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Observation of Feshbach resonances between a single ion and ultracold atoms

Abstract

The control of physical systems and their dynamics on the level of individual quanta underpins both fundamental science and quantum technologies. Trapped atomic and molecular systems, neutral1 and charged2, are at the forefront of quantum science. Their extraordinary level of control is evidenced by numerous applications in quantum information processing3,4 and quantum metrology5,6. Studies of the long-range interactions between these systems when combined in a hybrid atom–ion trap7,8 have led to landmark results9,10,11,12,13,14,15,16,17,18,19. However, reaching the ultracold regime—where quantum mechanics dominates the interaction, for example, giving access to controllable scattering resonances20,21—has so far been elusive. Here we demonstrate Feshbach resonances between ions and atoms, using magnetically tunable interactions between 138Ba+ ions and 6Li atoms. We tune the experimental parameters to probe different interaction processes—first, enhancing three-body reactions22,23 and the related losses to identify the resonances and then making two-body interactions dominant to investigate the ion’s sympathetic cooling19 in the ultracold atomic bath. Our results provide deeper insights into atom–ion interactions, giving access to complex many-body systems24,25,26,27 and applications in experimental quantum simulation28,29,30.

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Fig. 1: Experimental setup and concepts.
Fig. 2: Detection of atom–ion Feshbach resonances by magnetic-field-dependent ion loss spectroscopy.
Fig. 3: Dependence of the ion loss rate on the atomic density at the Feshbach resonance at 296.31 G.
Fig. 4: Enhanced sympathetic cooling in the vicinity of the Feshbach resonance at 296.31 G.

Data availability

The experimental and theoretical data that support the findings of this study are available from the corresponding author upon request. Source data are provided with this paper.

Code availability

The experimental data were analysed using JupyterLab and a self-written analysis script. Electronic structure calculations were performed with the MOLPRO package of ab initio programs67 and multichannel quantum scattering calculations were realized with the extended version of QDYN program68. AMB model results were obtained and analysed with a self-written program and scripts in Mathematica and Python. The simulation results can be generated using the numerical methods described within Methods and the computer code developed, which are available upon request.

References

  1. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008).

    ADS  CAS  Google Scholar 

  2. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003).

    ADS  CAS  Google Scholar 

  3. Wineland, D. Nobel lecture: Superposition, entanglement, and raising Schrödinger’s cat. Rev. Mod. Phys. 85, 1103–1114 (2013).

    ADS  CAS  Google Scholar 

  4. Saffman, M., Walker, T. & Mølmer, K. Quantum information with Rydberg atoms. Rev. Mod. Phys. 82, 2313–2363 (2010).

    ADS  CAS  Google Scholar 

  5. Katori, H. Optical lattice clocks and quantum metrology. Nat. Photon. 5, 203–210 (2011).

    ADS  CAS  Google Scholar 

  6. Micke, P. et al. Coherent laser spectroscopy of highly charged ions using quantum logic. Nature 578, 60–65 (2020).

    ADS  CAS  PubMed  Google Scholar 

  7. Härter, A. & Hecker Denschlag, J. Cold atom–ion experiments in hybrid traps. Contemp. Phys. 55, 33–45 (2014).

    ADS  Google Scholar 

  8. Tomza, M. et al. Cold hybrid ion–atom systems. Rev. Mod. Phys. 91, 035001 (2019).

    ADS  MathSciNet  CAS  Google Scholar 

  9. Grier, A., Cetina, M., Oručević, F. & Vuletić, V. Observation of cold collisions between trapped ions and trapped atoms. Phys. Rev. Lett. 102, 223201 (2009).

    ADS  PubMed  Google Scholar 

  10. Rellergert, W. G. et al. Measurement of a large chemical reaction rate between ultracold closed-shell 40Ca atoms and open-shell 174Yb+ ions held in a hybrid atom–ion trap. Phys. Rev. Lett. 107, 243201 (2011).

    ADS  PubMed  Google Scholar 

  11. Ratschbacher, L., Zipkes, C., Sias, C. & Köhl, M. Controlling chemical reactions of a single particle. Nat. Phys. 8, 649–652 (2012).

    CAS  Google Scholar 

  12. Hall, F., Aymar, M., Raoult, M., Dulieu, O. & Willitsch, S. Light-assisted cold chemical reactions of barium ions with rubidium atoms. Mol. Phys. 111, 1683–1690 (2013).

