Efficient Preparation of Entangled States in Cavity QED with Grover's Algorithm

Area of Science:

• Quantum Information Science
• Atomic Physics
• Quantum Computing

Background:

• Entangled states are crucial for quantum computing and communication.
• Efficiently preparing entangled states, especially for ensembles of qubits, remains a challenge.
• Existing methods often require individual atom addressing or complex experimental setups.

Purpose of the Study:

• To develop an efficient method for preparing entangled states of atomic ensembles.
• To leverage Grover's search algorithm for deterministic state preparation.
• To explore the creation of specific multi-atom entangled states like Dicke, GHZ, and Schrödinger cat states.

Main Methods:

• Utilizing the amplification mechanism of Grover's search algorithm.
• Implementing conditional sign change via photon scattering on an optical cavity with an atomic ensemble.
• Employing phase shifts of scattered photons to induce entanglement.

Main Results:

• Deterministic preparation of collective Dicke states, Greenberger-Horne-Zeilinger states, and Schrödinger cat superpositions.
• Achieving state preparation with a low number of photon scattering events (approximately N^{1/4}).
• Demonstrating the feasibility without the need for individual atom addressing.

Conclusions:

• The proposed method offers an efficient and deterministic route to multi-atom entanglement.
• Grover's algorithm provides a powerful framework for quantum state preparation in atomic ensembles.
• This approach has significant implications for building scalable quantum information processors.