# Multipartite W states for chains of atoms conveyed through an optical cavity

## TL;DR

This paper presents a deterministic scheme to generate multipartite W entangled states in chains of atoms transported through an optical cavity, with the entanglement quality controlled by atom spacing and velocity.

## Contribution

It introduces a novel method for creating entangled W states in atomic chains using laser-cavity interactions, with detailed parameter analysis for different chain sizes.

## Key findings

- Effective entanglement generation for N=2 to 5 atoms.
- Identification of optimal parameter regions for reliable W state creation.
- Analysis of entanglement sensitivity to atomic oscillations.

## Abstract

We propose and work out a scheme to generate the entangled W states for a chain of N four-level atoms which are transported through an optical cavity by means of an optical lattice. This scheme is based on the combined laser-cavity mediated interaction between distant and equally separated atoms and works in a completely deterministic way for qubits encoded by two hyperfine levels of the atoms. Only two parameters, namely the distance between the atoms and the velocity of the chain, determine the effective interaction among the atoms and, therefore, the degree of entanglement that is obtained for the overall chain of N qubits. In particular, we work out the parameter regions for which the W states are generated most reliably for chains of N = 2,3,4 and 5 atoms. In addition, we analyze the sensitivity in the formation of entanglement for such chains of qubits due to uncertainties produced by the oscillations of atoms in optical lattices.