Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Number-resolved detection of dark ions in Coulomb crystals

Fabian Schmid1,*, Johannes Weitenberg1, Jorge Moreno1, Theodor W. Hänsch1,2, Thomas Udem1,2, and Akira Ozawa1,†

  • 1Max-Planck-Institut für Quantenoptik, 85748 Garching, Germany
  • 2Fakultät für Physik, Ludwig-Maximilians-Universität München, 80799 München, Germany

  • *fabian.schmid@mpq.mpg.de
  • †akira.ozawa@mpq.mpg.de

Phys. Rev. A 106, L041101 – Published 4 October, 2022

DOI: https://doi.org/10.1103/PhysRevA.106.L041101

Abstract

While it is straightforward to count laser-cooled trapped ions by fluorescence imaging, detecting the number of dark ions embedded and sympathetically cooled in a mixed ion crystal is more challenging. We demonstrate a method to track the number of dark ions in real time with single-particle sensitivity. This is achieved by observing discrete steps in the amount of fluorescence emitted from the coolant ions while exciting secular motional resonances of dark ions. By counting the number of fluorescence steps, we can identify the number of dark ions without calibration and without relying on any physical model of the motional excitation. We demonstrate the scheme by detecting H2+ and H3+ ions embedded in a Be+ ion Coulomb crystal in a linear radio-frequency trap. Our method allows observing the generation and destruction of individual ions simultaneously for different types of ions. Besides high-resolution spectroscopy of dark ions, another application is the detection of chemical reactions in real time with single-particle sensitivity. This is demonstrated in this Letter.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. W. M. Itano, J. C. Bergquist, and D. J. Wineland, Early observations of macroscopic quantum jumps in single atoms, Int. J. Mass Spectrom. 377, 403 (2015).
  2. U. Eichmann, J. C. Bergquist, J. J. Bollinger, J. M. Gilligan, W. M. Itano, D. J. Wineland, and M. G. Raizen, Young's Interference Experiment with Light Scattered from Two Atoms, Phys. Rev. Lett. 70, 2359 (1993).
  3. Y. Stalgies, I. Siemers, B. Appasamy, T. Altevogt, and P. E. Toschek, The spectrum of single-atom resonance fluorescence, Europhys. Lett. 35, 259 (1996).
  4. J. Eschner, Ch. Raab, F. Schmidt-Kaler, and R. Blatt, Light interference from single atoms and their mirror images, Nature (London) 413, 495 (2001).
  5. D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Quantum dynamics of single trapped ions, Rev. Mod. Phys. 75, 281 (2003).
  6. M. Drewsen, I. Jensen, J. Lindballe, N. Nissen, R. Martinussen, A. Mortensen, P. Staanum, and D. Voigt, Ion Coulomb crystals: a tool for studying ion processes, Int. J. Mass Spectrom. 229, 83 (2003).
  7. B. Roth, P. Blythe, H. Wenz, H. Daerr, and S. Schiller, Ion-neutral chemical reactions between ultracold localized ions and neutral molecules with single-particle resolution, Phys. Rev. A 73, 042712 (2006).
  8. S. Willitsch, M. T. Bell, A. D. Gingell, S. R. Procter, and T. P. Softley, Cold Reactive Collisions between Laser-Cooled Ions and Velocity-Selected Neutral Molecules, Phys. Rev. Lett. 100, 043203 (2008).
  9. T. Yang, A. Li, G. K. Chen, C. Xie, A. G. Suits, W. C. Campbell, H. Guo, and E. R. Hudson, Optical control of reactions between water and laser-cooled Be+ ions, J. Phys. Chem. Lett. 9, 3555 (2018).
  10. M. Tomza, K. Jachymski, R. Gerritsma, A. Negretti, T. Calarco, Z. Idziaszek, and P. S. Julienne, Cold hybrid ion-atom systems, Rev. Mod. Phys. 91, 035001 (2019).
  11. S. A. Diddams, Th. Udem, J. C. Bergquist, E. A. Curtis, R. E. Drullinger, L. Hollberg, W. M. Itano, W. D. Lee, C. W. Oates, K. R. Vogel, and D. J. Wineland, An optical clock based on a single trapped Hg+199 ion, Science 293, 825 (2001).
  12. N. Huntemann, C. Sanner, B. Lipphardt, Chr. Tamm, and E. Peik, Single-Ion Atomic Clock with 3×10−18 Systematic Uncertainty, Phys. Rev. Lett. 116, 063001 (2016).
