. Rev. Lett. 107, 023002 (2011). 16. J. C. Berengut, V. A. Dzuba, V. V. Flambaum, Phys. Rev. Lett. 105, 120801 (2010). 17. J. C. Berengut, V. A. Dzuba, V. V. Flambaum, A. Ong, Phys. Rev. Lett. 106, 210802 (2011). 18. L. Gruber et al., Phys. Rev. Lett. 86, 636–639 (2001). 19. Z. Andelkovic et al., Phys. Rev. A 87, 033423 (2013). 20. S. Brewer, N. Guise, J. Tan, Phys. Rev. A 88, 063403 (2013). 21. P. Blythe, B. Roth, U. Fröhlich, H. Wenz, S. Schiller, Phys. Rev. Lett. 95, 183002 (2005). 22. L. Hornekaer, N. Kjaergaard, A. M. Thommesen, M. Drewsen, Phys. Rev. Lett. 86, 1994–1997 (2001). 23. V. Mäckel, R. Klawitter, G. Brenner, J. R. Crespo López-Urrutia, J. Ullrich, Phys. Rev. Lett. 107, 143002 (2011). 24. A. Lapierre et al., Phys. Rev. Lett. 95, 183001 (2005). 25. R. S. Orts et al., Phys. Rev. Lett. 97, 103002 (2006). 26. M. Schwarz et al., Rev. Sci. Instrum. 83, 083115 (2012). 27. A. K. Hansen et al., Nature 508, 76–79 (2014). 28. L. Schmöger, thesis, Heidelberg University (2013). 29. M. Drewsen, A. Mortensen, R. Martinussen, P. Staanum, J. L. Sørensen, Phys. Rev. Lett. 93, 243201 (2004). 30. H. C. Nägerl, W. Bechter, J. Eschner, F. Schmidt-Kaler, R. Blatt, Appl. Phys. B 66, 603–608 (1998). 31. T. P. Meyrath, D. F. V. James, Phys. Lett. A 240, 37–42 (1998). 32. S. Knünz et al., Phys. Rev. A 85, 023427 (2012). 33. D. H. Dubin, T. M. O’Neil, Phys. Rev. Lett. 60, 511–514 (1988). 34. H. Thomas et al., Phys. Rev. Lett. 73, 652–655 (1994). 35. L. Hornekær, M. Drewsen, Phys. Rev. A 66, 013412 (2002). 36. P. O. Schmidt et al., Science 309, 749–752 (2005). AC KNOWLED GME NTS
The project was supported by the Max-Planck Society and the Physikalisch-Technische Bundesanstalt. P.O.S. acknowledges the support of Deutsche Forschungsgemeinschaft through the Cluster of Excellence Quantum Engineering and Space-Time Research (QUEST). M.D. appreciates generous support through the Danish National Research Foundation Center for Quantum Optics (QUANTOP); The Danish Agency for Science, Technology and Innovation; the Carlsberg Foundation; the Lundbeck Foundation; and the European Commission under the Seventh Framework Programme FP7 GA 607491 COMIQ. J.P.-G., O.O.V., and M.S. acknowledge funding from Short-Term Scientific Missions travel grants from COST-Action IOTA. Last, the Max-Planck-Institut für Kernphysik mechanical workshops have been of crucial importance for the construction of the cryogenic traps.
SUPPLEMENTARY MATERIALS RE FERENCES AND NOTES
1. D. J. Wineland, Rev. Mod. Phys. 85, 1103–1114 (2013). 2. C. W. Chou, D. B. Hume, J. C. J. Koelemeij, D. J. Wineland, T. Rosenband, Phys. Rev. Lett. 104, 070802 (2010). 3. B. J. Bloom et al., Nature 506, 71–75 (2014). 4. C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland, Science 329, 1630–1633 (2010).
www.sciencemag.org/content/347/6227/1233/suppl/DC1 Materials and Methods Figs. S1 to S3 Reference (37) 13 November 2014; accepted 2 February 2015 10.1126/science.aaa2960
sciencemag.org SCIENCE
Coulomb crystallization of highly charged ions L. Schmöger et al. Science 347, 1233 (2015); DOI: 10.1126/science.aaa2960
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