Abstract
Chemical reactions at ultracold temperatures are expected to be dominated by quantum mechanical effects. Although progress towards ultracold chemistry has been made through atomic photoassociation1, Feshbach resonances2 and bimolecular collisions3, these approaches have been limited by imperfect quantum state selectivity. In particular, attaining complete control of the ground or excited continuum quantum states has remained a challenge. Here we achieve this control using photodissociation, an approach that encodes a wealth of information in the angular distribution of outgoing fragments. By photodissociating ultracold 88Sr2 molecules with full control of the low-energy continuum, we access the quantum regime of ultracold chemistry, observing resonant and nonresonant barrier tunnelling, matter–wave interference of reaction products and forbidden reaction pathways. Our results illustrate the failure of the traditional quasiclassical model of photodissociation4,5,6,7 and instead are accurately described by a quantum mechanical model8,9. The experimental ability to produce well-defined quantum continuum states at low energies will enable high-precision studies of long-range molecular potentials for which accurate quantum chemistry models are unavailable, and may serve as a source of entangled states and coherent matter waves for a wide range of experiments in quantum optics10,11.
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Acknowledgements
We gratefully acknowledge ONR grant N000-14-14-1-0802, NIST award 60NANB13D163, and NSF grant PHY-1349725 for partial support of this work, and thank A. T. Grier, G. Z. Iwata and M. G. Tarallo for discussions. R.M. acknowledges the Foundation for Polish Science for support through the MISTRZ programme.
Reviewer Information Nature thanks D. Chandler and the other anonymous reviewer(s) for their contribution to the peer review of this work.
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M.M., B.H.M., F.A., C.-H.L. and T.Z. designed the experiments, carried out the measurements and interpreted the data. I.M. and R.M. carried out the calculations and interpreted the data. All authors contributed to the manuscript.
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Extended data figures and tables
Extended Data Figure 1 Angular distributions for the M1/E2 photodissociation of 1g(vi = −1, Ji = 1, Mi = 0) state with p = 0 to the ground continuum.
Images are arranged as in Fig. 4. The experimental images are labelled by the continuum energy ε/h in MHz. To improve contrast, the strong centre dot from spontaneous decay, as seen in Fig. 3b, was removed before processing and is covered by a box. The theoretical images are calculated using a quantum chemistry model.
Extended Data Figure 2 Comparison of quasiclassical and quantum mechanical (QM) theory with experimental (Exp) images for selected cases from Fig. 4 and Extended Data Fig. 3.
The quasiclassical predictions follow from equations (3) and (4) assuming β20 = 2 for ΔΩ = 0 and −1 for |ΔΩ| = 1. (The quantum mechanical predictions slightly differ from those displayed in Fig. 4 and Extended Data Fig. 3 because they are the full quantum mechanical calculations given in Supplementary Tables 2 and 3.) As before, coloured dots indicate the level of quasiclassical agreement.
Extended Data Figure 3 Photodissociation of molecules near the 1S + 3P1 threshold to the ground-state continuum.
In contrast to Fig. 4, here the initial states are 
with (vi, Ji) = (−4, 1) or (−3, 3) as indicated. These initial states lead to nearly identical distributions as those with the 1u initial states, contrary to the quasiclassical picture. As before, compatibility with the quasiclassical approximation is indicated by the coloured dots.
Extended Data Figure 4 Spontaneous photodissociation of molecules prepared in 
states.
states.a, Absorption images of angular distributions versus Mi. Theoretical simulations using equation (5) are shown underneath. A short expansion time was used to increase visibility. b, For quantitative analysis, another image (inset) of the Mi = 0 case was taken with a longer expansion time and analysed with the pBasex algorithm. The extracted fragment radial distribution shows a focusing around a certain kinetic energy, which was determined by fitting with a Gaussian (red curve). Correcting for an offset due to the lattice depth35, this energy corresponds to a shape resonance with a binding energy of −66 ± 3 MHz. c, The extracted fragment angular distribution qualitatively matches the calculation (red curve) of equation (5).
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Supplementary Information
This file contains Supplementary Methods, Supplementary Tables 1-3 and Supplementary References. (PDF 181 kb)
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McDonald, M., McGuyer, B., Apfelbeck, F. et al. Photodissociation of ultracold diatomic strontium molecules with quantum state control. Nature 535, 122–126 (2016). https://doi.org/10.1038/nature18314
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DOI: https://doi.org/10.1038/nature18314
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