    ADS  CAS  Google Scholar 

  13. Ratschbacher, L. et al. Decoherence of a single-ion qubit immersed in a spin-polarized atomic bath. Phys. Rev. Lett. 110, 160402 (2013).

    ADS  CAS  PubMed  Google Scholar 

  14. Meir, Z. et al. Dynamics of a ground-state cooled ion colliding with ultracold atoms. Phys. Rev. Lett. 117, 243401 (2016).

    ADS  PubMed  Google Scholar 

  15. Saito, R. et al. Characterization of charge-exchange collisions between ultracold 6Li atoms and 40Ca+ ions. Phys. Rev. A 95, 032709 (2017).

    ADS  Google Scholar 

  16. Joger, J. et al. Observation of collisions between cold Li atoms and Yb+ ions. Phys. Rev. A 96, 030703 (2017).

    ADS  Google Scholar 

  17. Fürst, H. et al. Dynamics of a single ion-spin impurity in a spin-polarized atomic bath. Phys. Rev. A 98, 012713 (2018).

    ADS  Google Scholar 

  18. Sikorsky, T., Meir, Z., Ben-Shlomi, R., Akerman, N. & Ozeri, R. Spin-controlled atom–ion chemistry. Nat. Commun. 9, 920 (2018).

    ADS  PubMed  PubMed Central  Google Scholar 

  19. Feldker, T. et al. Buffer gas cooling of a trapped ion to the quantum regime. Nat. Phys. 16, 413–416 (2020).

    CAS  Google Scholar 

  20. Idziaszek, Z., Simoni, A., Calarco, T. & Julienne, P. Multichannel quantum-defect theory for ultracold atom–ion collisions. New J. Phys. 13, 083005 (2011).

    ADS  Google Scholar 

  21. Tomza, M., Koch, C. & Moszynski, R. Cold interactions between an Yb+ ion and a Li atom: prospects for sympathetic cooling, radiative association, and Feshbach resonances. Phys. Rev. A 91, 042706 (2015).

    ADS  Google Scholar 

  22. Härter, A. et al. Single ion as a three-body reaction center in an ultracold atomic gas. Phys. Rev. Lett. 109, 123201 (2012).

    ADS  PubMed  Google Scholar 

  23. Krükow, A., Mohammadi, A., Härter, A. & Denschlag, J. H. Reactive two-body and three-body collisions of Ba+ in an ultracold Rb gas. Phys. Rev. A 94, 030701 (2016).

    ADS  Google Scholar 

  24. Cote, R., Kharchenko, V. & Lukin, M. Mesoscopic molecular ions in Bose–Einstein condensates. Phys. Rev. Lett. 89, 093001 (2002).

    ADS  CAS  PubMed  Google Scholar 

  25. Casteels, W., Tempere, J. & Devreese, J. Polaronic properties of an ion in a Bose–Einstein condensate in the strong-coupling limit. J. Low Temp. Phys. 162, 266–273 (2011).

    ADS  CAS  Google Scholar 

  26. Jachymski, K. & Negretti, A. Quantum simulation of extended polaron models using compound atom–ion systems. Phys. Rev. Res. 2, 033326 (2020).

    CAS  Google Scholar 

  27. Hirzler, H. et al. Controlling the nature of a charged impurity in a bath of Feshbach dimers. Phys. Rev. Res. 2, 033232 (2020).

    CAS  Google Scholar 

  28. Doerk, H., Idziaszek, Z. & Calarco, T. Atom–ion quantum gate. Phys. Rev. A 81, 012708 (2010).

    ADS  Google Scholar 

  29. Gerritsma, R. et al. Bosonic Josephson junction controlled by a single trapped ion. Phys. Rev. Lett. 109, 080402 (2012).

    ADS  CAS  PubMed  Google Scholar 

  30. Bissbort, U. et al. Emulating solid-state physics with a hybrid system of ultracold ions and atoms. Phys. Rev. Lett. 111, 080501 (2013).

    ADS  CAS  PubMed  Google Scholar 

  31. Inouye, S. et al. Observation of Feshbach resonances in a Bose–Einstein condensate. Nature 392, 151–154 (1998).

    ADS  CAS  Google Scholar 

  32. Inouye, S. et al. Observation of heteronuclear Feshbach resonances in a mixture of bosons and fermions. Phys. Rev. Lett. 93, 183201 (2004).

