The discovery of the Higgs particle at CERN in 2012 represented exciting progress in the field of particle physics, providing strong proof for spontaneous symmetry breaking (SSB) and the existence of a Higgs field. The concept of SSB in particle physics, developed by Yoichiro Nambu, was partially triggered by the Bardeen-Cooper-Schrieffer (BCS) theory for superconductivity. This theory is based on an effect that arises when an interaction links pairs of electrons into bosonic states called Cooper pairs. The existence of a condensed matter analog of the Higgs boson (a collective amplitude mode that arises from oscillations of the superconducting order parameter: see Figure 1) was proposed by Philip W. Anderson nearly half a century ago,1 prior to the prediction of the Higgs boson in particle physics.2 This collective amplitude mode, which has only recently been referred to as the Higgs mode, has attracted much attention3 from a fundamental point of view (e.g., for the study of quantum phase transitions, nonequilibrium dynamics, and novel nonlinear phenomena, all of which can be investigated in tabletop experiments). Using external fields to artificially control the order parameter of superconducting materials represents another highly intriguing prospect. Clarifying the behavior of coherent light–matter interaction in superconductors would open up a new avenue for the study of unconventional superconductors, for photo-control of superconductivity, and potentially for photoinduced superconductivity.
Figure 1. A schematic picture of the Higgs mode (red arrow) on the free energy potential in the plane of the complex order parameter (Ψ). Re: Real. Im: Imaginary.
The Higgs mode in superconductors has, however, long evaded experimental detection. The essential difficulty lies in the fact that the Higgs mode itself does not directly couple with electromagnetic waves (light) in the linear response regime, due to the absence of electric or magnetic polarization. So far, the Higgs mode has only been observed in the superconductor niobium selenide (NbSe2), via Raman scattering. This observation is possible because the charge-density wave (CDW) in NbSe2 makes the Higgs mode Raman active.3, 4 For decades, it has remained unclear whether the Higgs mode can be observed in conventional superconductors without CDW.
We have observed the Higgs mode in the conventional superconductor niobium titanium nitride (Nb1−xTixN) using state-of-art terahertz (THz) pump–THz probe spectroscopy.5, 6 Although the Higgs mode does not couple directly to the radiation field, it can be excited by THz light. We irradiated an intense monocycle THz pulse, generated by optical rectification in a lithium niobate (LiNbO3) crystal,7 onto Nb1−xTixN. Cooper pairs are instantaneously broken by the intense THz pulse. Such a sudden (nonadiabatic) perturbation of the superconducting ground state induces a fluctuation of the order parameter amplitude.8, 9
The emergence of a superfluid density, which gives rise to the superconducting order parameter (Δ), appears in the optical conductivity spectra at a photon energy around the superconducting gap, 2Δ (i.e., in the THz frequency range). We are therefore able to probe the temporal evolution of this order parameter by using another probe THz pulse with sub-picosecond temporal resolution. Figure 2 shows the measured pump-probe signal as a function of pump-probe delay, clearly indicating that the order parameter oscillates after the THz pulse excitation.5 The oscillation frequency coincides with 2Δ (twice the magnitude of the superconducting order parameter after excitation), strongly reflecting a signature of the Higgs mode with frequency 2Δ.8
Figure 2. Temporal evolution of the pump-probe signal showing the oscillatory behavior of the order parameter. Oscillation frequency decreases as the terahertz (THz) pump pulse intensity increases, reflecting a reduction of the order parameter after the pumping. δEprobe: Change of probe electric field (i.e., the pump-probe signal reflecting the change of order parameter). Arb.: Arbitrary.
In contrast to the above nonadiabatic excitation scheme of the Higgs mode with monocycle THz pulses, the Higgs mode oscillation can also be induced through coherent nonlinear coupling between the Higgs mode and narrow-band multicycle THz pulses with a frequency tuned below the gap energy (ω< 2Δ). Although this sub-gap pump THz pulse is not able to break Cooper pairs, we found that the order parameter coherently oscillates with frequency 2ω (twice the pump frequency) during the THz pulse irradiation. We also found that this forced oscillation of the order parameter leads to a strong third-order harmonic generation (THG), as shown in Figure 3. The most striking result is that this forced oscillation of the order parameter and the THG are strongly enhanced when 2ω coincides with 2Δ (i.e., twice the pump pulse frequency is equal to the Higgs mode frequency).6 This result unveils resonance between the Higgs mode and electromagnetic waves in the nonlinear-response regime. This nonlinear coupling between the strong light field and the Higgs mode is described by the collective precession of Anderson's pseudospins.10
Figure 3. Power spectra of the transmitted pump THz pulse below and above the superconducting critical temperature (15K). The center frequency of the incident pump THz pulse is ω=0.6THz. Third-harmonic generation (THG) is observed at 3ω=1.8THz, below the critical temperature.
In summary, we have confirmed the existence of a Higgs mode in superconductors nearly half a century after its initial prediction. As well as prompting further study of the Higgs mode in unconventional superconductors, our results unveil a new type of nonlinear light–matter interaction associated with cooperative phenomena in correlated quantum systems. This new optical phenomenon shows promise for application in nonlinear THz photonics and provides a new approach for the study of superconductivity by optical means. In future work, we intend to use this scheme to study the behavior of unconventional superconductors.
Ryusuke Matsunaga, Ryo Shimano
Department of Physics
The University of Tokyo
1. P. W. Anderson, Coherent excited states in the theory of superconductivity: gauge invariance and the Meissner effect, Phys. Rev. 110, p. 827, 1958.
2. P. W. Higgs, Broken symmetries, massless particles and gauge fields, Phys. Lett. 12(2), p. 132-133, 1964.
3. D. Pekker, C. M. Varma, Amplitude/Higgs modes in condensed matter physics, Annu. Rev. Condens. Matter Phys. 6, 2015.
4. M.-A. Méasson, Y. Gallais, M. Cazayous, B. Clair, P. Rodière, L. Cairo, A. Sacuto, Amplitude Higgs mode in the 2H-NbSe2 superconductor, Phys. Rev. B 89, p. 060503(R), 2014.
5. R. Matsunaga, Y. I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, R. Shimano, Higgs amplitude mode in the BCS superconductors Nb1 - xTixN induced by terahertz pulse excitation, Phys. Rev. Lett. 111, p. 057002, 2013.
6. R. Matsunaga, N. Tsuji, H. Fujita, A. Sugioka, K. Makise, Y. Uzawa, H. Terai, Z. Wang, H. Aoki, R. Shimano, Light-induced collective pseudospin precession resonating with Higgs mode in a superconductor, Science 345(6201), p. 1145-1149, 2014.
7. J. Fülöp, L. Pálfalvi, G. Almási, J. Hebling, High energy THz pulse generation by tilted pulse front excitation and its nonlinear optical applications, J. Infrared Millim. Terahertz Waves 32(5), p. 553-561, 2011.
8. A. F. Volkov, Sh. M. Kogan, Collisionless relaxation of the energy gap in superconductors, Sov. Phys. JETP 38(5), p. 1018-1021, 1974.
9. R. A. Barankov, L. S. Levitov, B. Z. Spivak, Collective Rabi oscillations and solitons in a time-dependent BCS pairing problem, Phys. Rev. Lett. 93, p. 160401, 2004.
10. N. Tsuji, H. Aoki, Theory of Anderson pseudospin resonance with Higgs mode in superconductors, arXiv:1404.2711, 2014.