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# Spatial molecular interferometry via multidimensional high-harmonic spectroscopy

## Abstract

Interferometry is a basic tool to resolve coherent properties in a wide range of light or matter wave phenomena. In the strong-field regime, interferometry serves as a fundamental building block in revealing ultrafast electron dynamics. In this work we manipulate strong-field-driven electron trajectories and probe the coherence of a molecular wavefunction by inducing an interferometer on a microscopic level. The two arms of the interferometer are controlled by a two-colour field, while the interference pattern is read via advanced, three-dimensional high-harmonic spectroscopy. This scheme recovers the spectral phase information associated with the structure of molecular orbitals, as well as the spatial properties of the interaction itself. Zooming into one of the most fundamental strong-field phenomena—field-induced tunnel ionization—we reconstruct the angle at which the electronic wavefunction tunnels through the barrier and follow its evolution with attosecond precision.

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## Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank G. Orenstein and M. Kruger for helpful discussions and Z. Masin for his theoretical support. N.D. is the incumbent of the Robin Chemers Neustein Professorial Chair. N.D. acknowledges the Minerva Foundation, the Israeli Science Foundation, the Crown Center of Photonics and the European Research Council for financial support. O.S. and M.I. acknowledge support of the DFG QUTIF grants. M.I. acknowledges support of EPSRC/DSTL MURI grant no. EP/N018680/1.

## Author information

Authors

### Contributions

N.D., O.S., M.I. and B.P. supervised the study. A.J.U., H.S. and B.D.B. designed and built the experimental set-up. A.J.U., H.S. and O.P. carried out the measurements and analysed the data. M.I. and O.S. conceived and performed the theoretical calculations. A.C., S.L. and B.P. developed and studied the theoretical analysis of the Coulomb effects. A.J.U., H.S. and N.D. interpreted the experimental and theoretical results. All authors discussed the results and contributed to the final manuscript.

### Corresponding author

Correspondence to Nirit Dudovich.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–14, detailed description of the theory, numeric calculations and discussion.

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Uzan, A.J., Soifer, H., Pedatzur, O. et al. Spatial molecular interferometry via multidimensional high-harmonic spectroscopy. Nat. Photonics 14, 188–194 (2020). https://doi.org/10.1038/s41566-019-0584-2

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