# Hyperfine state entanglement of spinor BEC and scattering atom

## TL;DR

This paper investigates the entanglement between a spinor Bose-Einstein condensate and a scattering atom, deriving scattering amplitudes and entanglement entropy analytically, revealing potential for quantum thermal ensemble formation.

## Contribution

It introduces a rigorous method using fractional parentage coefficients to analyze spin degrees of freedom and demonstrates entanglement generation through scattering in spinor BECs.

## Key findings

- Channels with enhanced scattering cross sections proportional to atom number squared.
- Analytical expression for entanglement entropy for arbitrary initial states.
- Hints at establishing quantum thermal ensembles in hyperfine space.

## Abstract

Condensate of spin-1 atoms frozen in a unique spatial mode may possess large internal degrees of freedom. The scattering amplitudes of polarized cold atoms scattered by the condensate are obtained with the method of fractional parentage coefficients that treats the spin degrees of freedom rigorously. Channels with scattering cross sections enhanced by square of atom number of the condensate are found. Entanglement between the condensate and the propagating atom can be established by the scattering. The entanglement entropy is analytically obtained for arbitrary initial states. Our results also give hint for the establishment of quantum thermal ensembles in the hyperfine space.