# Complementarity between micro-micro and micro-macro entanglement in a Bose-Einstein condensate with two Rydberg impurities

## TL;DR

This paper explores how micro-micro and micro-macro entanglement in a Bose-Einstein condensate with Rydberg impurities are interconnected, showing that initial micro-micro entanglement can generate strong micro-macro entanglement despite decoherence effects.

## Contribution

It introduces a theoretical analysis of the complementarity between micro-micro and micro-macro entanglement in a BEC with Rydberg impurities, highlighting the role of initial micro-micro entanglement as a seed.

## Key findings

- Strong micro-macro entanglement can be generated from initial micro-micro entanglement.
- A complementarity relation between micro-micro and micro-macro entanglement is demonstrated.
- The complementarity persists despite decoherence effects.

## Abstract

We theoretically study complementarity between micro-micro and micro-macro entanglement in a Bose-Einstein condensate with two Rydberg impurities. We investigate quantum dynamics of micro-micro and micro-macro entanglement in the micro-macro system. It is found that strong micro-macro entanglement between Rydberg impurities and the BEC can be generated by the use of initial micro-micro entanglement between two Rydberg impurities, which acts as the seed entanglement to create micro-macro entanglement. We demonstrate a curious complementarity relation between micro-micro and micro-macro entanglement, and find that the complementarity property can be sustained to some extend even though in the presence of the BEC decoherence.