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.

  • Letter
  • Published:

Higgs mode in a strongly interacting fermionic superfluid

Abstract

Higgs and Goldstone modes are possible collective modes of an order parameter on spontaneously breaking a continuous symmetry. Whereas the low-energy Goldstone (phase) mode is always stable, additional symmetries are required to prevent the Higgs (amplitude) mode from rapidly decaying into low-energy excitations. In high-energy physics, where the Higgs boson1 has been found after a decades-long search, the stability is ensured by Lorentz invariance. In the realm of condensed-matter physics, particle–hole symmetry can play this role2 and a Higgs mode has been observed in weakly interacting superconductors3,4,5. However, whether the Higgs mode is also stable for strongly correlated superconductors in which particle–hole symmetry is not precisely fulfilled or whether this mode becomes overdamped has been the subject of numerous discussions6,7,8,9,10,11. Experimental evidence is still lacking, in particular owing to the difficulty of exciting the Higgs mode directly. Here, we observe the Higgs mode in a strongly interacting superfluid Fermi gas. By inducing a periodic modulation of the amplitude of the superconducting order parameter Δ, we observe an excitation resonance at the frequency 2Δ/h. For strong coupling, the peak width broadens and eventually the mode disappears when the Cooper pairs turn into tightly bound dimers signalling the eventual instability of the Higgs mode.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Principle of the Higgs mode excitation.
Fig. 2: Illustration of the excitation scheme for one modulation frequency.
Fig. 3: Excitation spectra of the Higgs mode.
Fig. 4: Observation of the Higgs mode.

Similar content being viewed by others

References

  1. Higgs, P. W. Broken symmetries and the masses of gauge bosons. Phys. Rev. Lett. 13, 508–509 (1964).

    Article  ADS  MathSciNet  Google Scholar 

  2. Littlewood, P. B. & Varma, C. M. Gauge-invariant theory of the dynamical interaction of charge density waves and superconductivity. Phys. Rev. Lett. 47, 811–814 (1981).

    Article  ADS  Google Scholar 

  3. Sooryakumar, R. & Klein, M. V. Raman scattering by superconducting-gap excitations and their coupling to charge-density waves. Phys. Rev. Lett. 45, 660–662 (1980).

    Article  ADS  Google Scholar 

  4. Matsunaga, R. et al. Higgs amplitude mode in the BCS superconductors Nb1−xTixN induced by terahertz pulse excitation. Phys. Rev. Lett. 111, 057002 (2013).

    Article  ADS  Google Scholar 

  5. Sherman, D. et al. The Higgs mode in disordered superconductors close to a quantum phase transition. Nat. Phys. 11, 188–192 (2015).

    Article  Google Scholar 

  6. Pekker, D. & Varma, C. Amplitude/Higgs modes in condensed matter physics. Annu. Rev. Condens. Matter Phys. 6, 269–297 (2015).

    Article  ADS  Google Scholar 

  7. Podolsky, D., Auerbach, A. & Arovas, D. P. Visibility of the amplitude (Higgs) mode in condensed matter. Phys. Rev. B 84, 174522 (2011).

    Article  ADS  Google Scholar 

  8. Scott, R. G., Dalfovo, F., Pitaevskii, L. P. & Stringari, S. Rapid ramps across the BEC–BCS crossover: A route to measuring the superfluid gap. Phys. Rev. A. 86, 053604 (2012).

    Article  ADS  Google Scholar 

  9. Barlas, Y. & Varma, C. M. Amplitude or Higgs modes in d-wave superconductors. Phys. Rev. B 87, 054503 (2013).

    Article  ADS  Google Scholar 

  10. Liu, B., Zhai, H. & Zhang, S. Evolution of the Higgs mode in a fermion superfluid with tunable interactions. Phys. Rev. A 93, 033641 (2016).

    Article  ADS  Google Scholar 

  11. Han, X., Liu, B. & Hu, J. Observability of Higgs mode in a system without Lorentz invariance. Phys. Rev. A 94, 033608 (2016).

    Article  ADS  Google Scholar 

  12. Littlewood, P. B. & Varma, C. M. Amplitude collective modes in superconductors and their coupling to charge-density waves. Phys. Rev. B 26, 4883–4893 (1982).

    Article  ADS  Google Scholar 

  13. Rüegg, C. et al. Quantum magnets under pressure: Controlling elementary excitations in TlCuCl3. Phys. Rev. Lett. 100, 205701 (2008).

    Article  ADS  Google Scholar 

  14. Halperin, W. & Varoquax, E. in Helium Three (eds Halperin, W. & Pitaevskii, L.) 353–522 (Elsevier, Amsterdam, 1990).

  15. Bissbort, U. et al. Detecting the amplitude mode of strongly interacting lattice bosons by Bragg scattering. Phys. Rev. Lett. 106, 205303 (2011).

    Article  ADS  Google Scholar 

  16. Endres, M. et al. The Higgs amplitude mode at the two-dimensional superfluid/Mott insulator transition. Nature 487, 454–458 (2012).

    Article  ADS  Google Scholar 

  17. Hoang, T. M. et al. Adiabatic quenches and characterization of amplitude excitations in a continuous quantum phase transition. Proc. Natl Acad. Sci. USA 113, 9475–9479 (2016).

    Article  ADS  Google Scholar 

  18. Leonard, J., Morales, A., Zupancic, P., Donner, T. & Esslinger, T. Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas. Science 358, 1415–1418 (2017).

    Article  ADS  Google Scholar 

  19. Yuzbashyan, E. A. & Dzero, M. Dynamical vanishing of the order parameter in a fermionic condensate. Phys. Rev. Lett. 96, 230404 (2006).

