Different insulator phases compete with each other in strongly correlated materials with simultaneous local and nonlocal interactions. It is known that the homogeneous Mott insulator converts into a charge-density-wave (CDW) phase when the nonlocal interactions are increased, but there is ongoing debate on whether, and in which parameter regimes, this transition is of first order or of second order with an intermediate bond-order wave phase. Here we show that strong-field optics applied to an extended Fermi-Hubbard system can serve as a powerful tool to reveal the nature of the quantum phase transition. Specifically, we show that for sufficiently strong on-site repulsion, characteristic excitations such as excitons, biexcitons, excitonic strings, and charge droplets can be tracked by the nonlinear optical response to an ultrafast and intense laser pulse. Subcycle analysis of high harmonic spectra unravels the ultrafast dynamics of these increasingly complex objects, which partially escape the scrutiny of linear optics. Their appearance in the high harmonic spectrum provides striking evidence of a first-order transition into the CDW phase, and makes a strong case for using strong-field optics as a powerful tool to reveal the nature of quasiparticles in strongly correlated matter, and to track the electron dynamics during a first-order quantum phase transition.

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• Charge density waves
• Ultrafast phenomena
• Mott insulators
• Strongly correlated systems
• Extended Hubbard model