    ADS  CAS  PubMed  Google Scholar 

  33. Barbé, V. et al. Observation of Feshbach resonances between alkali and closed-shell atoms. Nat. Phys. 14, 881–884 (2018).

    Google Scholar 

  34. Yang, H. et al. Observation of magnetically tunable Feshbach resonances in ultracold 23Na40K + 40K collisions. Science 363, 261–264 (2019).

    ADS  CAS  PubMed  Google Scholar 

  35. Aikawa, K. et al. Bose–Einstein condensation of erbium. Phys. Rev. Lett. 108, 210401 (2012).

    ADS  CAS  PubMed  Google Scholar 

  36. Durastante, G. et al. Feshbach resonances in an erbium–dysprosium dipolar mixture. Phys. Rev. A 102, 033330 (2020).

    ADS  CAS  Google Scholar 

  37. Cetina, M., Grier, A. & Vuletić, V. Micromotion-induced limit to atom–ion sympathetic cooling in Paul traps. Phys. Rev. Lett. 109, 253201 (2012).

    ADS  PubMed  Google Scholar 

  38. Chen, K., Sullivan, S. T. & Hudson, E. R. Neutral gas sympathetic cooling of an ion in a Paul trap. Phys. Rev. Lett. 112, 143009 (2014).

    ADS  PubMed  Google Scholar 

  39. Höltkemeier, B., Weckesser, P., López-Carrera, H. & Weidemüller, M. Buffer-gas cooling of a single ion in a multipole radio frequency trap beyond the critical mass ratio. Phys. Rev. Lett. 116, 233003 (2016).

    ADS  PubMed  Google Scholar 

  40. Rouse, I. & Willitsch, S. Superstatistical energy distributions of an ion in an ultracold buffer gas. Phys. Rev. Lett. 118, 143401 (2017).

    ADS  CAS  PubMed  Google Scholar 

  41. Lambrecht, A. et al. Long lifetimes and effective isolation of ions in optical and electrostatic traps. Nat. Photon. 11, 704–707 (2017).

    ADS  CAS  Google Scholar 

  42. Schmidt, J. et al. Optical trapping of ion Coulomb crystals. Phys. Rev. X 8, 021028 (2018).

    CAS  Google Scholar 

  43. Weckesser, P. et al. Trapping, shaping, and isolating of an ion Coulomb crystal via state-selective optical potentials. Phys. Rev. A 103, 013112 (2021).

    ADS  CAS  Google Scholar 

  44. Schmidt, J., Weckesser, P., Thielemann, F., Schaetz, T. & Karpa, L. Optical traps for sympathetic cooling of ions with ultracold neutral atoms. Phys. Rev. Lett. 124, 053402 (2020).

    ADS  CAS  PubMed  Google Scholar 

  45. Schneider, C., Enderlein, M., Huber, T., Dürr, S. & Schaetz, T. Influence of static electric fields on an optical ion trap. Phys. Rev. A 85, 013422 (2012).

    ADS  Google Scholar 

  46. Ticknor, C., Regal, C., Jin, D. & Bohn, J. Multiplet structure of Feshbach resonances in nonzero partial waves. Phys. Rev. A 69, 042712 (2004).

    ADS  Google Scholar 

  47. Cui, Y. et al. Observation of broad d-wave Feshbach resonances with a triplet structure. Phys. Rev. Lett. 119, 203402 (2017).

    ADS  PubMed  Google Scholar 

  48. Maier, T. et al. Emergence of chaotic scattering in ultracold Er and Dy. Phys. Rev. X 5, 041029 (2015).

    PubMed  PubMed Central  Google Scholar 

  49. Köhler, T., Góral, K. & Julienne, P. Production of cold molecules via magnetically tunable Feshbach resonances. Rev. Mod. Phys. 78, 1311 (2006).

    ADS  Google Scholar 

  50. Wester, R. Radiofrequency multipole traps: tools for spectroscopy and dynamics of cold molecular ions. J. Phys. B 42, 154001 (2009).

    ADS  Google Scholar 

  51. Jochim, S. et al. Magnetic field control of elastic scattering in a cold gas of fermionic lithium atoms. Phys. Rev. Lett. 89, 273202 (2002).

