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.

Simulating the vibrational quantum dynamics of molecules using photonics

Abstract

Advances in control techniques for vibrational quantum states in molecules present new challenges for modelling such systems, which could be amenable to quantum simulation methods. Here, by exploiting a natural mapping between vibrations in molecules and photons in waveguides, we demonstrate a reprogrammable photonic chip as a versatile simulation platform for a range of quantum dynamic behaviour in different molecules. We begin by simulating the time evolution of vibrational excitations in the harmonic approximation for several four-atom molecules, including H2CS, SO3, HNCO, HFHF, N4 and P4. We then simulate coherent and dephased energy transport in the simplest model of the peptide bond in proteins—N-methylacetamide—and simulate thermal relaxation and the effect of anharmonicities in H2O. Finally, we use multi-photon statistics with a feedback control algorithm to iteratively identify quantum states that increase a particular dissociation pathway of NH3. These methods point to powerful new simulation tools for molecular quantum dynamics and the field of femtochemistry.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Simulating the vibrational dynamics of four-atom molecules in the harmonic approximation.
Fig. 2: Quantum energy transfer and dephasing in NMA.
Fig. 3: Vibrational relaxation and anharmonic evolution for H2O.
Fig. 4: AFC algorithm for a dissociation pathway in NH3.

References

  1. 1.

    Gatti, F. Molecular Quantum Dynamics. (Springer, Berlin, 2014).

    Book  Google Scholar 

  2. 2.

    Brif, C., Chakrabarti, R. & Rabitz, H. Control of quantum phenomena: past, present and future. New J. Phys. 12, 075008 (2010).

    ADS  Article  Google Scholar 

  3. 3.

    Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    MathSciNet  Article  Google Scholar 

  4. 4.

    Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996).

    ADS  MathSciNet  Article  PubMed  MATH  CAS  Google Scholar 

  5. 5.

    Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

    Article  CAS  Google Scholar 

  6. 6.

    Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    ADS  Article  Google Scholar 

  7. 7.

    Shi, S., Woody, A. & Rabitz, H. Optimal control of selective vibrational excitation in harmonic linear chain molecules. J. Chem. Phys. 88, 6870–6883 (1988).

    ADS  Article  CAS  Google Scholar 

  8. 8.

    Shapiro, M. & Brumer, P. Coherent control of molecular dynamics. Rep. Prog. Phys. 66, 859–942 (2003).

    ADS  Article  CAS  Google Scholar 

  9. 9.

    Assion, A. et al. Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses. Science 282, 919–922 (1998).

    ADS  Article  PubMed  CAS  Google Scholar 

  10. 10.

    Hause, M. L., Yoon, Y. H. & Crim, F. F. Vibrationally mediated photodissociation of ammonia: the influence of NH stretching vibrations on passage through conical intersections. J. Chem. Phys. 125, 174309 (2006).

    ADS  Article  PubMed  CAS  Google Scholar 

  11. 11.

    Brinks, D. et al. Visualizing and controlling vibrational wave packets of single molecules. Nature 465, 905–908 (2010).

    ADS  Article  PubMed  CAS  Google Scholar 

  12. 12.

    Alnaser, A. et al. Subfemtosecond steering of hydrocarbon deprotonation through superposition of vibrational modes. Nat Commun. 5, 3800 (2014).

    Article  PubMed  CAS  Google Scholar 

  13. 13.

    Tong, X., Winney, A. H. & Willitsch, S. Sympathetic cooling of molecular ions in selected rotational and vibrational states produced by threshold photoionization. Phys. Rev. Lett. 105, 143001 (2010).

    ADS  Article  PubMed  CAS  Google Scholar 

  14. 14.

    Wolter, B. et al. Ultrafast electron diffraction imaging of bond breaking in di-ionized acetylene. Science 354, 308–312 (2016).

    ADS  Article  PubMed  CAS  Google Scholar 

  15. 15.

    Clark, J. B., Lecocq, F., Simmonds, R. W., Aumentado, J. & Teufel, J. D. Sideband cooling beyond the quantum backaction limit with squeezed light. Nature 541, 191–195 (2017).

    ADS  Article  PubMed  CAS  Google Scholar 

  16. 16.

    Dorfman, K. E., Schlawin, F. & Mukamel, S. Nonlinear optical signals and spectroscopy with quantum light. Rev. Mod. Phys. 88, 045008 (2016).

    ADS  MathSciNet  Article  Google Scholar 

  17. 17.

    Karpiński, M., Jachura, M., Wright, L. J. & Smith, B. J. Bandwidth manipulation of quantum light by an electro-optic time lens. Nat. Photon. 11, 53–57 (2017).

    ADS  Article  CAS  Google Scholar 

  18. 18.

