quantum games with atoms and cavities - Electrodynamique ...

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Algorithme quantique (1) Principe Calculer beaucoup de valeurs de f en utilisant le parallélisme et extraire la période (~ N) Deux registres de m qubits. q=2 m choisi tel que 2N 2 < q < 4N 2 État initial 0,0 Superposition de tous les nombres q−1 1 0,0 ⎯⎯→ ϕ = ∑ a,0 q a= 0 Pour chaque qubit: 1 0 ⎯⎯→ ( 0 + 1 ) 2 Exponentiation modulaire q−1 1 a ϕ ⎯⎯→ ∑ ax , N q Possible de façon efficace Utilise le parallélisme Mesure du second registre Obtention d'une valeur aléatoire y Projection du premier registre sur les antécédents de y Florence, Mai 2004 280 k+jr a= 0 [ ] k aléatoire, j entier Le premier registre contient une superposition d'états répartis périodiquement avec la période r 1 A ∑ j k + jr
Amplitude Algorithme quantique (2) Répartition des amplitudes Après la transformation de Fourier k k+r k+2r k+jr Vecteur La mesure du premier registre en l'état ne donne aucune information ("offset" k aléatoire) Extraire la période: réaliser une transformation de Fourier discrète Possible de façon efficace (en un temps polynomial) Amélioration exponentielle/FFT classique q/ r 2q/ r Mesure du registre: une valeur de la forme p q/r p entier arbitraire Par un calcul classique efficace, extraction, avec une probabilité finie, de r et factorisation de N Énormes conséquences pratiques si on peut réaliser cet algorithme Florence, Mai 2004 281
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Entanglement, complementarity and d
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A century of quantum mechanics One
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A century of quantum mechanics •
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The “strangeness” of the quantu
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• No cloning theorem The “stran
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• Bell inequalities. The “stran
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A severe test The “strangeness”
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Main features of decoherence Very f
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Why explorations of the quantum wor
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Quantum teleportation Principle Exp
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- Initial state Quantum teleportati
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Organisation of a quantum computer
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Tools for fundamental quantum mecha
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Tools for fundamental quantum mecha
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• Mesoscopic circuits Tools for f
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A short history of cavity QED • T
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Microwave CQED • A single Rydberg
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An “appetizer” chapter • A br
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Circular Rydberg atoms High princip
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General scheme of the experiments R
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An object at the quantum/classical
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Rabi oscillation in a small coheren
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Rabi oscillation in a small coheren
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Field quantization • Many evidenc
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Three "stitches" to "knit" quantum
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A “modern” version of Bohr’s
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Complementarity and uncertainty rel
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Entanglement and complementarity En
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Experimental requirements • Ramse
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Quantum/classical limit for an inte
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Ramsey “quantum eraser” • A s
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An EPR experiment revisited Conditi
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Another experiment on complementari
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A laboratory version of the Schröd
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Decoherence features • Faster tha
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Structure of the lectures • I) In
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II) The tools of CQED • 1) Quantu
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• Hamiltonian A mechanical oscill
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A mechanical oscillator • Operato
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Field normalisation • Energy of F
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Field quadratures • Coordinates f
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Fock states • Fock states have a
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Coherent state as a displacement of
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Displacement and annihilation opera
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• Again Glauber Fock states expan
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Pictorial representation of a coher
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Coherent states wavefunctions • U
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Quasi-probability distributions •
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Examples of Q functions • Five ph
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Wigner function: an insight into a
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Wigner function • Wigner function
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Vacuum |0> Examples of Wigner funct
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An alternative simple expression of
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Schrödinger cat states • An exam
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Graphical interpretation of quadrat
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Wigner function of phase-cat states
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The Kraus approach • Any mapping
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Physical interpretation of the L i
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A more standard approach • A simp
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One term out of 16 • One of the t
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Heisenberg picture: Langevin forces
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Thermal field vs coherent field Flo
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Quantum Monte Carlo trajectories
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Equivalence with Lindblad • Avera
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Relaxation of a Fock state • Fock
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Relaxation in terms of characterist
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Relaxation of a Schrödinger cat
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Understanding fast decoherence •
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Illustrated cat relaxation Florence
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Beamsplitters • A semi transparen
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A simple quantum model • With and
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• Fock state input Action on simp
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Action on simple states • Modes a
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• Two interfering paths • Coher
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Single photon interferences in a Ma
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• Coherent input Sensitivity of t
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An insight into coherent field rela
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Bloch sphere • Most general state
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• Global hamiltonian Atom-cavity
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The dressed levels • Eigenstates
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The quantum Rabi oscillation • An
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Non resonant case • Position of d
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Action of an atom on a coherent fie
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Taking into account atomic motion -
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Rabi rotation on the Bloch sphere
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The Ramsey interferometer • Two
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Ramsey fringes with cold atoms •
