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Non-equilibrium quantum dynamics and formation of the Bose polaron

Nature Physics volume 17, pages 731–735 (2021)Cite this article

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Abstract

Advancing our understanding of non-equilibrium phenomena in quantum many-body systems remains one of the greatest challenges in physics. Here we report on the experimental observation of a paradigmatic many-body problem, namely the non-equilibrium dynamics of a quantum impurity immersed in a bosonic environment1,2. We use an interferometric technique to prepare coherent superposition states of atoms in a Bose–Einstein condensate with a small impurity-state component, and monitor the evolution of such quantum superpositions into polaronic quasiparticles. These results offer a systematic picture of polaron formation3,4,5,6,7 from weak to strong impurity interactions. They reveal three distinct regimes of evolution with dynamical transitions that provide a link between few-body processes and many-body dynamics. Our measurements reveal universal dynamical behaviour in interacting many-body systems and demonstrate new pathways to study non-equilibrium quantum phenomena.

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Fig. 1: Dynamical regimes of impurity evolution and the experimental method.
Fig. 2: Impurity dynamics at weak interaction strength.
Fig. 3: Impurity dynamics at intermediate interaction strength.
Fig. 4: Impurity dynamics at unitarity.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code that supports the findings of this study is available from the corresponding author upon reasonable request.

References

  1. Landau, L. D. Über die Bewegung der Elektronen in Kristalgitter. Phys. Z. Sowjet. 3, 644–645 (1933).

    Google Scholar 

  2. Pekar, S. I. Autolocalization of the electron in an inertially polarizable dielectric medium. Zh. Eksp. Teor. Fiz. 16, 335 (1946).

    Google Scholar 

  3. Shashi, A., Grusdt, F., Abanin, D. A. & Demler, E. Radio-frequency spectroscopy of polarons in ultracold Bose gases. Phys. Rev. A 89, 053617 (2014).

    Article  ADS  Google Scholar 

  4. Shchadilova, Y. E., Schmidt, R., Grusdt, F. & Demler, E. Quantum dynamics of ultracold Bose polarons. Phys. Rev. Lett. 117, 113002 (2016).

    Article  ADS  Google Scholar 

  5. Nielsen, K. K., Ardila, L. A. P., Bruun, G. M. & Pohl, T. Critical slowdown of non-equilibrium polaron dynamics. New J. Phys. 21, 043014 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  6. Mistakidis, S. I., Katsimiga, G. C., Koutentakis, G. M., Busch, T. & Schmelcher, P. Quench dynamics and orthogonality catastrophe of Bose polarons. Phys. Rev. Lett. 122, 183001 (2019).

    Article  ADS  Google Scholar 

  7. Drescher, M., Salmhofer, M. & Enss, T. Theory of a resonantly interacting impurity in a Bose–Einstein condensate. Phys. Rev. Res. 2, 032011 (2020).

    Article  Google Scholar 

  8. Mannella, N. et al. Nodal quasiparticle in pseudogapped colossal magnetoresistive manganites. Nature 438, 474–478 (2005).

    Article  ADS  Google Scholar 

  9. Lee, P. A., Nagaosa, N. & Wen, X.-G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).

    Article  ADS  Google Scholar 

  10. Bloch, I., Dalibard, J. & Nascimbène, S. Quantum simulations with ultracold quantum gases. Nat. Phys. 8, 267–276 (2012).

    Article  Google Scholar 

  11. Schirotzek, A., Wu, C.-H., Sommer, A. & Zwierlein, M. W. Observation of Fermi polarons in a tunable Fermi liquid of ultracold atoms. Phys. Rev. Lett. 102, 230402 (2009).

    Article  ADS  Google Scholar 

  12. Kohstall, C. et al. Metastability and coherence of repulsive polarons in a strongly interacting Fermi mixture. Nature 485, 615–618 (2012).

    Article  ADS  Google Scholar 

  13. Koschorreck, M. et al. Attractive and repulsive Fermi polarons in two dimensions. Nature 485, 619–622 (2012).

    Article  ADS  Google Scholar 

  14. Massignan, P., Zaccanti, M. & Bruun, G. M. Polarons, dressed molecules and itinerant ferromagnetism in ultracold fermi gases. Rep. Prog. Phys. 77, 034401 (2014).

    Article  ADS  Google Scholar 

  15. Cetina, M. et al. Ultrafast many-body interferometry of impurities coupled to a Fermi sea. Science 354, 96–99 (2016).

    Article  ADS  Google Scholar 

  16. Scazza, F. et al. Repulsive Fermi polarons in a resonant mixture of ultracold 6Li atoms. Phys. Rev. Lett. 118, 083602 (2017).

    Article  ADS  Google Scholar 

  17. Schmidt, R. et al. Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress. Rep. Prog. Phys. 81, 024401 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  18. Yan, Z. et al. Boiling a unitary Fermi liquid. Phys. Rev. Lett. 122, 093401 (2019).

