Visualization and quantum control of light-accelerated condensates by terahertz multi-dimensional coherent spectroscopy

Characterizing and controlling high-order correlation of quantum systems is key for developing quantum devices and switching technologies. Although conventional static and ultrafast spectroscopy gives access to collective excitations characterizing quantum states, more exotic correlations cannot be easily separated from other contributions. Here we develop density matrix simulations to show that seventh-order-wave-mixing peaks with distinct temperature and field dependences in two-dimensional terahertz nonlinear spectra reveal light-induced correlations in non-equilibrium superconducting states. Above critical terahertz driving, these emerging peaks split from conventional peaks along the second axis introduced by pump-probe relative phase in two-dimensional frequency space. They are photo-generated by correlations between two-photon fluctuations and interacting quasi-particle and quasi-particle/Higgs superconductor excitations. By photo-inducing persistent symmetry breaking via light-wave propagation, we also demonstrate seventh-order-wave-mixing sensing of Higgs collective modes. Our theory suggests to use multi-dimensional spectroscopy for quantum sensing of light-driven superconductivity and paves a path for quantum operations by few-cycle-THz-periodic photocurrent modulation. At ultrafast time scales, for example, through light-matter interactions, exotic phases in quantum systems can be realised but identifying and characterising these phases from other excitations is complex. Here, the authors theoretically demonstrate how to identify the experimental signatures of a non-equilibrium superconducting state using multi-dimensional coherent spectroscopy in the terahertz regime.