# Bose-Hubbard lattice as a controllable environment for open quantum systems

## TL;DR

This paper explores how a Bose-Hubbard lattice can serve as a controllable environment for open quantum systems, enabling simulation of different dynamical regimes and characterization of excitations as information carriers.

## Contribution

It introduces a method to use the Bose-Hubbard lattice as a tunable environment to simulate Markovian and non-Markovian dynamics in quantum impurity systems.

## Key findings

- The lattice can simulate both Markovian and non-Markovian dynamics.
- Memory effects depend on the superfluid or Mott insulator phase.
- Excitations act as information carriers in different phases.

## Abstract

We investigate the open dynamics of an atomic impurity embedded in a one-dimensional Bose-Hubbard lattice. We derive the reduced evolution equation for the impurity and show that the Bose-Hubbard lattice behaves as a tunable engineered environment allowing to simulate both Markovian and non-Markovian dynamics in a controlled and experimentally realisable way. We demonstrate that the presence or absence of memory effects is a signature of the nature of the excitations induced by the impurity, being delocalized or localized in the two limiting cases of superfluid and Mott insulator, respectively. Furthermore, our findings show how the excitations supported in the two phases can be characterized as information carriers.