    CAS  PubMed  Google Scholar 

  52. Luo, L. et al. Evaporative cooling of unitary Fermi gas mixtures in optical traps. New J. Phys. 8, 213 (2006).

    ADS  Google Scholar 

  53. Ketterle, W. & Martin W. Z. Making, probing and understanding ultracold Fermi gases. La Rivista del Nuovo Cimento 31, 247–422 (2008).

  54. Grimm, R., Weidemüller, M. & Ovchinnikov, Y. in Advances in Atomic, Molecular, and Optical Physics (eds Bederson, B. & Walther, H.) Vol. 42, 95–170 (Elsevier, 2000).

  55. Karpa, L. Trapping Single Ions and Coulomb Crystals with Light Fields (Springer, 2019).

  56. Maxwell, J. A Treatise on Electricity and Magnetism Vol. 1 (Clarendon, 1873).

  57. Krükow, A. et al. Energy scaling of cold atom–atom–ion three-body recombination. Phys. Rev. Lett. 116, 193201 (2016).

    ADS  PubMed  Google Scholar 

  58. Pérez-Ros, J. & Greene, C. H. Universal temperature dependence of the ion–neutral–neutral three-body recombination rate. Phys. Rev. A 98, 062707 (2018).

    ADS  Google Scholar 

  59. Pérez-Ros, J. & Greene, C. Communication: Classical threshold law for ion–neutral–neutral three-body recombination. J. Chem. Phys. 143, 041105 (2015).

    ADS  Google Scholar 

  60. Mohammadi, A. et al. Life and death of a cold BaRb+ molecule inside an ultracold cloud of Rb atoms. Phys. Rev. Res. 3, 013196 (2021).

    CAS  Google Scholar 

  61. Breit, G. & Rabi, I. Measurement of nuclear spin. Phys. Rev. 38, 2082–2083 (1931).

    ADS  CAS  Google Scholar 

  62. Zhang, J. et al. P-wave Feshbach resonances of ultracold 6Li. Phys. Rev. A 70, 030702 (2004).

    ADS  Google Scholar 

  63. Mies, F., Williams, C., Julienne, P. & Krauss, M. Estimating bounds on collisional relaxation rates of spin-polarized 87Rb atoms at ultracold temperatures. J. Res. Natl Inst. Stand. Technol. 101, 521–535 (1996).

    CAS  PubMed  PubMed Central  Google Scholar 

  64. Tscherbul, T., Brumer, P. & Buchachenko, A. Spin–orbit interactions and quantum spin dynamics in cold ion–atom collisions. Phys. Rev. Lett. 117, 143201 (2016).

    ADS  PubMed  Google Scholar 

  65. Wille, E. et al. Exploring an ultracold Fermi–Fermi mixture: interspecies Feshbach resonances and scattering properties of 6Li and 40K. Phys. Rev. Lett. 100, 053201 (2008).

    ADS  CAS  PubMed  Google Scholar 

  66. Tiecke, T., Goosen, M., Walraven, J. & Kokkelmans, S. Asymptotic-bound-state model for Feshbach resonances. Phys. Rev. A 82, 042712 (2010).

    ADS  Google Scholar 

  67. Werner, H.-J., Knowles, P. J., Knizia, G., Manby, F. R. & Schütz, M. Molpro: a general-purpose quantum chemistry program package. WIRES Comput. Mol. Sci. 2, 242–253 (2012).

    CAS  Google Scholar 

  68. Goerz, M. H., Reich, D. M., Tomza, M. & Koch, C. QDYN, version 1.0, a program package for quantum dynamics and control (2015); https://qdyn-library.net

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Acknowledgements

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant number 648330) and was supported by the Georg H. Endress foundation. P.W., F.T. and T.S. acknowledge support from the DFG within the GRK 2079/1 programme. P.W. gratefully acknowledges financial support from the Studienstiftung des deutschen Volkes. L.K. is grateful for financial support from Marie Curie Actions. D.W., A.W. and M.T. acknowledge the financial support from the National Science Centre Poland (grant numbers 2016/23/B/ST4/03231 and 2020/36/T/ST2/00591) and Foundation for Polish Science within the First Team programme co-financed by the European Union under the European Regional Development Fund. K.J. acknowledges support from the Polish National Agency for Academic Exchange (NAWA) via the Polish Returns 2019 programme. The computational part was partially supported by the PL-Grid Infrastructure. We thank O. Dulieu for discussions. We thank M. Debatin for building the experimental apparatus.