    Article  ADS  Google Scholar 

  19. Darkwah Oppong, N. et al. Observation of coherent multiorbital polarons in a two-dimensional Fermi gas. Phys. Rev. Lett. 122, 193604 (2019).

    Article  ADS  Google Scholar 

  20. Jørgensen, N. B. et al. Observation of attractive and repulsive polarons in a Bose–Einstein condensate. Phys. Rev. Lett. 117, 055302 (2016).

    Article  ADS  Google Scholar 

  21. Hu, M.-G. et al. Bose polarons in the strongly interacting regime. Phys. Rev. Lett. 117, 055301 (2016).

    Article  ADS  Google Scholar 

  22. Yan, Z. Z., Ni, Y., Robens, C. & Zwierlein, M. W. Bose polarons near quantum criticality. Science 368, 190–194 (2020).

    Article  ADS  Google Scholar 

  23. Peña Ardila, L. A. et al. Analyzing a Bose polaron across resonant interactions. Phys. Rev. A 99, 063607 (2019).

    Article  ADS  Google Scholar 

  24. Parish, M. M. & Levinsen, J. Quantum dynamics of impurities coupled to a Fermi sea. Phys. Rev. B 94, 184303 (2016).

    Article  ADS  Google Scholar 

  25. Wacker, L. et al. Tunable dual-species Bose–Einstein condensates of 39K and 87Rb. Phys. Rev. A 92, 053602 (2015).

    Article  ADS  Google Scholar 

  26. Lysebo, M. & Veseth, L. Feshbach resonances and transition rates for cold homonuclear collisions between 39K and 41K atoms. Phys. Rev. A 81, 032702 (2010).

    Article  ADS  Google Scholar 

  27. Tanzi, L. et al. Feshbach resonances in potassium Bose–Bose mixtures. Phys. Rev. A 98, 062712 (2018).

    Article  ADS  Google Scholar 

  28. Cetina, M. et al. Decoherence of impurities in a Fermi sea of ultracold atoms. Phys. Rev. Lett. 115, 135302 (2015).

    Article  ADS  Google Scholar 

  29. Fletcher, R. J. et al. Two- and three-body contacts in the unitary Bose gas. Science 355, 377–380 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  30. Braaten, E., Kang, D. & Platter, L. Short-time operator product expansion for rf spectroscopy of a strongly interacting Fermi gas. Phys. Rev. Lett. 104, 223004 (2010).

    Article  ADS  Google Scholar 

  31. Rath, S. P. & Schmidt, R. Field-theoretical study of the Bose polaron. Phys. Rev. A 88, 053632 (2013).

    Article  ADS  Google Scholar 

  32. Knap, M. et al. Time-dependent impurity in ultracold fermions: orthogonality catastrophe and beyond. Phys. Rev. X 2, 041020 (2012).

    Google Scholar 

  33. Sommer, A., Ku, M. & Zwierlein, M. W. Spin transport in polaronic and superfluid Fermi gases. New J. Phys. 13, 055009 (2011).

    Article  ADS  Google Scholar 

  34. Bardon, A. B. et al. Transverse demagnetization dynamics of a unitary Fermi gas. Science 344, 722–724 (2014).

    Article  ADS  Google Scholar 

  35. Camacho-Guardian, A. & Bruun, G. M. Landau effective interaction between quasiparticles in a Bose–Einstein condensate. Phys. Rev. X 8, 031042 (2018).

    Google Scholar 

  36. Alexandrov, A. S. & Devreese, J. T. Advances in Polaron Physics Vol. 159 (Springer, 2010).

  37. Camacho-Guardian, A., Peña Ardila, L. A., Pohl, T. & Bruun, G. M. Bipolarons in a Bose–Einstein condensate. Phys. Rev. Lett. 121, 013401 (2018).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank L. A. Peña Ardila for helpful discussions. This work was supported by the Villum Foundation, the Carlsberg Foundation, the Danish Council for Independent Research, the Danish National Research Foundation through the Center of Excellence ‘CCQ’ (grant no. DNRF156) and T.P. acknowledges support through a Niels Bohr Professorship.

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Authors and Affiliations

  1. Center for Complex Quantum Systems, Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark

    Magnus G. Skou, Thomas G. Skov, Nils B. Jørgensen, Kristian K. Nielsen, Arturo Camacho-Guardian, Thomas Pohl, Georg M. Bruun & Jan J. Arlt

  2. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, China

    Georg M. Bruun

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Contributions

M.G.S., T.G.S., N.B.J. and J.J.A. designed and carried out the experiment. M.G.S. performed the data analysis. K.K.N., A.C.-G., T.P. and G.M.B. provided the theoretical predictions. All authors contributed to writing the manuscript.

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Correspondence to Magnus G. Skou.

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The authors declare no competing interests.

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

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Skou, M.G., Skov, T.G., Jørgensen, N.B. et al. Non-equilibrium quantum dynamics and formation of the Bose polaron. Nat. Phys. 17, 731–735 (2021). https://doi.org/10.1038/s41567-021-01184-5

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