Quantum criticality from in situ density imaging

We perform large- scale quantum Monte Carlo (QMC) simulations for strongly interacting bosons in a two-dimensional optical lattice trap and confirm an excellent agreement with the benchmarking in situ density measurements by the Chicago group [N. Gemelke et al., Nature (London) 460, 995 (2009)]. We further present a general finite-temperature phase diagram for both the uniform and the trapped systems, demonstrating how the universal scaling properties near the superfluid-to-Mott insulator transition can be observed from the in situ density profile. The characteristic temperature to find such quantum criticality is estimated to be of the order of the single-particle bandwidth, which should be achievable in the present experiments. Finally, we examine the validity regime of the local fluctuation-dissipation theorem, which can be a used as a thermometry in the strongly interacting regime.