Efficient preparation of entangled states in cavity QED with Grover's algorithm

TL;DR

This paper introduces a method using Grover's algorithm to efficiently generate various entangled states in cavity QED systems, significantly reducing the number of photon scattering events needed.

Contribution

It presents a novel approach leveraging Grover's amplification mechanism for deterministic entangled state preparation in atomic ensembles within optical cavities.

Findings

Preparation of Dicke, GHZ, and Schrödinger cat states achieved.

Number of photon scattering events scales as approximately N^{1/4}.

Method does not require individual atom addressing.

Abstract

We propose to employ the amplification mechanism of Grover's search algorithm to efficiently prepare entangled states of an ensemble of qubits. The conditional change of sign employed in the algorithm can be implemented by the phase shift of photons scattered on an optical cavity hosting an atomic ensemble. We show that collective Dicke states, GHZ states, and Schr\"odinger cat superpositions of $N$ atoms may be prepared deterministically by few ($\sim N^{1/4}$) photon scattering events without individual addressing of the atoms.