Effective Hamiltonian Theory and Its Applications in Quantum Information

Abstract

This paper presents a useful compact formula for deriving an effective Hamiltonian describing the time-averaged dynamics of detuned quantum systems. The formalism also works for ensemble-averaged dynamics of stochastic systems. To illustrate the technique we give examples involving Raman processes, Bloch-Siegert shifts and Quantum Logic Gates.

5 pages, 3 figures, to be published in Canadian Journal of Physics

References in corpus (8)

• Quantum computation with ions in thermal motion
• Entanglement and quantum computation with ions in thermal motion
• Quantum dynamics of cold trapped ions, with application to quantum computation
• Quantum Computation with hot and cold ions:An assessment of proposed schemes
• Entangling atoms in bad cavities
• Light-shift-induced quantum gates for ions in thermal motion
• Scheme for the implementation of a universal quantum cloning machine via cavity-assisted atomic collisions in cavity QED
• Effective Hamiltonians in quantum optics: a systematic approach

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