Impurity dephasing in a Bose-Hubbard model

We study the dynamics of a two-level impurity embedded in a two-dimensional Bose-Hubbard (BH) model at zero temperature from an open quantum system perspective. Results for the decoherence dynamics of the impurity across the whole phase diagram are presented, with a focus on the critical region close to the Mott-superfluid transition. In particular, we show how the decoherence and its deviation from a Markovian behaviour are sensitive to whether the phase transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the BH environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method [1] - closely related to slave boson approaches - that enables us to capture quantum correlations across the BH phases and provides deep insights into the physics of pure dephasing from the point of view of the many-body excitations of the environment. References [1] - F. Caleffi, M. Capone, C. Menotti, I. Carusotto and A. Recati, Quantum fluctuations beyond the Gutzwiller approximation in the Bose-Hubbard model, Phys. Rev. Res. 2, 033276 (2020) [2] - F. Caleffi, M. Capone, I. de Vega and A. Recati, Impurity dephasing in a Bose-Hubbard model, New J. Phys. 23, 033018 (2021)