quantum games with atoms and cavities - Electrodynamique ...

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The “strangeness” of the quantum • Complementarity and Heisenberg uncertainty relations Particle's momentum p=h/λ Momentum transfer ∆P=pd/D Measure screen momentum within ∆P: ∆x=a Position uncertainty ∆X=h/∆P d D Position uncertainty= interfrange. Complete washing out of fringes Localisation and wave behavior are incompatible Florence, Mai 2004 14
• No cloning theorem The “strangeness” of the quantum – It is impossible to produce two exact copies of an arbitrary quantum states (violates unitarity of Schrödinger evolution): No quantum fax Florence, Mai 2004 15
Page 1 and 2: Entanglement, complementarity and d
Page 3 and 4: A century of quantum mechanics One
Page 5 and 6: A century of quantum mechanics •
Page 11 and 12: The “strangeness” of the quantu
Page 13: The “strangeness” of the quantu
Page 17 and 18: • Bell inequalities. The “stran
Page 19 and 20: The “strangeness” of the quantu
Page 21 and 22: A severe test The “strangeness”
Page 23 and 24: Main features of decoherence Very f
Page 25 and 26: Why explorations of the quantum wor
Page 27 and 28: Quantum teleportation Principle Exp
Page 29 and 30: - Initial state Quantum teleportati
Page 31 and 32: Organisation of a quantum computer
Page 33 and 34: Tools for fundamental quantum mecha
Page 35 and 36: Tools for fundamental quantum mecha
Page 37 and 38: • Mesoscopic circuits Tools for f
Page 39 and 40: A short history of cavity QED • T
Page 41 and 42: Microwave CQED • A single Rydberg
Page 43 and 44: An “appetizer” chapter • A br
Page 45 and 46: Circular Rydberg atoms High princip
Page 47 and 48: General scheme of the experiments R
Page 49 and 50: An object at the quantum/classical
Page 51 and 52: Rabi oscillation in a small coheren
Page 53 and 54: Rabi oscillation in a small coheren
Page 55 and 56: Field quantization • Many evidenc
Page 57 and 58: Three "stitches" to "knit" quantum
Page 59 and 60: A “modern” version of Bohr’s
Page 61 and 62: Complementarity and uncertainty rel
Page 63 and 64: Entanglement and complementarity En
Page 65 and 66:
Experimental requirements • Ramse
Page 67 and 68:
Quantum/classical limit for an inte
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Ramsey “quantum eraser” • A s
Page 71 and 72:
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
Page 81 and 82:
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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Page 213 and 214:
III) Experimental illustrations of
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• ∆ c /2π=150 kHz Light shifts
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Page 219 and 220:
• 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
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A repeated QND measurement Measure
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Page 233 and 234:
RESULTATS EXPERIMENTAUX Smithey et
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Other methods • Use the link betw
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Our approach - Proposed by Lutterba
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For φ=φ* : If N even, detection i
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Testing the method: vacuum state Wi
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Single photon Wigner function measu
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Towards other states - Cavity QED s
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Generation of a single photon state
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Two-photon generation with a single
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Measuring the photon number • Use
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IV) Quantum information with atoms
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Ordinateurs classiques et complexit
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Principe d'un ordinateur quantique
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Parallélisme quantique massif On p
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Portes logiques quantiques Théorè
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Portes (suite 2) Portes à n bits
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Calcul de fonctions élémentaires
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Les problèmes posés sous forme d
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Exemple élémentaire Algorithme de
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Généralisation : Deutsch-Josza po
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Remarques 1. Où est l’intricatio
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Détermination de la période incon
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Factorisation Un problème classiqu
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Exemple élémentaire Factoriser 15
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Amplitude Algorithme quantique (2)
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Simulation quantique Un autre domai
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Quantum Rabi oscillations Initial a
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Three "stitches" to "knit" quantum
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• Final signal Coherent informati
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Preparation and detection of a sing
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Testing entanglement Two complement
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Fidelity Fidelity estimate F = Tr(
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A quantum phase gate Principle 2π
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A single atom phase-shifts the fiel
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Tuning the quantum gate phase Role
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• prepared state: The "GHZ" state
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Measurement of σ z1 . σ z2 . σ z
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Measurement results: • measuremen
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Fidelity of preparation of the GHZ
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IV) Quantum information with atoms
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Cavity-assisted van der Waals colli
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Advantage of non-resonant method of
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Tests of entanglement Population tr
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Next step: solve the simplest quant
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We are looking for a particular sta
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• CAVITY QED: (N=4) = H = SI QPG
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e e g t = e iλt [ cos ( λt ) e g
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• The search algorithm: Q = SI QP
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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
Page 405 and 406:
C Teleportation of an atomic state
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Quantum feedback • Preserve a Sch
Page 409 and 410:
Feedback efficiency Florence, Mai 2
Page 411 and 412:
New non-locality explorations • U
Page 413 and 414:
Bell inequalities violation • Opt
Page 415 and 416:
A difficult but feasible experiment
Page 417 and 418:
What we want • Long State Lifetim
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Rydberg Atom Trapping Candidate Tec
Page 421 and 422:
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
Page 431 and 432:
Very long coherence times Coherence
Page 433 and 434:
The team PhD • Frédérick .Berna
Page 435 and 436:
References (2) • QND measurement
Page 437 and 438:
References (4) • Reviews on CQED
Page 439:
• THANK YOU ….. Florence, Mai 2
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