  13. R. Blatt and D. Wineland, Entangled states of trapped atomic ions, Nature (London) 453, 1008 (2008).
  14. S. Debnath, N. M. Linke, C. Figgatt, K. A. Landsman, K. Wright, and C. Monroe, Demonstration of a small programmable quantum computer with atomic qubits, Nature (London) 536, 63 (2016).
  15. I. Pogorelov, T. Feldker, C. D. Marciniak, L. Postler, G. Jacob, O. Krieglsteiner, V. Podlesnic, M. Meth, V. Negnevitsky, M. Stadler, B. Höfer, C. Wächter, K. Lakhmanskiy, R. Blatt, P. Schindler, and T. Monz, Compact ion-trap quantum computing demonstrator, PRX Quantum 2, 020343 (2021).
  16. L. Hornekær, N. Kjærgaard, A. M. Thommesen, and M. Drewsen, Structural Properties of Two-Component Coulomb Crystals in Linear Paul Traps, Phys. Rev. Lett. 86, 1994 (2001).
  17. P. Blythe, B. Roth, U. Fröhlich, H. Wenz, and S. Schiller, Production of Ultracold Trapped Molecular Hydrogen Ions, Phys. Rev. Lett. 95, 183002 (2005).
  18. S. Alighanbari, G. S. Giri, F. L. Constantin, V. I. Korobov, and S. Schiller, Precise test of quantum electrodynamics and determination of fundamental constants with HD+ ions, Nature (London) 581, 152 (2020).
  19. S. Patra, M. Germann, J.-Ph. Karr, M. Haidar, L. Hilico, V. I. Korobov, F. M. J. Cozijn, K. S. E. Eikema, W. Ubachs, and J. C. J. Koelemeij, Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level, Science 369, 1238 (2020).
  20. J. Schmidt, T. Louvradoux, J. Heinrich, N. Sillitoe, M. Simpson, J.-Ph. Karr, and L. Hilico, Trapping, Cooling, and Photodissociation Analysis of State-Selected H2+ Ions Produced by (3+1) Multiphoton Ionization, Phys. Rev. Appl. 14, 024053 (2020).
  21. I. V. Kortunov, S. Alighanbari, M. G. Hansen, G. S. Giri, V. I. Korobov, and S. Schiller, Proton-electron mass ratio by high-resolution optical spectroscopy of ion ensembles in the resolved-carrier regime, Nat. Phys. 17, 569 (2021).
  22. P. O. Schmidt, T. Rosenband, C. Langer, W. M. Itano, J. C. Bergquist, and D. J. Wineland, Spectroscopy using quantum logic, Science 309, 749 (2005).
  23. S. M. Brewer, J.-S. Chen, A. M. Hankin, E. R. Clements, C. W. Chou, D. J. Wineland, D. B. Hume, and D. R. Leibrandt, Al+27 Quantum-Logic Clock with a Systematic Uncertainty Below 10−18, Phys. Rev. Lett. 123, 033201 (2019).
  24. M. G. Kozlov, M. S. Safronova, J. R. Crespo López-Urrutia, and P. O. Schmidt, Highly charged ions: Optical clocks and applications in fundamental physics, Rev. Mod. Phys. 90, 045005 (2018).
  25. P. Micke, T. Leopold, S. A. King, E. Benkler, L. J. Spieß, L. Schmöger, M. Schwarz, J. R. Crespo López-Urrutia, and P. O. Schmidt, Coherent laser spectroscopy of highly charged ions using quantum logic, Nature (London) 578, 60 (2020).
  26. T. Baba and I. Waki, Chemical reaction of sympathetically laser-cooled molecular ions, J. Chem. Phys. 116, 1858 (2002).
  27. S. Willitsch, M. T. Bell, A. D. Gingell, and T. P. Softley, Chemical applications of laser- and sympathetically-cooled ions in ion traps, Phys. Chem. Chem. Phys. 10, 7200 (2008).
  28. F. H. J. Hall and S. Willitsch, Millikelvin Reactive Collisions between Sympathetically Cooled Molecular Ions and Laser-Cooled Atoms in an Ion-Atom Hybrid Trap, Phys. Rev. Lett. 109, 233202 (2012).
  29. K. Okada, T. Suganuma, T. Furukawa, T. Takayanagi, M. Wada, and H. A. Schuessler, Cold ion–polar-molecule reactions studied with a combined Stark-velocity-filter–ion-trap apparatus, Phys. Rev. A 87, 043427 (2013).
  30. C. Schneider, S. J. Schowalter, K. Chen, S. T. Sullivan, and E. R. Hudson, Laser-Cooling-Assisted Mass Spectrometry, Phys. Rev. Appl. 2, 034013 (2014).
  31. K. A. E. Meyer, L. L. Pollum, L. S. Petralia, A. Tauschinsky, C. J. Rennick, T. P. Softley, and B. R. Heazlewood, Ejection of Coulomb crystals from a linear Paul ion trap for ion-molecule reaction studies, J. Phys. Chem. A 119, 12449 (2015).