    Aaronson, S. & Arkhipov, A. The computational complexity of linear optics. Theor. Comput. 9, 143–252 (2013).

    MathSciNet  Article  MATH  Google Scholar 

  19. 19.

    Berry, D. W., Childs, A. M., Cleve, R., Kothari, R. & Somma, R. D. Simulating Hamiltonian dynamics with a truncated Taylor series. Phys. Rev. Lett. 114, 090502 (2015).

    ADS  Article  PubMed  CAS  Google Scholar 

  20. 20.

    Lanyon, B. P. et al. Universal digital quantum simulation with trapped ions. Science 334, 57–61 (2011).

    ADS  Article  PubMed  CAS  Google Scholar 

  21. 21.

    Kassal, I., Jordan, S. P., Love, P. J., Mohseni, M. & Aspuru-Guzik, A. Polynomial-time quantum algorithm for the simulation of chemical dynamics. Proc. Natl Acad. Sci. USA 105, 18681–18686 (2008).

    ADS  Article  PubMed  PubMed Central  Google Scholar 

  22. 22.

    Lidar, D. A. & Wang, H. Calculating the thermal rate constant with exponential speedup on a quantum computer. Phys. Rev. E 59, 2429–2438 (1999).

    ADS  Article  CAS  Google Scholar 

  23. 23.

    Campbell, E. T., Terhal, B. M. & Vuillot, C. Roads towards fault-tolerant universal quantum computation. Nature 549, 172–179 (2017).

    ADS  Article  PubMed  CAS  Google Scholar 

  24. 24.

    Wecker, D., Bauer, B., Clark, B. K., Hastings, M. B. & Troyer, M. Gate-count estimates for performing quantum chemistry on small quantum computers. Phys. Rev. A 90, 022305 (2014).

    ADS  Article  CAS  Google Scholar 

  25. 25.

    Peruzzo, A. et al. A variational eigenvalue solver on a photonic quantum processor. Nat. Commun.  5, 4213 (2014).

    ADS  Article  CAS  Google Scholar 

  26. 26.

    Kandala, A. et al. Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets. Nature 549, 242–246 (2017).

    ADS  Article  PubMed  CAS  Google Scholar 

  27. 27.

    Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

    ADS  Article  PubMed  CAS  Google Scholar 

  28. 28.

    Crespi, A. et al. Integrated photonic quantum gates for polarization qubits. Nat. Commun. 2, 566 (2011).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  29. 29.

    Harris, N. C. et al. Quantum transport simulations in a programmable nanophotonic processor. Nat. Photon. 11, 447–452 (2017).

    ADS  Article  CAS  Google Scholar 

  30. 30.

    Carolan, J. et al. Universal linear optics. Science 349, 711–716 (2015).

    MathSciNet  Article  PubMed  MATH  CAS  Google Scholar 

  31. 31.

    Silverstone, J. W. et al. On-chip quantum interference between silicon photon-pair sources. Nat. Photon. 8, 104–108 (2014).

    ADS  Article  CAS  Google Scholar 

  32. 32.

    Spring, J. B. et al. Chip-based array of near-identical, pure, heralded single-photon sources. Optica 4, 90–96 (2017).

    Article  Google Scholar 

  33. 33.

    Najafi, F. et al. On-chip detection of non-classical light by scalable integration of single-photon detectors. Nat. Commun. 6, 5873 (2015).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  34. 34.

    Wang, H. et al. Near-transform-limited single photons from an efficient solid-state quantum emitter. Phys. Rev. Lett. 116, 213601 (2016).

    ADS  Article  PubMed  CAS  Google Scholar 

  35. 35.

    Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).

    ADS  Article  CAS  Google Scholar 

  36. 36.

    Neville, A. et al. Classical boson sampling algorithms with superior performance to near-term experiments. Nat. Phys. 13, 1153–1157 (2017).

    Article  CAS  Google Scholar 

  37. 37.

    Cubitt, T., Montanaro, A. & Piddock, S. Universal quantum Hamiltonians. Preprint at https://arxiv.org/abs/1701.05182 (2017).

  38. 38.

    Leitner, D. M. Energy flow in proteins. Annu. Rev. Phys. Chem. 59, 233–259 (2008).

    ADS  Article  PubMed  CAS  Google Scholar 

  39. 39.

    Kobus, M., Nguyen, P. H. & Stock, G. Coherent vibrational energy transfer along a peptide helix. J. Chem. Phys. 134, 124518 (2011).

    ADS  Article  PubMed  CAS  Google Scholar 

  40. 40.

    Arkhipov, A. & Kuperberg, G. The bosonic birthday paradox. Geometry Topology Monogr. 18, 1–7 (2012).

    MathSciNet  Article  MATH  Google Scholar 

  41. 41.

