Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Photodissociation of ultracold diatomic strontium molecules with quantum state control

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.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Photodissociation of diatomic molecules in an optical lattice.
Figure 2: Photodissociation to a multichannel continuum.
Figure 3: E1-forbidden photodissociation experiment and theory.
Figure 4: Photodissociation of singly excited (1S + 3P1) molecules to the ground-state continuum with energies of several millikelvin.
Figure 5: Energy-dependent photodissociation near a shape resonance.

References

  1. Jones, K. M., Tiesinga, E., Lett, P. D. & Julienne, P. S. Ultracold photoassociation spectroscopy: long-range molecules and atomic scattering. Rev. Mod. Phys. 78, 483–535 (2006)

    Article  ADS  CAS  Google Scholar 

  2. Chin, C., Grimm, R., Julienne, P. & Tiesinga, E. Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225–1286 (2010)

    Article  ADS  CAS  Google Scholar 

  3. Ospelkaus, S. et al. Quantum-state controlled chemical reactions of ultracold potassium-rubidium molecules. Science 327, 853–857 (2010)

    Article  ADS  CAS  Google Scholar 

  4. Zare, R. N. & Herschbach, D. R. Doppler line shape of atomic fluorescence excited by molecular photodissociation. Proc. IEEE 51, 173–182 (1963)

    Article  Google Scholar 

  5. Zare, R. N. Photoejection dynamics. Mol. Photochem. 4, 1–37 (1972)

    CAS  Google Scholar 

  6. Choi, S. E. & Bernstein, R. B. Theory of oriented symmetric-top molecule beams: precession, degree of orientation, and photofragmentation of rotationally state-selected molecules. J. Chem. Phys. 85, 150–161 (1986)

    Article  ADS  CAS  Google Scholar 

  7. Zare, R. N. Photofragment angular distributions from oriented symmetric-top precursor molecules. Chem. Phys. Lett. 156, 1–6 (1989)

    Article  ADS  CAS  Google Scholar 

  8. Skomorowski, W., Pawłowski, F., Koch, C. P. & Moszynski, R. Rovibrational dynamics of the strontium molecule in the A1, c3u, and a3 manifold from state-of-the-art ab initio calculations. J. Chem. Phys. 136, 194306 (2012)

    Article  ADS  Google Scholar 

  9. Borkowski, M. et al. Mass scaling and nonadiabatic effects in photoassociation spectroscopy of ultracold strontium atoms. Phys. Rev. A 90, 032713 (2014)

    Article  ADS  Google Scholar 

  10. Grangier, P., Aspect, A. & Vigue, J. Quantum interference effect for two atoms radiating a single photon. Phys. Rev. Lett. 54, 418–421 (1985)

    Article  ADS  CAS  Google Scholar 

  11. Kheruntsyan, K. V., Olsen, M. K. & Drummond, P. D. Einstein–Podolsky–Rosen correlations via dissociation of a molecular Bose–Einstein condensate. Phys. Rev. Lett. 95, 150405 (2005)

    Article  ADS  CAS  Google Scholar 

  12. McGuyer, B. H. et al. Precise study of asymptotic physics with subradiant ultracold molecules. Nature Phys. 11, 32–36 (2015)

    Article  ADS  CAS  Google Scholar 

  13. Reid, K. L. Photoelectron angular distributions. Annu. Rev. Phys. Chem. 54, 397–424 (2003)

    Article  ADS  CAS  Google Scholar 

  14. Hockett, P., Wollenhaupt, M., Lux, C. & Baumert, T. Complete photoionization experiments via ultrafast coherent control with polarization multiplexing. Phys. Rev. Lett. 112, 223001 (2014)

    Article  ADS  CAS  Google Scholar 

  15. Rakitzis, T. P., Kandel, S. A., Alexander, A. J., Kim, Z. H. & Zare, R. N. Photofragment helicity caused by matter–wave interference from multiple dissociative states. Science 281, 1346–1349 (1998)

    Article  ADS  CAS  Google Scholar 

  16. Garcia, G. A., Nahon, L. & Powis, I. Two-dimensional charged particle image inversion using a polar basis function expansion. Rev. Sci. Instrum. 75, 4989–4996 (2004)

    Article  ADS  CAS  Google Scholar 

  17. McGuyer, B. H. et al. High-precision spectroscopy of ultracold molecules in an optical lattice. New J. Phys. 17, 055004 (2015)

    Article  ADS  Google Scholar 

  18. McGuyer, B. H. et al. Control of optical transitions with magnetic fields in weakly bound molecules. Phys. Rev. Lett. 115, 053001 (2015)