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Rabi oscillation in a mesoscopic fi
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Atomic relaxation • Atomic densit
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Spontaneous emission in a Monte Car
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General scheme of the experiments R
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Circular states wavefunction • Si
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• Ionization threshold A classica
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52 F m=2 Circular state preparation
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Velocity selection Doppler selectiv
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Superconducting cavity Design Highl
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Two cavity modes • Two modes with
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Ring and coherent atomic state mani
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Aim: Cavity cooling Get rid of a re
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III) Experimental illustrations of
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• ∆ c /2π=150 kHz Light shifts
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III) Experimental illustrations of
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• A gain/loss analysis A semi-cla
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Quantum model • Equation for the
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Photon number variance • Strong s
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2π quantum Rabi pulse Initial stat
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Absorption-free detection of a sing
Page 229 and 230: A repeated QND measurement Measure
Page 231 and 232: III) Experimental illustrations of
Page 233 and 234: RESULTATS EXPERIMENTAUX Smithey et
Page 235 and 236: Other methods • Use the link betw
Page 237 and 238: Our approach - Proposed by Lutterba
Page 239 and 240: For φ=φ* : If N even, detection i
Page 241 and 242: Testing the method: vacuum state Wi
Page 243 and 244: Single photon Wigner function measu
Page 245 and 246: Towards other states - Cavity QED s
Page 247 and 248: Generation of a single photon state
Page 249 and 250: Two-photon generation with a single
Page 251 and 252: Measuring the photon number • Use
Page 253 and 254: IV) Quantum information with atoms
Page 255 and 256: Ordinateurs classiques et complexit
Page 257 and 258: Principe d'un ordinateur quantique
Page 259 and 260: Parallélisme quantique massif On p
Page 261 and 262: Portes logiques quantiques Théorè
Page 263 and 264: Portes (suite 2) Portes à n bits
Page 265 and 266: Calcul de fonctions élémentaires
Page 267 and 268: Les problèmes posés sous forme d
Page 269 and 270: Exemple élémentaire Algorithme de
Page 271 and 272: Généralisation : Deutsch-Josza po
Page 273 and 274: Remarques 1. Où est l’intricatio
Page 275 and 276: Détermination de la période incon
Page 277 and 278: Factorisation Un problème classiqu
Page 279: Exemple élémentaire Factoriser 15
Page 283 and 284: Simulation quantique Un autre domai
Page 285 and 286: Quantum Rabi oscillations Initial a
Page 287 and 288: Three "stitches" to "knit" quantum
Page 289 and 290: • Final signal Coherent informati
Page 291 and 292: Preparation and detection of a sing
Page 293 and 294: Testing entanglement Two complement
Page 295 and 296: Fidelity Fidelity estimate F = Tr(
Page 297 and 298: A quantum phase gate Principle 2π
Page 299 and 300: A single atom phase-shifts the fiel
Page 301 and 302: Tuning the quantum gate phase Role
Page 303 and 304: • prepared state: The "GHZ" state
Page 305 and 306: Measurement of σ z1 . σ z2 . σ z
Page 307 and 308: Measurement results: • measuremen
Page 309 and 310: Fidelity of preparation of the GHZ
Page 311 and 312: IV) Quantum information with atoms
Page 313 and 314: Cavity-assisted van der Waals colli
Page 315 and 316: Advantage of non-resonant method of
Page 317 and 318: Tests of entanglement Population tr
Page 319 and 320: Next step: solve the simplest quant
Page 321 and 322: We are looking for a particular sta
Page 323 and 324: • CAVITY QED: (N=4) = H = SI QPG
Page 325 and 326: e e g t = e iλt [ cos ( λt ) e g
Page 327 and 328: • The search algorithm: Q = SI QP
Page 329 and 330: Structure of the lectures • I) In
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V) Schrödinger cats and decoherenc
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Main features of decoherence Very f
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1.0 0.5 0.0 Fringes and field state
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A laboratory version of the Schröd
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A decoherence study Atomic correlat
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Theoretical decoherence signal Atom
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V) Schrödinger cats and decoherenc
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Rabi oscillation in a mesoscopic fi
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An insightful quasi-exact solution
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An insightful quasi-exact solution
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‘Automatic’ preparation of a Sc
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Link with Rabi oscillation + Rabi o
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Field states phase spreading • On
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Direct observation of field phase e
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Experimental coherent field phase d
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Phase splitting in quantum Rabi osc
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Phase (degrees) Phase splitting in
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Stopped Rabi oscillation 1,0 Rabi Z
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Test of coherence: induced quantum
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Induced quantum revivals 0,9 0,8 0,
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Phase shift with dispersive atom-fi
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Towards a 100% efficiency atomic de
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Historical reference St Paul's Cath
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Production of microspheres Preparat
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The core of the experiment Florence
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Tuning WGM´s TE TM • FSR = 810 G
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Reversibility and Stability Tuning
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Which experiments • Non linearit
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Atom-Chip : Conveyor-Belt Florence,
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Longitudinal Confinement • Multip
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Long Distance Transport 23,5 cm in
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Quantum dots and microspheres • A
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Effects of Sample on WGM’s Gap g2
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Q-Dots Laser Experimental Set Up Em
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Two main directions • A two-cavit
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C Teleportation of an atomic state
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Quantum feedback • Preserve a Sch
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Feedback efficiency Florence, Mai 2
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New non-locality explorations • U
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Bell inequalities violation • Opt
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A difficult but feasible experiment
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What we want • Long State Lifetim
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Rydberg Atom Trapping Candidate Tec
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Trap Geometry U V(t) U V(t) U V(t)
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Electric Field Tilt F 0 (x,y,z) F l
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A Tighter Trap Same field variation
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Ground-State Atoms Trapping Require
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Coherence preservation scheme • U
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Very long coherence times Coherence
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The team PhD • Frédérick .Berna
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References (2) • QND measurement
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References (4) • Reviews on CQED
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• THANK YOU ….. Florence, Mai 2
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