quantum games with atoms and cavities - Electrodynamique ...

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• Ions in traps Tools for fundamental quantum mechanics studies – Single addressable long-lived quantum systems – Two ion quantum gates – Simple algorithms, teleportation. – One of the most promising systems for few qubits implementations – Great experimental difficulties Florence, Mai 2004 36
• Mesoscopic circuits Tools for fundamental quantum mechanics studies – Long-lived two level systems (artificial atoms) – Two qubits quantum gates – Promising for ‘large scale’ integration – Decoherence not well understood Florence, Mai 2004 37
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 15 and 16: • No cloning theorem The “stran
Page 17 and 18: • Bell inequalities. The “stran
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: Tools for fundamental quantum mecha
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
Page 69 and 70: Ramsey “quantum eraser” • A s
Page 71 and 72: An EPR experiment revisited Conditi
Page 73 and 74: Another experiment on complementari
Page 75 and 76: A laboratory version of the Schröd
Page 77 and 78: Decoherence features • Faster tha
Page 79 and 80: Structure of the lectures • I) In
Page 81 and 82: II) The tools of CQED • 1) Quantu
Page 83 and 84: • Hamiltonian A mechanical oscill
Page 85 and 86: A mechanical oscillator • Operato
Page 87 and 88:
Field normalisation • Energy of F
Page 89 and 90:
Field quadratures • Coordinates f
Page 91 and 92:
Fock states • Fock states have a
Page 93 and 94:
Coherent state as a displacement of
Page 95 and 96:
Displacement and annihilation opera
Page 97 and 98:
• Again Glauber Fock states expan
Page 99 and 100:
Pictorial representation of a coher
Page 101 and 102:
Coherent states wavefunctions • U
Page 103 and 104:
Quasi-probability distributions •
Page 105 and 106:
Examples of Q functions • Five ph
Page 107 and 108:
Wigner function: an insight into a
Page 109 and 110:
Wigner function • Wigner function
Page 111 and 112:
Vacuum |0> Examples of Wigner funct
Page 113 and 114:
An alternative simple expression of
Page 115 and 116:
Schrödinger cat states • An exam
Page 117 and 118:
Graphical interpretation of quadrat
Page 119 and 120:
Wigner function of phase-cat states
Page 121 and 122:
II) The tools of CQED • 1) Quantu
Page 123 and 124:
The Kraus approach • Any mapping
Page 125 and 126:
Physical interpretation of the L i
Page 127 and 128:
A more standard approach • A simp
Page 129 and 130:
One term out of 16 • One of the t
Page 131 and 132:
Heisenberg picture: Langevin forces
Page 133 and 134:
Thermal field vs coherent field Flo
Page 135 and 136:
Quantum Monte Carlo trajectories
Page 137 and 138:
Equivalence with Lindblad • Avera
Page 139 and 140:
Relaxation of a Fock state • Fock
Page 141 and 142:
Relaxation in terms of characterist
Page 143 and 144:
Relaxation of a Schrödinger cat
Page 145 and 146:
Understanding fast decoherence •
Page 147 and 148:
Illustrated cat relaxation Florence
Page 149 and 150:
Beamsplitters • A semi transparen
Page 151 and 152:
A simple quantum model • With and
Page 153 and 154:
• Fock state input Action on simp
Page 155 and 156:
Action on simple states • Modes a
Page 157 and 158:
• Two interfering paths • Coher
Page 159 and 160:
Single photon interferences in a Ma
Page 161 and 162:
• Coherent input Sensitivity of t
Page 163 and 164:
An insight into coherent field rela
Page 165 and 166:
II) The tools of CQED • 1) Quantu
Page 167 and 168:
Bloch sphere • Most general state
Page 169 and 170:
• Global hamiltonian Atom-cavity
Page 171 and 172:
The dressed levels • Eigenstates
Page 173 and 174:
The quantum Rabi oscillation • An
Page 175 and 176:
Non resonant case • Position of d
Page 177 and 178:
Action of an atom on a coherent fie
Page 179 and 180:
Taking into account atomic motion -
Page 181 and 182:
Rabi rotation on the Bloch sphere
Page 183 and 184:
The Ramsey interferometer • Two
Page 185 and 186:
Ramsey fringes with cold atoms •
Page 187 and 188:
Rabi oscillation in a mesoscopic fi
Page 189 and 190:
Atomic relaxation • Atomic densit
Page 191 and 192:
Spontaneous emission in a Monte Car
Page 193 and 194:
General scheme of the experiments R
Page 195 and 196:
Circular states wavefunction • Si
Page 197 and 198:
• Ionization threshold A classica
Page 199 and 200:
52 F m=2 Circular state preparation
Page 201 and 202:
Velocity selection Doppler selectiv
Page 203 and 204:
Superconducting cavity Design Highl
Page 205 and 206:
Two cavity modes • Two modes with
Page 207 and 208:
Ring and coherent atomic state mani
Page 209 and 210:
Aim: Cavity cooling Get rid of a re
Page 211 and 212:
Structure of the lectures • I) In
Page 213 and 214:
III) Experimental illustrations of
Page 215 and 216:
• ∆ c /2π=150 kHz Light shifts
Page 217 and 218:
Page 219 and 220:
• A gain/loss analysis A semi-cla
Page 221 and 222:
Quantum model • Equation for the
Page 223 and 224:
Photon number variance • Strong s
Page 225 and 226:
2π quantum Rabi pulse Initial stat
Page 227 and 228:
Absorption-free detection of a sing
Page 229 and 230:
A repeated QND measurement Measure
Page 231 and 232:
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 and 280:
Exemple élémentaire Factoriser 15
Page 281 and 282:
Amplitude Algorithme quantique (2)
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:
Page 331 and 332:
V) Schrödinger cats and decoherenc
Page 333 and 334:
Main features of decoherence Very f
Page 335 and 336:
1.0 0.5 0.0 Fringes and field state
Page 337 and 338:
A laboratory version of the Schröd
Page 339 and 340:
A decoherence study Atomic correlat
Page 341 and 342:
Theoretical decoherence signal Atom
Page 343 and 344:
V) Schrödinger cats and decoherenc
Page 345 and 346:
Rabi oscillation in a mesoscopic fi
Page 347 and 348:
An insightful quasi-exact solution
Page 349 and 350:
An insightful quasi-exact solution
Page 351 and 352:
‘Automatic’ preparation of a Sc
Page 353 and 354:
Link with Rabi oscillation + Rabi o
Page 355 and 356:
Field states phase spreading • On
Page 357 and 358:
Direct observation of field phase e
Page 359 and 360:
Experimental coherent field phase d
Page 361 and 362:
Phase splitting in quantum Rabi osc
Page 363 and 364:
Phase (degrees) Phase splitting in
Page 365 and 366:
Stopped Rabi oscillation 1,0 Rabi Z
Page 367 and 368:
Test of coherence: induced quantum
Page 369 and 370:
Induced quantum revivals 0,9 0,8 0,
Page 371 and 372:
Phase shift with dispersive atom-fi
Page 373 and 374:
Towards a 100% efficiency atomic de
Page 375 and 376:
Page 377 and 378:
Historical reference St Paul's Cath
Page 379 and 380:
Production of microspheres Preparat
Page 381 and 382:
The core of the experiment Florence
Page 383 and 384:
Tuning WGM´s TE TM • FSR = 810 G
Page 385 and 386:
Reversibility and Stability Tuning
Page 387 and 388:
Which experiments • Non linearit
Page 389 and 390:
Atom-Chip : Conveyor-Belt Florence,
Page 391 and 392:
Longitudinal Confinement • Multip
Page 393 and 394:
Long Distance Transport 23,5 cm in
Page 395 and 396:
Quantum dots and microspheres • A
Page 397 and 398:
Effects of Sample on WGM’s Gap g2
Page 399 and 400:
Q-Dots Laser Experimental Set Up Em
Page 401 and 402:
Page 403 and 404:
Two main directions • A two-cavit
Page 405 and 406:
C Teleportation of an atomic state
Page 407 and 408:
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
Page 419 and 420:
Rydberg Atom Trapping Candidate Tec
Page 421 and 422:
Trap Geometry U V(t) U V(t) U V(t)
Page 423 and 424:
Electric Field Tilt F 0 (x,y,z) F l
Page 425 and 426:
A Tighter Trap Same field variation
Page 427 and 428:
Ground-State Atoms Trapping Require
Page 429 and 430:
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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