  32. D. Rösch, H. Gao, A. Kilaj, and S. Willitsch, Design and characterization of a linear quadrupole ion trap for high-resolution Coulomb-crystal time-of-flight mass spectrometry, EPJ Tech. Instrum. 3, 1 (2016).
  33. P. C. Schmid, J. Greenberg, M. I. Miller, K. Loeffler, and H. J. Lewandowski, An ion trap time-of-flight mass spectrometer with high mass resolution for cold trapped ion experiments, Rev. Sci. Instrum. 88, 123107 (2017).
  34. M. Germann, X. Tong, and S. Willitsch, Observation of electric-dipole-forbidden infrared transitions in cold molecular ions, Nat. Phys. 10, 820 (2014).
  35. K. Okada, M. Ichikawa, M. Wada, and H. A. Schuessler, Quasiequilibrium Characterization of Mixed-Ion Coulomb Crystals, Phys. Rev. Appl. 4, 054009 (2015).
  36. B. Roth, P. Blythe, and S. Schiller, Motional resonance coupling in cold multispecies Coulomb crystals, Phys. Rev. A 75, 023402 (2007).
  37. C. B. Zhang, D. Offenberg, B. Roth, M. A. Wilson, and S. Schiller, Molecular-dynamics simulations of cold single-species and multispecies ion ensembles in a linear Paul trap, Phys. Rev. A 76, 012719 (2007).
  38. B.-m. Ann, F. Schmid, J. Krause, T. W. Hänsch, T. Udem, and A. Ozawa, Motional resonances of three-dimensional dual-species Coulomb crystals, J. Phys. B: At., Mol. Opt. Phys. 52, 035002 (2019).
  39. J. Biesheuvel, J.-Ph. Karr, L. Hilico, K. S. E. Eikema, W. Ubachs, and J. C. J. Koelemeij, High-precision spectroscopy of the HD+ molecule at the 1-p.p.b. level, Appl. Phys. B 123, 23 (2017).
  40. M. Herrmann, M. Haas, U. D. Jentschura, F. Kottmann, D. Leibfried, G. Saathoff, C. Gohle, A. Ozawa, V. Batteiger, S. Knünz, N. Kolachevsky, H. A. Schüssler, T. W. Hänsch, and Th. Udem, Feasibility of coherent xuv spectroscopy on the 1S–2S transition in singly ionized helium, Phys. Rev. A 79, 052505 (2009).
  41. L. Ratschbacher, C. Zipkes, C. Sias, and M. Köhl, Controlling chemical reactions of a single particle, Nat. Phys. 8, 649 (2012).
  42. A. C. Wilson, C. Ospelkaus, A. P. VanDevender, J. A. Mlynek, K. R. Brown, D. Leibfried, and D. J. Wineland, A 750-mW, continuous-wave, solid-state laser source at 313 nm for cooling and manipulating trapped 9Be+ ions, Appl. Phys. B 105, 741 (2011).
  43. J. R. Fuhr and W. L. Wiese, Tables of atomic transition probabilities for beryllium and boron, J. Phys. Chem. Ref. Data 39, 013101 (2010).
  44. H.-Y. Lo, J. Alonso, D. Kienzler, B. C. Keitch, L. E. de Clercq, V. Negnevitsky, and J. P. Home, All-solid-state continuous-wave laser systems for ionization, cooling and quantum state manipulation of beryllium ions, Appl. Phys. B 114, 17 (2014).
  45. M. T. Bowers, D. D. Elleman, and J. King, Analysis of the ion-molecule reactions in gaseous H2, D2, and HD by ion cyclotron resonance techniques, J. Chem. Phys. 50, 4787 (1969).
  46. J. K. Kim and W. T. Huntress, Ion cyclotron resonance studies on the reaction of H2+ and D2+ ions with various simple molecules and hydrocarbons, J. Chem. Phys. 62, 2820 (1975).
  47. J. A. Burt, J. L. Dunn, M. J. McEwan, M. M. Sutton, A. E. Roche, and H. I. Schiff, Some ion-molecule reactions of H3+ and the proton affinity of H2, J. Chem. Phys. 52, 6062 (1970).
  48. A. P. Thompson, H. M. Aktulga, R. Berger, D. S. Bolintineanu, W. M. Brown, P. S. Crozier, P. J. in 't Veld, A. Kohlmeyer, S. G. Moore, T. D. Nguyen, R. Shan, M. J. Stevens, J. Tranchida, C. Trott, and S. J. Plimpton, LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales, Comput. Phys. Commun. 271, 108171 (2022).
  49. E. Bentine, C. J. Foot, and D. Trypogeorgos, (py)LIon: A package for simulating trapped ion trajectories, Comput. Phys. Commun. 253, 107187 (2020).
  50. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevA.106.L041101 for additional details on the molecular dynamics simulations.

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation