Cavity QED and Quantum Computation in the Weak Coupling Regime

Abstract

In this paper we consider a model of quantum computation based on n atoms of laser-cooled and trapped linearly in a cavity and realize it as the n atoms Tavis-Cummings Hamiltonian interacting with n external (laser) fields. We solve the Schr{\" o}dinger equation of the model in the case of n=2 and construct the controlled NOT gate by making use of a resonance condition and rotating wave approximation associated to it. Our method is not heuristic but completely mathematical, and the significant feature is a consistent use of Rabi oscillations. We also present an idea of the construction of three controlled NOT gates in the case of n=3 which gives the controlled-controlled NOT gate.

Latex file, 22 pages, revised version. To appear in Journal of Optics B : Quantum and Semiclassical Optics

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Cited by in corpus (16)

• General Solution of the Quantum Damped Harmonic Oscillator
• Cavity QED and Quantum Computation in the Weak Coupling Regime II : Complete Construction of the Controlled-Controlled NOT Gate
• General Solution of the Quantum Damped Harmonic Oscillator II : Some Examples
• More on the Isomorphism $SU(2)\otimes SU(2)\cong SO(4)$
• From Quantum Optics to Non-Commutative Geometry : A Non-Commutative Version of the Hopf Bundle, Veronese Mapping and Spin Representation
• Quantum Mechanics with Complex Time : A Comment to the Paper by Rajeev
• Study on Dynamics of N Level System of Atom by Laser Fields
• An Approximate Solution of the Master Equation with the Dissipator being a Set of Projectors
• Exact Solution of a Master Equation Applied to the Two Level System of an Atom
• A Master Equation with Generalized Lindblad Form and a Unitary Transformation by the Squeezing Operator
• Jaynes-Cummings Model and a Non-Commutative "Geometry" : A Few Problems Noted
• A Generalization of the Preceding Paper ``A Rabi Oscillation in Four and Five Level Systems"
• Cavity QED and Quantum Computation in the Strong Coupling Regime II : Two Atoms Case
• Flow Representation of the Bose-Hubbard Hamiltonian : General Case
• Universal Yang-Mills Action on Four Dimensional Manifolds
• An Approximate Solution of the Jaynes-Cummings Model with Dissipation II : Another Approach