We study the ultrafast Kerr effect and high-harmonic generation in type-II superconductors by formulating a new model for a time-varying electromagnetic pulse normally incident on a thin-film superconductor. It is found that type-II superconductors exhibit exceptionally large χ (3) due to the progressive destruction of Cooper pairs, and display high-harmonic generation at low incident intensities, and the highest nonlinear susceptibility of all known materials in the THz regime. Our theory opens up new avenues for accessible analytical and numerical studies of the ultrafast dynamics of superconductors.
Quantum nonlinear optics is a quickly growing field with large technological promise, at the same time involving complex and novel many-body phenomena. In the usual scenario, optical nonlinearities originate from the interactions between polaritons, which are hybrid quasi-particles mixing matter and light degrees of freedom. Here we introduce a type of polariton which is intrinsically nonlinear and emerges as the natural quasi-particle in presence quantum degenerate fermionic matter. It is a composite object made of a fermion trapped inside an optical soliton forming a topological defect in a spontaneously formed crystalline structure. Each of these soliton-polaritons carries a Z2 topological quantum number, as they create a domain wall between two crystalline regions with opposite dimerization so that the fermion is trapped in an interphase state. These composite objects are formally equivalent to those appearing in the Su-Schrieffer-Heeger (SSH) model for electrons coupled to lattice phonons. arXiv:1809.06151v2 [cond-mat.quant-gas]
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