Impurity dephasing in a Bose-Hubbard model

TL;DR

This paper investigates how a two-level impurity's decoherence is affected by the phase of a 2D Bose-Hubbard environment, especially near the superfluid-Mott insulator transition, revealing sensitivity to density and spectrum effects.

Contribution

It introduces a semi-analytical method to analyze impurity decoherence across the entire phase diagram, including critical regions, considering non-Gaussian environment statistics.

Findings

Decoherence behavior varies near the phase transition.

Deviations from Markovian dynamics depend on density conditions.

Spectrum and non-Gaussian statistics significantly influence decoherence.

Abstract

We study the dynamics of a two-level impurity embedded in a two-dimensional Bose-Hubbard model at zero temperature from an open quantum system perspective. Results for the decoherence across the whole phase diagram are presented, with a focus on the critical region close to the transition between superfluid and Mott insulator. In particular, we show how the decoherence and the deviation from a Markovian behaviour are sensitive to whether the transition is crossed at commensurate or incommensurate densities. The role of the spectrum of the Bose-Hubbard environment and its non-Gaussian statistics, beyond the standard independent boson model, is highlighted. Our analysis resorts on a recently developed method [Phys. Rev. Research 2, 033276 (2020)] - closely related to slave boson approaches - that enables us to capture the correlations across the whole phase diagram. This semi-analytical method provides us with a deep insight into the physics of the spin decoherence in the superfluid and Mott phases as well as close to the phase transitions.