Control of Supercurrents and Collective Modes in Superconductors by Terahertz Lightwave Propagation

Terahertz (THz) lightwave driving of supercurrents as a dynamical symmetry-breaking principle in superconductors allows for control of collective modes and excitation of non-equilibrium phases such as gapless superconductivity. Here we demonstrate that THz light-induced nonlinear response together with THz lightwave propagation can induce an unipolar ac electric field pulse inside the superconductor for sufficiently weak current relaxation. The resulting dynamical inversion symmetry breaking in form of the induced Cooper-pair condensate flow manifests itself by high harmonic generation at equilibrium-symmetry forbidden frequencies and allows for control of collective modes by THz-pulse shaping. To systematically describe the dynamic interplay of THz lightwave acceleration of Cooper-pair condensate and THz lightwave propagation inside the superconductor, we solve full nonlinear gauge-invariant Maxwell-Bloch equations beyond the Anderson pseudo-spin precession model that we derived by using a gauge-invariant non-equilibrium density matrix approach.