    Article  ADS  CAS  Google Scholar 

  19. Beswick, J. A. & Zare, R. N. On the quantum and quasiclassical angular distributions of photofragments. J. Chem. Phys. 129, 164315 (2008)

    Article  ADS  Google Scholar 

  20. Seideman, T. The analysis of magnetic-state-selected angular distributions: a quantum mechanical form and an asymptotic approximation. Chem. Phys. Lett. 253, 279–285 (1996)

    Article  ADS  CAS  Google Scholar 

  21. González-Férez, R. & Koch, C. P. Enhancing photoassociation rates by nonresonant-light control of shape resonances. Phys. Rev. A 86, 063420 (2012)

    Article  ADS  Google Scholar 

  22. Volz, T. et al. Feshbach spectroscopy of a shape resonance. Phys. Rev. A 72, 010704(R) (2005)

    Article  ADS  Google Scholar 

  23. Mark, M. et al. Stückelberg interferometry with ultracold molecules. Phys. Rev. Lett. 99, 113201 (2007)

    Article  ADS  CAS  Google Scholar 

  24. Knoop, S. et al. Metastable Feshbach molecules in high rotational states. Phys. Rev. Lett. 100, 083002 (2008)

    Article  ADS  CAS  Google Scholar 

  25. Zhang, X. et al. Spectroscopic observation of SU(N)-symmetric interactions in Sr orbital magnetism. Science 345, 1467–1473 (2014)

    Article  ADS  CAS  Google Scholar 

  26. Bartenstein, M. et al. Precise determination of 6Li cold collision parameters by radio-frequency spectroscopy on weakly bound molecules. Phys. Rev. Lett. 94, 103201 (2005)

    Article  ADS  CAS  Google Scholar 

  27. Salumbides, E. J. et al. Bounds on fifth forces from precision measurements on molecules. Phys. Rev. D 87, 112008 (2013)

    Article  ADS  Google Scholar 

  28. Lane, I. C. Production of ultracold hydrogen and deuterium via Doppler-cooled Feshbach molecules. Phys. Rev. A 92, 022511 (2015)

    Article  ADS  Google Scholar 

  29. Lemeshko, M., Krems, R. V., Doyle, J. M. & Kais, S. Manipulation of molecules with electromagnetic fields. Mol. Phys. 111, 1648–1682 (2013)

    Article  ADS  CAS  Google Scholar 

  30. Stapelfeldt, H. & Seideman, T. Colloquium: Aligning molecules with strong laser pulses. Rev. Mod. Phys. 75, 543–557 (2003)

    Article  ADS  CAS  Google Scholar 

  31. Reinaudi, G., Osborn, C. B., McDonald, M., Kotochigova, S. & Zelevinsky, T. Optical production of stable ultracold 88Sr2 molecules. Phys. Rev. Lett. 109, 115303 (2012)

    Article  ADS  CAS  Google Scholar 

  32. McGuyer, B. H. et al. Nonadiabatic effects in ultracold molecules via anomalous linear and quadratic Zeeman shifts. Phys. Rev. Lett. 111, 243003 (2013)

    Article  ADS  CAS  Google Scholar 

  33. Reinaudi, G., Lahaye, T., Wang, Z. & Guéry-Odelin, D. Strong saturation absorption imaging of dense clouds of ultracold atoms. Opt. Lett. 32, 3143–3145 (2007)

    Article  ADS  CAS  Google Scholar 

  34. Wrede, E., Wouters, E. R., Beckert, M., Dixon, R. N. & Ashfold, M. N. R. Quasiclassical and quantum mechanical modeling of the breakdown of the axial recoil approximation observed in the near threshold photolysis of IBr and Br2 . J. Chem. Phys. 116, 6064–6071 (2002)

    Article  ADS  CAS  Google Scholar 

  35. Apfelbeck, F. Photodissociation Dynamics of Ultracold Strontium Dimers. MSc thesis, Ludwig Maximilian University of Munich (2015)

  36. O’Keeffe, P. et al. A photoelectron velocity map imaging spectrometer for experiments combining synchrotron and laser radiations. Rev. Sci. Instrum. 82, 033109 (2011)

    Article  ADS  Google Scholar 

Download references

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.

Author information

Authors and Affiliations

Authors

Contributions

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.

Corresponding author

Correspondence to T. Zelevinsky.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

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.

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).

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Tables 1-3 and Supplementary References. (PDF 181 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature18314

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing