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# Observation of a molecular bond between ions and Rydberg atoms

## Abstract

Atoms with a highly excited electron, called Rydberg atoms, can form unusual types of molecular bonds1,2,3,4. The bonds differ from the well-known ionic and covalent bonds5,6 not only by their binding mechanisms, but also by their bond lengths ranging up to several micrometres. Here we observe a new type of molecular ion based on the interaction between the ionic charge and a flipping-induced dipole of a Rydberg atom with a bond length of several micrometres. We measure the vibrational spectrum and spatially resolve the bond length and the angular alignment of the molecule using a high-resolution ion microscope7. As a consequence of the large bond length, the molecular dynamics is extremely slow. These results pave the way for future studies of spatio-temporal effects in molecular dynamics (for example, beyond Born–Oppenheimer physics).

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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 Matlab and a self-written analysis script. The molecular potentials were calculated using the pairinteraction program38 and Python. Matlab and self-written scripts were used to calculate the angular-dependent excitation probability. The simulation results can be generated using the numerical methods described in the Methods and the computer code developed, which are available upon request.

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## Acknowledgements

We thank T. Schmid and C. Veit for their work and support in building the ion microscope. Further, we thank O. A. Herrera-Sancho for support during the calibration of the microscope and S. Weber for help with the pairinteraction code. We are indebted to the mechanics and electronics workshop for manufacturing the ion microscope and the high-voltage power supplies. This work was supported by the Deutsche Forschungsgemeinschaft (DFG; project numbers Pf 381/17-1 and Pf 381/17-2) as part of the SPP 1929 “Giant Interactions in Rydberg Systems (GiRyd)” and has received funding from the QuantERA ERANET programme under the project “Theory-Blind Quantum Control—TheBlinQC’’ (grant no. 13N14847). The project received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement number 101019739 - LongRangeFermi). F.M. acknowledges support from the Carl Zeiss Foundation through IQST and is indebted to the Baden-Württemberg-Stiftung for the financial support by the Eliteprogramm for Postdocs.

## Author information

Authors

### Contributions

The experiments were carried out by N.Z., V.S.V.A., M.B. and Y.-Q.Z.; data analysis was performed by N.Z. and Y.-Q.Z.; the presented simulations and theoretical calculations were conducted by N.Z. and Y.-Q.Z.; project guidance was provided by F.M., R.L. and T.P.; the manuscript was written by N.Z. with contributions from all authors.

### Corresponding author

Correspondence to Tilman Pfau.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature thanks Michal Tomza and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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## Extended data figures and tables

### Extended Data Fig. 1 Potential energy curves with bound vibrational states and measured spectrum.

a, Potential energy curves corresponding to the 69P-state with $$|{m}_{J}|=1/2$$. b, Magnified view of the region marked with a grey box in a with the two potential curves containing the vibrational bound states. Grey lines indicate the energy of vibrational states with vibrational wave functions plotted in blue. c, Normalised molecular signal as a function of the Rydberg laser detuning Δ. Error bars denote standard error of the mean.

### Extended Data Fig. 2 Lifetime measurement with in situ images.

Molecular signal strength measured for different wait times t between the molecule creation and imaging. The exponential fit (blue line) results in a 1/e lifetime of 2.6 μs ± 0.2 μs for the lowest vibrational state in the molecular potential corresponding to the |69P1/2-state. The insets show two in situ images for 0.7 μs and 3.5 μs wait time. Error bars denote one standard deviation.

### Extended Data Fig. 3 Admixture of Ryberg states.

Contributions $$|{c}_{l}|$$ of states mixed into the electronic molecular state below the |69P1/2 asymptote. Here only those states are shown which can be excited with the two-photon scheme from the ground state $$|g\rangle$$. In calculation of the two-photon excitation probability the electronic molecular state is truncated after the first six states with the largest contribution (coloured). The nuclear radial probability density (light grey) indicates the extend of the lowest vibrational state ν = 0.

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Zuber, N., Anasuri, V.S.V., Berngruber, M. et al. Observation of a molecular bond between ions and Rydberg atoms. Nature 605, 453–456 (2022). https://doi.org/10.1038/s41586-022-04577-5

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• DOI: https://doi.org/10.1038/s41586-022-04577-5