Quantum chaos - Physique des Lasers, Atomes et Molecules

phlam.univ.lille1.fr

Quantum chaos - Physique des Lasers, Atomes et Molecules

Presentation Title 1

Jean-Claude Garreau

Quantum meets chaotic

SFP/BPS Congress

Lille – August 2005

Laboratoire de Physique des Lasers, Atomes et Molécules

Université des Sciences et Technologies de Lille


Presentation « Quantum chaos » group 2

Presentation

1. Title

The group

→ 2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Permanent researchers

Pascal Szriftgiser – Véronique Zehnlé - JCG

Post-doc

Hugo Cavalcante

Ph.D.

Julien Chabé – Quentin Thommen - Hans Lignier

Collaboration

Dominique Delande – LKB - Paris


Introduction Introduction 3

Presentation

1. Title

The group

2. The group

Introduction

→ 3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum x classical

- Quantum dynamics ≠ classical dynamics

- Linear x nonlinear, reversible x nonreversible

- Decoherence: “Large” system in interaction

Nano(quantum)technologies

- Quantum information

- Quantum computing

- But also: miniaturization

- “Model” systems allow understanding

the underlying physics

R. P. Feynman (1959 !!!): http://www.fotuva.org/online/frameload.htm/online/nanotechnology.htm


Introduction Tracks 4

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

→ 4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum chaos

Quantum chaos”: quantum dynamics of classically

chaotic systems

Nonlinear Newton equation

2

d x

m =

2

dt

F(

x)

Linear Schrödinger equation

∂ψ

i h =

∂t

H (x) ψ


Introduction Atoms and photons 5

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

→ 5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Cold atoms interacting with photons

Spontaneous transitions: Random character of the photon

Dissipative force: radiation pressure

Stimulated transitions: Coherent momentum exchanges

conservative force: optical potential

∆p = 2hk L


Introduction Optical potential 6

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

→ 6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Optical potential

V

opt

~

r r

d ⋅ ε

h∆

L

2

I

~ sin(2k

L

x)

V opt


Introduction Quanticity 7

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

→ 7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Coherence

L ~ λ deBroglie

Controlling decoherence

Decoherence time >> evolution time

~

Γ

Ω

2

1

2

∆ L

λ ~

λ L L

2 3

Spontaneous emission rate


Introduction Model system 8

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential


7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Advantages

Simple system: 1D

1 st principles modeling

Controlled decoherence

Too simple!

2D phase space: no classical chaos

“Free particle” dynamics

Adding complexity

Temporal complexity: modulation

Spatial complexity: interferences


Quantum chaos Kicked rotor 9

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Kicked modulation: the kicked rotor

T

K = 0,9

2

P

H = + K sinθ∑δ

( t − n)

2

n

K = 10

t


Quantum chaos Quantum dynamics 10

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

2

p

400

300

200

Quantum evolution

|ψ| 2

momentum

Classical diffusion “frozen” by destructive

quantum interferences: Dynamical localization

100

0

0 100 200 300 400 500

kicks

G. Casati, B. V. Chirikov, J. Ford and F. M. Izrailev, Lect. Notes Phys. 93, 334 (1979)

F. L. Moore, J. C. Robinson, C. F. Bharucha, P. E. Williams and M. G. Raizen, Phys. Rev. Lett. 73, 2974 (1994)


Quantum chaos Quasiperiodic modulation 11

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Destructing dynamical localization

Freezing of classical diffusion = quantum interferences

Temporal periodicity = destructive quantum interferences

Mixing the quantum phases: breaking periodicity

T

t


Quantum chaos Localization “spectrum” 12

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Localization “spectrum”

2

0.4

-500 -300 -100 100 300 500

Π(v=0)

1.1

1.0

0.9

0.8

0.7

1:1

1:2 2:1

2:3 5:3

3:4 4:3 3:2

0.06

0.02

0.004

0.6

0.0 0.5 1.0 1.5 2.0 2.5 3.0

r = f 2

/f 1

1

0.4

-600 -400 -200 0 200 400 600

5:2

J. Ringot, P. Szriftgiser, J. C. Garreau, D. Delande, Phys. Rev. Lett. 85, 2741 (2000)


Quantum chaos Phase mixing x decoherence 13

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Remixing or decoherence

Decoherence = random remixing of quantum phases

Irreversible!

