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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.

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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.

References

  1. 1.

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

    ADS  MathSciNet  Article  Google Scholar 

  2. 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).

    ADS  Article  Google Scholar 

  3. 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).

    ADS  Article  Google Scholar 

  4. 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).

    ADS  Article  Google Scholar 

  5. 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. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

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

    ADS  Article  Google Scholar 

  8. 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).

    ADS  Article  Google Scholar 

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 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).

    ADS  Article  Google Scholar 

  11. 11.

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

    ADS  Article  Google Scholar 

  12. 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).

    ADS  Article  Google Scholar 

  13. 13.

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

    ADS  Article  Google Scholar 

  14. 14.

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

  15. 15.

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

    ADS  Article  Google Scholar 

  16. 16.

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

    ADS  Article  Google Scholar 

  17. 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).

    ADS  Article  Google Scholar 

  18. 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).

    ADS  Article  Google Scholar 

  19. 19.

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

    ADS  Article  Google Scholar 

  20. 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).

    ADS  Article  Google Scholar 

  21. 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).

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  Article  Google Scholar 

  23. 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. 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).

    ADS  Article  Google Scholar 

  25. 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).

    ADS  Article  Google Scholar 

  26. 26.

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

    ADS  Article  Google Scholar 

  27. 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).

    ADS  Article  Google Scholar 

  28. 28.

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

    ADS  Article  Google Scholar 

  29. 29.

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

  30. 30.

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

    ADS  Article  Google Scholar 

  31. 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).

    ADS  Article  Google Scholar 

  32. 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. 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).

    ADS  Article  Google Scholar 

  34. 34.

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

    ADS  Article  Google Scholar 

  35. 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).

    ADS  Article  Google Scholar 

  36. 36.

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

    ADS  Article  Google Scholar 

  37. 37.

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

    ADS  Article  Google Scholar 

  38. 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).

    ADS  Article  Google Scholar 

  39. 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).

    ADS  Article  Google Scholar 

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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.

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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.

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The authors declare no competing interests.

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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

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