# Quantum Spin Lenses in Atomic Arrays

## TL;DR

The paper introduces quantum spin lenses that coherently focus delocalized spin excitations in atomic arrays to single atoms, enabling advanced quantum information processing and entanglement distribution.

## Contribution

It proposes Hamiltonians for quantum spin lenses in inhomogeneous spin models realizable with Rydberg atoms and trapped ions, including linear, non-linear, and multifocal variants.

## Key findings

- Quantum spin lenses can focus delocalized excitations to single atoms.
- Non-linear lenses enable conditional focusing based on excitation number.
- Multifocal lenses can generate and distribute entanglement across atomic arrays.

## Abstract

We propose and discuss `quantum spin lenses', where quantum states of delocalized spin excitations in an atomic medium are `focused' in space in a coherent quantum process down to (essentially) single atoms. These can be employed to create controlled interactions in a quantum light-matter interface, where photonic qubits stored in an atomic ensemble are mapped to a quantum register represented by single atoms. We propose Hamiltonians for quantum spin lenses as inhomogeneous spin models on lattices, which can be realized with Rydberg atoms in 1D, 2D and 3D, and with strings of trapped ions. We discuss both linear and non-linear quantum spin lenses: in a non-linear lens, repulsive spin-spin interactions lead to focusing dynamics conditional to the number of spin excitations. This allows the mapping of quantum superpositions of delocalized spin excitations to superpositions of spatial spin patterns, which can be addressed by light fields and manipulated. Finally, we propose multifocal quantum spin lenses as a way to generate and distribute entanglement between distant atoms in an atomic lattice array.