    Lindner, J. et al. Vibrational relaxation of pure liquid water. Chem. Phys. Lett. 421, 329–333 (2006).

    ADS  Article  CAS  Google Scholar 

  42. 42.

    Ramasesha, K., De Marco, L., Mandal, A. & Tokmakoff, A. Water vibrations have strongly mixed intra- and intermolecular character. Nat. Chem. 5, 935–940 (2013).

    Article  PubMed  CAS  Google Scholar 

  43. 43.

    Horn, R. A. & Johnson, C. R. Topics in Matrix Analysis 57–59 (Cambridge Univ. Press, Cambridge, 1991.

    Book  MATH  Google Scholar 

  44. 44.

    Kirchmair, G. et al. Observation of quantum state collapse and revival due to the single-photon Kerr effect. Nature 495, 205–209 (2013).

    ADS  Article  PubMed  CAS  Google Scholar 

  45. 45.

    Shomroni, I. et al. All-optical routing of single photons by a one-atom switch controlled by a single photon. Science 345, 903–906 (2014).

    ADS  Article  PubMed  CAS  Google Scholar 

  46. 46.

    De Santis, L. et al. A solid-state single-photon filter. Nat. Nanotechnol. 12, 663–667 (2017).

    ADS  Article  PubMed  CAS  Google Scholar 

  47. 47.

    Knill, E., Laflamme, R. & Milburn, G. A scheme for efficient quantum computation with linear optics. Nature 409, 46–52 (2001).

    ADS  Article  PubMed  MATH  CAS  Google Scholar 

  48. 48.

    Huh, J., Guerreschi, G. G., Peropadre, B., McClean, J. R. & Aspuru-Guzik, A. Boson sampling for molecular vibronic spectra. Nat. Photon. 9, 615–620 (2015).

    ADS  Article  CAS  Google Scholar 

  49. 49.

    Russell, N. J., Chakhmakhchyan, L., O’Brien, J. L. & Laing, A. Direct dialling of Haar random unitary matrices. New J. Phys. 19, 033007 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  50. 50.

    Lee, H., Chen, T., Li, J., Painter, O. & Vahala, K. J. Ultra-low-loss optical delay line on a silicon chip. Nat. Commun. 3, 867 (2012).

    ADS  Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgements

We thank A. Orr-Ewing and R. Santagati for helpful conversations, and J. Barton for assistance with figures. This work was supported by the Engineering and Physical Sciences Research Council (EPSRC), European Commission QUCHIP (H2020-FETPROACT-3-2014: quantum simulation) and the European Research Council (ERC). A.N. is grateful for support from the Wilkinson Foundation. J.C. is supported by EU H2020 Marie Sklodowska-Curie grant number 751016. Y.N.J. was supported by NSF grant number DMR-1054020. J.L.O’B. acknowledges a Royal Society Wolfson Merit Award and a Royal Academy of Engineering Chair in Emerging Technologies. Fellowship support from EPSRC is acknowledged by A.L. (EP/N003470/1).

Reviewer information

Nature thanks A. Aspuru-Guzik and F. Gatti for their contribution to the peer review of this work.

Author information

Affiliations

Authors

Contributions

All authors contributed to discussions and project development. The concept of simulating molecular vibrations with photonics was proposed by A.L. The methodology for simulating evolutions in localized bases was developed by E.M.-L. and D.P.T., with input from A.L. and C.S. Chemical calculations were done by D.P.T., based on which C.S. and E.M.-L. developed and simulated datasets. Methods for simulating open-system dynamics were developed by C.S. with input from Y.N.J. and A.L. The concept of simulating anharmonics with nonlinear gates was proposed by A.L., with the methodology for finding the nonlinear phase shift gates developed by C.S. and A.N.; A.N. also developed this code. The concept of incorporating AFC into simulations was proposed by A.L., with methodology by C.S., N.Mar., A.N. and A.L.; A.N. also developed this code. The photonic chip was developed by N.Mat. and T.H. with input from A.L. and J.L.O’B. The experiment was built by C.H., J.C., N. Mat., N.Mar. and A.L. Data were collected by N.Mar., C.H., E.M.-L. and J.C. Data were analysed by C.S., E.M.-L., N.Mar., A.N. and A.L. The manuscript was written by A.L., C.S. and E.M.-L. with input from D.P.T. and N.Mar. The project was conceived and managed by A.L.

Corresponding author

Correspondence to Anthony Laing.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-7 and Supplementary References.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Sparrow, C., Martín-López, E., Maraviglia, N. et al. Simulating the vibrational quantum dynamics of molecules using photonics. Nature 557, 660–667 (2018). https://doi.org/10.1038/s41586-018-0152-9

Download citation

Further reading

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