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Direct observation of geometric-phase interference in dynamics around a conical intersection

Nature Chemistry volume 15, pages 1503–1508 (2023)Cite this article

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Abstract

Conical intersections are ubiquitous in chemistry and physics, often governing processes such as light harvesting, vision, photocatalysis and chemical reactivity. They act as funnels between electronic states of molecules, allowing rapid and efficient relaxation during chemical dynamics. In addition, when a reaction path encircles a conical intersection, the molecular wavefunction experiences a geometric phase, which can affect the outcome of the reaction through quantum-mechanical interference. Past experiments have measured indirect signatures of geometric phases in scattering patterns and spectroscopic observables, but there has been no direct observation of the underlying wavepacket interference. Here we experimentally observe geometric-phase interference in the dynamics of a wavepacket travelling around an engineered conical intersection in a programmable trapped-ion quantum simulator. To achieve this, we develop a technique to reconstruct the two-dimensional wavepacket densities of a trapped ion. Experiments agree with the theoretical model, demonstrating the ability of analogue quantum simulators—such as those realized using trapped ions—to accurately describe nuclear quantum effects.

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Fig. 1: Directly detecting a geometric phase through wavepacket interference.
Fig. 2: Experimental protocol for geometric-phase dynamics simulation and wavepacket reconstruction.
Fig. 3: Wavepacket dynamics around an engineered conical intersection.

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Data availability

A repository containing data plotted in Fig. 3 and in Extended Data Fig. 1 is available at https://doi.org/10.5281/zenodo.7955887 (ref. 55).

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Acknowledgements

We thank J. Whitlow and K. Brown for valuable discussions. We were supported by the US Office of Naval Research Global (N62909-20-1-2047), by the US Army Research Office Laboratory for Physical Sciences (W911NF-21-1-0003), by the US Intelligence Advanced Research Projects Activity (W911NF-16-1-0070), by Lockheed Martin, by the Australian Government’s Defence Science and Technology Group, by the Sydney Quantum Academy (V.C.O.-A., A.D.R., M.J.M. and T.R.T.), by a USyd–UCSD Partnership Collaboration Award (J.B.P.-S., J.Y.-Z. and I.K.), by H. and A. Harley, and by computational resources from the Australian Government’s National Computational Infrastructure (Gadi) through the National Computational Merit Allocation Scheme.

Author information

Author notes

  1. R. J. MacDonell

    Present address: Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada

  2. These authors contributed equally: C. H. Valahu, V. C. Olaya-Agudelo.

Authors and Affiliations

  1. School of Physics, University of Sydney, Sydney, New South Wales, Australia

    C. H. Valahu, T. Navickas, A. D. Rao, M. J. Millican, M. J. Biercuk, C. Hempel & T. R. Tan

  2. ARC Centre of Excellence for Engineered Quantum Systems, University of Sydney, Sydney, New South Wales, Australia

    C. H. Valahu, V. C. Olaya-Agudelo, R. J. MacDonell, T. Navickas, A. D. Rao, M. J. Millican, M. J. Biercuk, C. Hempel, T. R. Tan & I. Kassal

  3. School of Chemistry, University of Sydney, Sydney, New South Wales, Australia

    V. C. Olaya-Agudelo, R. J. MacDonell & I. Kassal

  4. University of Sydney Nano Institute, University of Sydney, Sydney, New South Wales, Australia

    R. J. MacDonell & I. Kassal

  5. Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, USA

    J. B. Pérez-Sánchez & J. Yuen-Zhou

  6. Institute for Quantum Electronics, ETH Zürich, Zürich, Switzerland

    C. Hempel

  7. ETH Zurich-PSI Quantum Computing Hub, Paul Scherrer Institut, Villigen, Switzerland

    C. Hempel

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Contributions

R.J.M., I.K., C.H. and T.R.T. conceived the original idea. V.C.O.-A., R.J.M., J.B.P.-S., J.Y.-Z. and I.K. developed the theoretical methods. C.H.V., T.N., A.D.R., M.J.M. and T.R.T. carried out the experiments. C.H.V., V.C.O.-A., T.R.T. and I.K. wrote the manuscript with feedback from all authors. All authors discussed the results and interpreted the data.

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Correspondence to T. R. Tan or I. Kassal.

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Nature Chemistry thanks Jeffrey Cina 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 Characteristic functions of the wavepacket measured for various evolution times.

a-d Joint two-dimensional characteristic function χ(iβ1, iβ2) = p↓χ↓(iβ1, iβ2) + p↑χ↑(iβ1, iβ2) measured at times t = {0, 0.9T, T, 2T} using the full pulse sequence of Fig. 2. The real (left) and imaginary (right) parts are measured with and without an Rx(π/2) pulse in the reconstruction. The top row shows theoretical predictions and the bottom experimental results. χ(iβ1, iβ2) were measured in the range β1, β2 ∈ [0, 4] with 11 × 11 equidistant samples (dashed quadrant). Values in the remaining three quadrants are obtained from the symmetry of χ(iβ1, iβ2). e One-dimensional characteristic functions χ↓(iβ2) and χ↑(iβ2) obtained by omitting displacements on B1 in the reconstruction. β2 was uniformly sampled in the range [0, 5] with 26 points. Each two- and one-dimensional characteristic function was averaged over 1000 and 2000 measurements, respectively. Error bars in e represent one standard deviation based on quantum projection noise.

Extended Data Fig. 2 Frequency drifts of radial motional modes.

a Time series of motional frequencies ω1,2 corresponding to B1,2, measured using the calibration routine detailed in the text and plotted as the frequency offset from ω1 measured at t = 0. b Allan deviation of ω1, and of the difference between the two frequencies (ω1 − ω2).

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Valahu, C.H., Olaya-Agudelo, V.C., MacDonell, R.J. et al. Direct observation of geometric-phase interference in dynamics around a conical intersection. Nat. Chem. 15, 1503–1508 (2023). https://doi.org/10.1038/s41557-023-01300-3

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