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Echo in a single vibrationally excited molecule


Echoes occur in many physical systems, typically in inhomogeneously broadened ensembles of nonlinear objects. They are often used to eliminate the effects of dephasing caused by interactions with the environment as well as to enable the observation of proper, inherent object properties. Here, we report the experimental observation of quantum wave-packet echoes in a single, isolated molecule. The entire dephasing–rephasing cycle occurs without any inhomogeneous spread of molecular properties, or any interaction with the environment, and offers a way to probe the internal coherent dynamics of single molecules. In our experiments, we impulsively excite a vibrational wave packet in an anharmonic molecular potential and observe its oscillations and eventual dispersion with time. A second, delayed pulse gives rise to an echo—a partial recovery of the initial coherent oscillations. The vibrational dynamics of single molecules is visualized by a time-delayed probe pulse dissociating them, one at a time. Two mechanisms for the echo formation are discussed: a.c. Stark-induced molecular potential shaking and creation of a depletion-induced ‘hole’ in the nuclear spatial distribution. The single-molecule wave-packet echoes may lead to the development of new tools for probing ultrafast intramolecular processes in various molecules.

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Fig. 1: Classical phase space dynamics.
Fig. 2: Experimental set-up.
Fig. 3: KER distribution build-up.
Fig. 4: KER distribution and yield of the \({{\rm{Ar}}}_{2}\left(1,0\right)\) channel as a function of the probe delay in the presence of a kick pulse.
Fig. 5: Quantum mechanical simulations of the echo dynamics.
Fig. 6: KER distributions as a function of probe delay.

Data availability

The data represented in Figs. 1, 2b and 36 are available through the figshare depository at All other data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


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We acknowledge useful discussions with D. Oron, D. Raanan and G. Stupakov. This work is supported by the National Key R&D Program of China (grant no. 2018YFA0306303), the National Natural Science Foundation of China (grants nos. 11425416, 11834004, 61690224, 11621404 and 11761141004), the 111 Project of China (grant no. B12024), the Israel Science Foundation (grant no. 746/15), the ICORE programme ‘Circle of Light’, ISF-NSFC (grant no. 2520/17) and Projects from Shanghai Science and Technology Commission (19JC1412200). I.A. acknowledges support as the Patricia Elman Bildner Professorial Chair, and acknowledges the hospitality extended to him by the UBC Department of Physics & Astronomy during a sabbatical stay. This research was made possible, in part, by the historic generosity of the Harold Perlman Family.

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Authors and Affiliations



J.W., I.A., Y.P., Y.S., J.Q. and I.T. conceived the idea and initiated the study. J.Q., P.L., K.L., W.Z. and F.S. designed and carried out the experiments. I.T. and J.Q. performed the simulations. J.Q., I.T., K.L., J.W., I.A. and Y.P. contributed to the data analysis and writing the manuscript. J.W., I.A. and Y.P. supervised and guided the work.

Corresponding authors

Correspondence to Yehiam Prior, Ilya Sh. Averbukh or Jian Wu.

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The authors declare no competing interests.

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

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Extended data

Extended Data Fig. 1 Magnified parts of Figs. 3d and 4b.

a, Yield without the kick pulse. b, Yield with the kick pulse. Both curves represent the yield of ion fragments with KER in the range \(0.7\ {\rm{eV}}\ \le \ {\rm{KER}}\ \le \ 1.6\ {\rm{eV}}\).

Supplementary information

Supplementary Video 1

Gradual build-up (from single-molecule events) of the kinetic energy release (KER) distribution of molecular fragments as a function of the probe delay following excitation by a pump pulse. By the end of the movie there is a total of 2.0 million events.

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Qiang, J., Tutunnikov, I., Lu, P. et al. Echo in a single vibrationally excited molecule. Nat. Phys. 16, 328–333 (2020).

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