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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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## 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.

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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.

## Author information

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.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## 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).

### 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 $${}^{+}(5{{\rm{D}}}_{5/2})$$.

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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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• DOI: https://doi.org/10.1038/s41586-021-04112-y

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