Quantum fluctuations beyond the Gutzwiller approximation in the Bose-Hubbard model

Abstract

We develop a quantum many-body theory of the Bose-Hubbard model based on the canonical quantization of the action derived from a Gutzwiller mean-field ansatz. Capitalizing on the ability of this latter to describe both the Mott insulator and the superfluid phases, our theory is a systematic generalization of the Bogoliubov theory of weakly interacting gases and provides accurate results across the whole phase diagram. We characterize the superfluid-insulator phase transition studying the two-point correlation functions, the local number fluctuations, and the superfluid stiffness across the whole phase diagram. Two different universality classes are recovered at integer and non-integer filling and the density fluctuations are successfully compared to accurate quantum Monte Carlo data. To conclude we highlight the potential of our theory in view of including interactions between collective modes to describe their finite lifetime and their quantum optical properties.

Quantum Geometry and Flat Band Bose-Einstein Condensation

“…The results presented here are thus relevant for efforts of realizing strongly correlated photons, important for both fundamental research and optoelectronic components. In the future, it would be interesting to explore how quantum geometry affects the spatial and temporal dependence of the first-and second-order correlation functions, the physics of the strong interaction limit [49], and driven-dissipative BECs.…”

Impurity dephasing in a Bose-Hubbard model

“…Before proceeding, we briefly review the structure of the BH excitation spectrum ω α,k along the phase diagram, since its knowledge gives important insights in the dephasing dynamics of the spin impurity, as we show in Section 3. The spectrum is well-known and can be obtained also from linear-response theory applied to the time-dependent Gutzwiller approximation [24,32]. For convenience, in Figure 1 a summary of the phase diagram and of the excitation spectra in different regimes is shown.…”

“…The QGW approach provides a recipe to express operators and observables of the BH bath in terms of the excitations operators bα,k (see [24] and Appendix A). In particular, the impurity dynamics due to the weak coupling with the bath as described by Eq.…”

“…Under such approximation, it is well-known that the impurity dynamics is fully characterized by the time correlation function of the environment coupling operator, n0 . We estimate the latter by using a recently developed quantum Gutzwiller (QGW) approach [24], that has been proven to be very accurate to describe the quantum correlations of the BH model across the whole phase diagram. For completeness, we briefly review the method in the following.…”

“…Here we take a leap forward by considering a 2D BH model and characterizing the impurity dynamics along the whole phase diagram, focusing on the critical regions. Our goal can be reached thanks to the use of a Gutzwiller technique that we recently developed [24]. The method allows us to include the relevant correlations of the bath -in particular the ones responsible for non-Gaussian effects -without being computationally demanding.…”