We theoretically study dynamical formation of a quantum droplet in a two-component Bose-Hubbard system with an external trap potential. Specifically, the superfluid in the central region surrounded by the Mott insulator with double filling forms a quantum droplet, which is self-bound thanks to the discontinuous nature of the quantum phase transition between the two phases. We show how to induce the characteristic behavior of the droplet through the control of the trap potential by using the time-dependent Gutzwiller simulations in a two-dimensional system. The static and dynamical properties of the droplet can be described qualitatively by the effective Ginzburg-Landau field theory with cubic-quintic nonlinearities where the attractive cubic nonlinearity emerges, although all the bare interparticle interactions are repulsive.

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• Cold atoms & matter waves
• Cold gases in optical lattices
• Mixtures of atomic and/or molecular quantum gases
• Gutzwiller approximation