Transient optical response of correlated electrons

Recent discoveries of non-equilibrium higher order harmonic response of the superconducting condensate in cuprates, enhancement of the transient superconductivity in organic superconductor K₃C₆₀ and signature of the Higgs mode in BCS superconductor has attracted much attention. To understand the underlying physics behind such collective response of correlated electrons to electromagnetic field requires an understanding of response functions in the time domain. In our work, we calculate transient optical conductivity using a non-equilibrium Green’s function method. We study a phonon mediated superconducting state. In the equilibrium state, we observe the normal superconducting gap in the real part of conductivity, and the 1/ω divergence in the imaginary part. In a pump driven non-equilibrium state we observe suppression and the oscillatory recovery of the order parameter - the Higgs amplitude mode. We use different quantifiers – probe current, phonon-valley, coherence peak and the gap edge – to study the Higgs mode and the transient superconducting state. Our calculation helps in the understanding of transient superconducting state and provide a general framework to analyze the transient response of correlated electrons.