[Paper Review] Generation of maximally entangled states of two cavity modes

Farhan Saif, Mahmoud Abdel‐Aty+3 more|ArXiv.org|May 20, 2006

Quantum Information and Cryptography3 citations

TL;DR

This paper proposes a cavity quantum electrodynamics scheme using a Rydberg-dressed three-level atom to generate maximally entangled Bell states between two cavity modes. By controlling the atom's interaction time with the cavity fields—via Rabi oscillations and Stark shifts—it implements universal quantum logic gates, including a controlled-NOT gate and a Hadamard gate, enabling full preparation of the Bell basis with simple initial states.

ABSTRACT

In this letter we present a scheme for generating maximally entangled states of two cavity modes which enables us to generate complete set of Bell basis states having rather simple initial state preparation. Furthermore, we study the interaction of a two-level atom with two modes of electromagnetic field in a high Q cavity. The two-level atom acts as a control qubit and the two mode electromagnetic field serves as a target qubit. This simple system of quantum electrodynamics provides us experimentally feasible universal quantum logic gates.

Motivation & Objective

• To develop an experimentally feasible method for generating all four Bell basis states in a two-mode cavity field.
• To realize universal quantum logic gates—specifically CNOT and Hadamard gates—using a single two-level atom as a control qubit.
• To enable complete preparation of maximally entangled states with minimal initial state complexity.
• To demonstrate the feasibility of implementing quantum algorithms and protocols such as quantum teleportation and cryptography in a high-Q superconducting cavity setup.

Proposed method

• Use a three-level V-configuration atom with two excited states and a ground state, prepared in a superposition of the two upper levels.
• Employ a high-Q superconducting cavity supporting two orthogonal TEM modes (MA and MB) with distinct frequencies and photon damping times.
• Apply a Stark field to shift the atomic transition frequency, enabling resonant interaction with one cavity mode at a time.
• Control interaction times to be odd multiples of half-Rabi cycles to generate entanglement between the two cavity modes.
• Use Rabi oscillation periods (T_Rabi = 2π/Ω) to engineer conditional dynamics: one photon is transferred to a target mode only when the atom is in the excited state.
• Implement a Hadamard gate by interacting the atom with a cavity mode for a quarter Rabi period, creating a superposition state.

Experimental results

Research questions

• RQ1 Can a single two-level atom in a cavity be used to generate all four Bell states of two cavity modes?
• RQ2 How can the interaction time and Stark field control be used to engineer a universal quantum CNOT gate between the atom and two-mode field?
• RQ3 What initial atomic state preparation and interaction sequence are required to achieve maximal entanglement between two cavity fields?
• RQ4 Is the proposed scheme experimentally realizable with current Rydberg atom and cavity QED technology?
• RQ5 Can this system serve as a platform for implementing multi-qubit quantum gates and quantum communication protocols?

Key findings

• The scheme successfully generates all four Bell states of two cavity modes using a single atom and controlled interaction times.
• Maximal entanglement is achieved when the atom interacts with the cavity for odd multiples of half the Rabi period, leading to equal superposition of vacuum and one-photon states in the two modes.
• A Hadamard gate is realized by a quarter-Rabi-period interaction, creating a superposition state between the atom's ground and excited states with the field in a Fock state.
• The CNOT gate is implemented by using the atom as control: when the atom is in the excited state, it induces a phase flip or photon transfer in the target mode, depending on the field state.
• The system achieves a fidelity close to 100% for Bell state generation under ideal conditions, with experimental feasibility demonstrated via 51Rb Rydberg states and millisecond photon lifetimes.
• The scheme enables field swapping and entanglement swapping between cavity modes, supporting scalable quantum information processing.