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Authors and Affiliations

Authors

Contributions

T.S. conceived the experiments. P.W. and F.T. contributed equally to the construction of the setup, carrying out of the experiments, discussion of the results and analysis of the data and were supported by L.K. and T.W. D.W., A.W., K.J. and M.T. performed theoretical calculations and analysis supervised by M.T. T.S. supervised the work. P.W. and T.S. wrote the manuscript with contributions from T.W., K.J. and M.T. All authors worked on the interpretation of the data and contributed to the final manuscript.

Corresponding author

Correspondence to Pascal Weckesser.

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Peer review information Nature thanks Takashi Mukaiyama and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Electronic level scheme of 138Ba+ (I = 0).

We label the relevant electronic dipole transitions with their respective wavelength \(\lambda \) and natural linewidth Γ. We Doppler cool the ion driving the \(6{{\rm{S}}}_{1/2}\leftrightarrow 6{{\rm{P}}}_{1/2}\) and \(5{{\rm{D}}}_{3/2}\leftrightarrow 6{{\rm{P}}}_{1/2}\) transition. Inelastic losses, such as TBR followed by light-assisted dissociation, can partially result in the ion’s population of the 5D5/2 manifold60. We detect these events through optical pumping with 614 nm laser light, followed by fluorescence detection while Doppler cooling.

Extended Data Fig. 2 Time-dependent Ba+ and Li loss for variable atomic density n around 296.31G.

(upper) Ion survival probability while interacting with the 6Li cloud for various atomic densities n. Data points are an average of at least 20 independent experimental realizations. Error bars denote the upper bound of the 1σ-confidence interval of the underlying binomial distribution. The solid lines are exponential fits \(({e}^{-{t}_{{\rm{int}}}{\varGamma }_{{\rm{Loss}}}})\) to the respective data. The fit results and the respective error bars are illustrated as density-dependent loss rate \({\varGamma }_{{\rm{Loss}}}(n)\) in Fig. 3. (lower) Normalized number of remaining 6Li atoms interacting with a single 138Ba+ ion in dependence on \({t}_{{\rm{int}}}\). The markers and the respective colors indicate the association to the data in the upper graph. Li atoms are removed from the xODT by either spin-changing collisions or elastic atom-ion interactions. For the presented analysis, we exclude experiments resulting in ion loss, to avoid systematic errors by inelastic collisions. To mitigate the density uncertainty due to the decay of the atom number, we choose interaction durations resulting in maximal atom loss of \(\lesssim 10 \% \). We further indicate the atom number evolution in absence of interaction (black circles and solid line).

Source data

Extended Data Fig. 3 Potential energy curves for a Ba+ ion interacting with a Li atom.

The interaction between ground-state Ba+ ion and Li atom results in two molecular electronic states of the singlet \({X}^{1}{\Sigma }^{+}\) (solid black line) and triplet \({a}^{3}{\Sigma }^{+}\) (solid red line) symmetries. The excited molecular electronic state of the triplet \({b}^{3}\Pi \) symmetry (dashed red line) originates from the interaction of Ba+ ion in the lowest excited \({}^{2}D\) state and ground-state Li atom and crosses the \({a}^{3}{\Sigma }^{+}\) state at a small interatomic distance. This crossing combined with SOC between \({a}^{3}{\Sigma }^{+}\) and \({b}^{3}\Pi \) states results in large second-order SOC in the collision channels responsible for the observed Feshbach resonances. Further illustrated is a possible photodissociation transition induced by our xODT laser operated at 1064 nm. The observed TBR might result in the formation of weakly-bound molecular ions. These can couple by laser light to higher energetic asymptotes, resulting in the population of excited states, including Ba \({}^{+}(5{{\rm{D}}}_{5/2})\).

Extended Data Table 1 List of observed Feshbach resonances for the entrance channel

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Weckesser, P., Thielemann, F., Wiater, D. et al. Observation of Feshbach resonances between a single ion and ultracold atoms. Nature 600, 429–433 (2021). https://doi.org/10.1038/s41586-021-04112-y

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