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Collective excitation modes are a characteristic feature of symmetry-brokenphases of matter. For example, superconductors exhibit an amplitude Higgs modeand a phase mode, which are the radial and angular excitations in theMexican-hat potential of the free energy. In two-band superconductors thereexists in addition a Leggett phase mode, which corresponds to collectivefluctuations of the interband phase difference. In equilibrium systemsamplitude and phase modes are decoupled, since they are mutually orthogonalexcitations. The direct detection of Higgs and Leggett modes by linear-responsemeasurements is challenging, because they are often overdamped and do notcouple directly to the electromagnetic field. In this work, using numericalexact simulations we show for the case of two-gap superconductors, that opticalpump-probe experiments excite both Higgs and Leggett modes out of equilibrium.We find that this non-adiabatic excitation process introduces a stronginteraction between the collective modes. Moreover, we predict that the coupledHiggs and Leggett modes are clearly visible in the pump-probe absorptionspectra as oscillations at their respective frequencies.

Coupling of Higgs and Leggett modes in nonequilibrium superconductors