Mott transition in a cavity-boson system: A quantitative comparison between theory and experiment.

The competition between short-range and cavity-mediated infinite-range interactions in a cavity-boson system leads to the existence of a superfluid phase and a Mott-insulator phase within the self-organized regime. We quantitatively compare the steady-state phase boundaries of this transition measured in experiments and simulated using the Multiconfigurational Time-Dependent Hartree Method for Indistinguishable Particles. To make the problem computationally viable, we represent the full system by the exact many-body wave function of a two-dimensional four-well potential. We argue that the validity of this representation comes from the nature of both the cavity-atomic system and the Bose-Hubbard physics, and verify that it only induces small systematic errors. The experimentally measured and theoretically predicted phase boundaries agree reasonably. We thus propose a new approach for the quantiative numerical determination of the superfluid--Mott-insulator phase boundary.