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Quantum Optics and applications to Quantum Information
(July - August 2010)
Prof. Gaetan Messin
Institut d¡¯Optique, Palaiseau, France

Outline of the course:

Week starting Monday July 12:

The quantum field and its states

•        Electromagnetic field quantization: Single mode quantization, single mode fluctuation, quadrature operators and non-commutation, multimode fields, photons.
•        Quantum states of the field: States of a monomode quantum field: number state, coherent state, squeezed state, thermal state, vacuum fluctuations, entangled states.
                - Problem #1 on calculations of variances of the Electromagnetic field.

Week starting Monday July 19

Quantum optics tools and methods (1)

•        State characterization: Single photon photodetection theory, action of a beamsplitter on a quantum field, multiple photodetection, bunching and anti-bunching, homodyne detection, noise spectrum.
•         Saturated single emitter: Light-matter interaction, dipolar approximation, spontaneous emission, Fermi¡¯s golden rule. Illustration: Single photon emission with a single trapped atom.
                - Problem#2 on Wigner-Weisskopf theory

Week starting Monday July 26

Quantum optics tools and methods (2)

•         Nonlinear quantum optics: Parametric down conversion, photon pairs, application to single photon sources, production of squeezed vacuum, 4-wave mixing, squeezing of coherent states.
•        Entanglement: Producing entangled states of the light, fidelity, Bell¡¯s inequality violation, indistinguishable photons, 2-photon interferences, entanglement swapping.
                - Problem #3 on the Hong-Ou-Mandel effect

Week starting Monday August 2

Applications to Quantum information (1)

•         Single photon sources and application to quantum cryptography: Single photon emission with NV centers, CdSe nanocrystals and single rubidium trapped atom. Bunching and antibunching effects. Practical realization of BB84 with single photons.
                - Problem#4 on single photon emission by a two level emitter

•        Sources of photons pairs for quantum teleportation. Production of photon pairs with PPLN & PPKTP. Teleportation protocol. Introduction to quantum repeaters.

Week starting Monday August 9

Applications to Quantum information (2)

•        Single photons emitters and application to quantum computing. Emission of indistinguishable photons by two single trapped atoms, two-photon interferences. Conditionnal entanglement of two emitters. Single atoms turned to single quantum bits. C-Not gate using Rydberg states.
•        Final examination followed by the correction of the exam problem.

Reference£º

"Quantum Optics, an introduction", Mark Fox, (Oxford Master Series, 2006)

¡°The quantum Theory of light", R. Loudon, (Oxford Univ. Press 3rd Ed., 2003)

"Introductory Quantum Optics¡±, C.C. Gerry and P.L. Knight, (Cambridge Univ. Press, 2005)

¡°Atom-Photon Interactions, basic processes and applications¡±, C. Cohen-Tannoudji, J. Dupont-Roc, G. Grynberg, Wiley (1992).
¡°Two-dimensional transport and transfer of a single atomic qubit in optical tweezers¡±, J. Beugnon, C. Tuchendler, H. Marion, A. Gaëtan, G. Messin, A. Browaeys, P. Grangier.£¬Nature Physics 3, 696-699 (2007).
¡°Quantum interference between two single photons emitted by independently trapped atoms¡±, J. Beugnon, G. Messin, A. Browaeys, P. Grangier.£¬Nature 440, 779-782 (2006).
¡°Controlled Single-Photon Emission from a Single trapped Two-Level Atom¡±, B. Darqui¨¦, M. P. A. Jones, J. Dingjan, G. Messin, A. Browaeys, P. Grangier.£¬Science 309, 454-456 (2005).
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