Strongly interacting impurity in the Bose-hubbard model

The detection of quantum phase transitions in many-body systems can be a challenging task. Here, we study the effect of Mott insulator to superfluid phase transition (MI-SF) in a Bose Hubbard lattice on an impurity immersed within it. By exploiting the quantum Gutzwiller approach and generalizing it to the strongly interacting limit, using a novel theoretical approach, we show that the energy of the quasiparticle jumps at the critical point and the nature of the jump depends on the crossing point of the transition, proving that the impurity can certainly be used as a probe for the transition. We discuss the characteristics of the low-lying excitations of the Bose gas including the Goldstone and Higgs modes across the transition and how that plays a significant role in explaining the behavior of the polaron energy. We also show that the polaron energy can be used to detect the transition with high accuracy and to gain insights into the underlying physics of these phenomena.