    Article  ADS  Google Scholar 

  20. Hannibal, S. et al. Quench dynamics of an ultracold Fermi gas in the BCS regime: Spectral properties and confinement-induced breakdown of the Higgs mode. Phys. Rev. A 91, 043630 (2015).

    Article  ADS  Google Scholar 

  21. Greiner, M., Regal, C. A. & Jin, D. S. Probing the excitation spectrum of a Fermi gas in the BCS–BEC crossover regime. Phys. Rev. Lett. 94, 070403 (2005).

    Article  ADS  Google Scholar 

  22. Chin, C. et al. Observation of the pairing gap in a strongly interacting Fermi gas. Science 305, 1128–1130 (2004).

    Article  ADS  Google Scholar 

  23. Ketterle, W. & Zwierlein, M. W in Ultracold Fermi Gases, Proceedings of the International School of Physics “Enrico Fermi” (eds M. Inguscio, W. Ketterle, and C. Salomon) 164, 95–287 (IOS, Amsterdam, 2007).

  24. Stewart, J. T., Gaebler, J. P. & Jin, D. S. Using photoemission spectroscopy to probe a strongly interacting Fermi gas. Nature 454, 744–747 (2008).

    Article  ADS  Google Scholar 

  25. Feld, M., Fröhlich, B., Vogt, E., Koschorreck, M. & Köhl, M. Observation of a pairing pseudogap in a two-dimensional Fermi gas. Nature 480, 75–78 (2011).

    Article  ADS  Google Scholar 

  26. Bruun, G. M. Low-energy monopole modes of a trapped atomic Fermi gas. Phys. Rev. Lett. 89, 263002 (2002).

    Article  ADS  Google Scholar 

  27. Korolyuk, A., Kinnunen, J. J. & Törmä, P. Density response of a trapped Fermi gas: A crossover from the pair vibration mode to the Goldstone mode. Phys. Rev. A 84, 033623 (2011).

    Article  ADS  Google Scholar 

  28. Korolyuk, A., Kinnunen, J. J. & Törmä, P. Collective excitations of a trapped Fermi gas at finite temperature. Phys. Rev. A 89, 013602 (2014).

    Article  ADS  Google Scholar 

  29. Tokimoto, J., Tsuchiya, S., & Nikuni, T. Higgs mode in a trapped superfluid Fermi gas. J. Low Temp. Phys. 187, 765–770 (2017).

  30. Ries, M. G. et al. Observation of pair condensation in the quasi-2D BEC–BCS crossover. Phys. Rev. Lett. 114, 230401 (2015).

    Article  ADS  Google Scholar 

  31. Schirotzek, A., Shin, Y.-i, Schunck, C. H. & Ketterle, W. Determination of the superfluid gap in atomic Fermi gases by quasiparticle spectroscopy. Phys. Rev. Lett. 101, 140403 (2008).

    Article  ADS  Google Scholar 

  32. Hoinka, S. et al. Goldstone mode and pair-breaking excitations in atomic Fermi superfluids. Nat. Phys. 13, 943–946 (2017).

    Article  Google Scholar 

  33. Chang, S. Y., Pandharipande, V. R., Carlson, J. & Schmidt, K. E. Quantum Monte Carlo studies of superfluid Fermi gases. Phys. Rev. A 70, 043602 (2004).

    Article  ADS  Google Scholar 

  34. Gezerlis, A. & Carlson, J. Strongly paired fermions: Cold atoms and neutron matter. Phys. Rev. C 77, 032801 (2008).

    Article  ADS  Google Scholar 

  35. Bulgac, A., Drut, J. E. & Magierski, P. Quantum Monte Carlo simulations of the BCS–BEC crossover at finite temperature. Phys. Rev. A 78, 023625 (2008).

    Article  ADS  Google Scholar 

  36. Chen, Q. Effect of the particle–hole channel on BCS–Bose–Einstein condensation crossover in atomic Fermi gases. Sci. Rep. 6, 25772 (2016).

    Article  ADS  Google Scholar 

  37. Haussmann, R., Rantner, W., Cerrito, S. & Zwerger, W. Thermodynamics of the BCS-BEC crossover. Phys. Rev. A 75, 023610 (2007).

    Article  ADS  Google Scholar 

  38. Pieri, P., Pisani, L. & Strinati, G. C. BCS–BEC crossover at finite temperature in the broken-symmetry phase. Phys. Rev. B 70, 094508 (2004).

    Article  ADS  Google Scholar 

  39. Ohashi, Y. & Griffin, A. Superfluidity and collective modes in a uniform gas of Fermi atoms with a Feshbach resonance. Phys. Rev. A 67, 063612 (2003).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank E. Demler, W. Zwerger and M. Zwierlein for fruitful discussion. This work has been supported by BCGS, the Alexander-von-Humboldt Stiftung, ERC (grant nos 616082 and 648166), DFG (SFB/TR 185 project B4), ITN COMIQ and Studienstiftung des Deutschen Volkes.

Author information

Authors and Affiliations

Authors

Contributions

The study was conceived by C.K. and M.K.; the experimental set-up was designed and constructed by A.B., T.H., K.G. and M.K.; data collection was performed by A.B., T.H., K.G. and M.L.; data analysis was performed by T.H.; numerical modelling and analysis was performed by J.K., J.-S.B. and C.K.; the manuscript was written by C.K. and M.K. with contributions from all co-authors.

Corresponding authors

Correspondence to K. Gao or M. Köhl.

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 Figures

Supplementary Figures 1–6

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Behrle, A., Harrison, T., Kombe, J. et al. Higgs mode in a strongly interacting fermionic superfluid. Nature Phys 14, 781–785 (2018). https://doi.org/10.1038/s41567-018-0128-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-018-0128-6

This article is cited by

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