Breaking periodicity = deterministic remixing

of quantum phases

Reversible!


Quantum chaos Testing reversibility 14

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Reconstructing dynamical localization

180

165

150

135

120

105

90

0 20 40 60 80

Kicks

p

p


Quantum chaos Decoherence 15

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

What about decoherence

180

160

140

120

Resonant laser beam

0 photons/atom

100

80

Kicks

0,5 photons/atom

1 photon/atom

1,5 photons/atom

0 20 40 60 80


Quantum chaos 3D 16

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Decoherence x reversibility


Quantum x chaotic What about chaos 17

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

What about chaos

Newton: nonlinear

2

d x

m =

2

dt

F(

x)

Schrödinger: linear

∂ψ

i h =

∂t

Schrödinger : one-body problem

H (x) ψ

Interacting particles ⇒ Nonlinearity

Preserve quanticity ⇒ coherent interactions

Bose-Einstein condensate!


Quantum x chaotic Gross-Pitaevskii 18

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Gross-Pitaevskii equation

ih

ψ

=

∂t




2

∂ 2

P

2M

+ V

+

g

Ψ


⎥ψ


Mean-field approach for the interactions

Can it produce chaos in a quantum system


Quantum x chaotic Tilted lattice 19

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Standing wave + acceleration

Atoms in a tilted lattice

Bloch oscillations

M. Ben Dahan, E. Peik, J. Reichel, Y. Castin and C. Salomon, Phys. Rev. Lett. 76, 4508 (1996) .


t

Quantum x chaotic Condensate dynamics 20

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Condensate in a tilted lattice

〈X〉


Quantum x chaotic Poincaré 21

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum” phase space

∆ϕ

|a 1 | 2


Quantum x chaotic Poincaré 21

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum” phase space

∆ϕ

|a 1 | 2

“Bloch” oscillations


Quantum x chaotic Poincaré 21

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum” phase space

∆ϕ

|a 1 | 2

Resonances

or frequency

locking


Quantum x chaotic Poincaré 21

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Quantum” phase space

∆ϕ

|a 1 | 2

Chaos !!!

Komolgorov-Arnold-Moser structure


Quantum x chaotic “Quasiclassical” chaos 22

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

“Quasiclassical” chaos

∆ϕ

|a 1 | 2

Quantum object

Quantum phase

space

Classical

organization

KAM-like

structure

Q. Thommen, J. C. Garreau, V. Zehnlé, Phys. Rev. Lett. 91, 210405 (2003)


Conclusion Prospects 23

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

Model system

Experimentally “simple”

First principles modeling

Controlled decoherence

Quantum chaos

Sensitivity to quantum interference

Quantum/classical x reversible/irreversible

Quasiclassical chaos

Quantum/classical x linear/nonlinear

“Chaotic” dynamics of a “mesoscopically coherent”

object


Conclusion The end 24

Presentation

1. Title

The group

2. The group

Introduction

3. Introduction

4. Tracks

5. Atoms and photons

6. Optical potential

7. Quanticity

8. Model system

Quantum chaos

9. Kicked rotor

10. Quantum dyn.

11. Quasiperiodic mod

12. Loc. spectrum

13. Mixing x decoh.

14. Testing revers...

15. Decoherence

16. 3D

Quantum x chaotic

17. Chaos

18. Gross-Pitaevskii

19. Tilted potential

20. Dynamics

21. Poincaré

22. Quasiclassical

Conclusion

23. Prospects

24. The End

More magazines by this user
Similar magazines