State engineering of impurities in a lattice by coupling to a Bose gas

TL;DR

This paper explores how impurities in a lattice coupled to a Bose gas can be engineered to localize in specific patterns by tuning interactions and boundary conditions, demonstrating robust control over their quantum states.

Contribution

It introduces a systematic method to control impurity localization patterns in a lattice-Bose gas system through interaction tuning and boundary condition manipulation.

Findings

Impurities localize in different patterns depending on interaction strength and lattice depth.

Tuning parameters allows systematic control over impurity localization.

Ground state degeneracy can be manipulated via boundary conditions.

Abstract

We investigate the localization pattern of interacting impurities, which are trapped in a lattice potential and couple to a Bose gas. For small interspecies interaction strengths, the impurities populate the energetically lowest Bloch state or localize separately in different wells with one extra particle being delocalized over all the wells, depending on the lattice depth. In contrast, for large interspecies interaction strengths we find that due to the fractional filling of the lattice and the competition of the repulsive contact interaction between the impurities and the attractive interaction mediated by the Bose gas, the impurities localize either pairwise or completely in a single well. Tuning the lattice depth, the interspecies and intraspecies interaction strength correspondingly allows for a systematic control and engineering of the two localization patterns. The sharpness of the crossover between the two states as well as the broad region of their existence supports the robustness of the engineering. Moreover, we are able to manipulate the ground state's degeneracy in form of triplets, doublets and singlets by implementing different boundary conditions, such as periodic and hard wall boundary conditions.