Emergence of coherence and the dynamics of quantum phase transitions

The dynamics of quantum phase transitions pose one of the most challenging problems in modern many-body physics. Here, we study a prototypical example in a clean and well-controlled ultracold atom setup by observing the emergence of coherence when crossing the Mott insulator to superfluid quantum phase transition. In the 1D Bose-Hubbard model, we find perfect agreement between experimental observations and numerical simulations for the resulting coherence length. We, thereby, perform a largely certified analog quantum simulation of this strongly correlated system reaching beyond the regime of free quasiparticles. Experimentally, we additionally explore the emergence of coherence in higher dimensions, where no classical simulations are available, as well as for negative temperatures. For intermediate quench velocities, we observe a power-law behavior of the coherence length, reminiscent of the Kibble-Zurek mechanism. However, we find nonuniversal exponents that cannot be captured by this mechanism or any other known model.