Effetto Zenone quantistico e controllo della decoerenza

1. Effetto Zenone quantisticoe controllo della decoerenza Paolo Facchi Dipartimento di Matematica, Università di Bari Milano, 23 marzo 2007

2. Quantum Zeno effect: fundamentals

3. QZE: fundamentals ..…. P P P P P P U U U U Quantum Zeno effect: repeated observation in succession inhibit transitions outside

4. Theorem Misra and Sudarshan, J. Math. Phys. 18, 756 (1977) Quantum Zeno paradox: an observed particle does not evolve.

5. Zeno of Elea Zeno was an Eleatic philosopher, a native of Elea in Italy, son of Teleutagoras, and the favorite disciple of Parmenides. He was born about 488 BC, and at the age of forty accompanied Parmenides to Athens The flying arrow is at rest. At any given moment it is in a space equal to its own length, and therefore is at rest at that moment. So, it's at rest at all moments. The sum of an infinite number of these positions of rest is not a motion.

6. Example: spin Peres, Am. J. Phys. 48, 931 (1980)

7. Increasing N Neutron spin Pascazio, Namiki, Badurek, Rauch, Phys. Lett. A 169, 155 (1993)

8. von Neumann,1932 Beskow and Nilsson,1967 Khalfin 1968 Friedman 1972 Misra and Sudarshan, 1977 History Experiments (Cook 1988) Itano, Heinzen, Bollinger, and Wineland 1990 Nagels, Hermans, and Chapovsky 1997 Balzer, Huesmann, Neuhauser, and Toschek, 2000 Wunderlich, Balzer, and Toschek, 2001 Wilkinson, Bharucha, Fischer, Madison, Morrow, Niu, Sundaram, and Raizen, 1997. Fischer, B. Gutierrez-Medina, and Raizen, 2001 Theory and interesting Mathematics (not quoted)

9. VESTA II @ ISIS Jericha, Schwab, Jakel, Carlile, Rauch, Physica B 283, 414 (2000); Rauch, Physica B 297, 299 (2001).

10. Are projections à la von Neumann necessary? No: a dynamical explanation can be given, in terms of the Schroedinger equation (and involving no projection operators). Wigner, Am. J. Phys. 1963 Petrosky, Tasaki, Prigogine, PLA 1990; Physica 1991 Pascazio, Namiki, PRA 1994 This is best proven by looking at some examples.

11. What really provokes Zeno Zeno

12. Incomplete measurements

13. Nonselective measurements P. F. and Pascazio, Phys. Rev. Lett. 89, 080401 (2002)

14. Uc Uc Uc Uc Uc Uc ..…. U U U U Unitary kicks Quantum maps Berry, Balazs, Tabor,Voros (1979) Casati, Chirikov, Ford and Izrailev (1979) Viola and Lloyd, Phys. Rev. A 58, 2733 (1998)Viola, Knill and Lloyd, Phys. Rev. Lett. 82, 2417 (1999)Byrd and Lidar, Quant. Inf. Proc. 1, 19 (2002)P.F., Lidar, Pascazio, Phys. Rev. A 69, 032314 (2004) Dynamical decoupling“Bang-bang” control

15. system “apparatus” K coupling Continuous coupling P. F. and Pascazio, Phys. Rev. Lett. 89, 080401 (2002)

16. Dynamical superselection sectors Quantum Zeno subspaces Couplingor N

17. ? The quantum Zeno dynamics Is the Zeno dynamics unitary? (Misra and Sudarshan 1977: semigroup) Answer: under general hypotheses YES Friedman 1972Facchi, Gorini, Marmo, Pascazio, Sudarshan 2000Facchi, Pascazio, Scardicchio, Schulman 2002Exner, Ichinose 2003

18. W Free particle in D dimensions How does the particle move inside W? Does it leaks out? Free particle in a box with perfectly reflecting hard walls …although there is NO wall! P.F., Pascazio, Scardicchio, Schulman 2002P.F., Marmo, Pascazio, Scardicchio, Sudarshan 2003

19. Different manifestations of the same physical phenomenon Measurements à la von Neumann (projections) Unitary kicks (bang-bang control) Continuous coupling

20. Projections Zeno limit

21. Kicks Zeno limit

22. Continuous coupling Simonius 1978 Harris & Stodolsky 1982 Zeno limit

23. Main objective: understand and suppress decoherence Benenti, Casati, Montangero, Shepelyansky (2001) Vitali, Tombesi, Milburn (1997, 1998) Fortunato, Raimond, Tombesi, Vitali (1999) Kofman, Kurizki (2001) Calarco, Datta, Fedichev, Pazy, Zoller, “Spin-based all-optical quantum computation with quantum dots: understanding and suppressing decoherence” (2003) Falci (2003) Decoherence-free subspaces Palma, Suominen and Ekert (1996) Duan and Guo (1997) Zanardi and Rasetti (1997) Lidar, Chuang and Whaley (1998) Viola, Knill and Lloyd (1999) Vitali and Tombesi (1999, 2001) Beige, Braun, Tregenna and Knight (2000) … Tasaki, Tokuse, P.F., Pascazio (2002) P.F:, Lidar and Pascazio (2004)

24. NOTICE: How frequent or strongmust be the coupling? Relevant timescales QZE P.F., Nakazato and Pascazio, Phys. Rev. Lett. 86, 2699 (2001) UNDISTURBED IZE Experiment by Fischer, Gutièrrez-Medina and Raizen, Phys. Rev. Lett. 87, 040402 (2001)

25. Main idea ? Enhancement of decoherence Control of decoherence coupling K frequency N

26. The problem Unstable systems ? Unstable systems and Inverse Zeno

27. Framework decoherence Liouvillian Hilbert spaces

28. Framework (cont’d) initial state of total system evolved state of system Decoherence if not unitarily equivalent to

29. Computational subspace

30. System-bath interaction (Gardiner & Zoller) form factor

31. Polynomial and exponential case

32. inverse temperature bandwidth Form factors Full line: exponential; dashed line: polynomial form factor.

33. Controlled Dynamics important !! control(protection) enhancement P.F., Tasaki, Pascazio, Nakazato,Tokuse, Lidar, Phys. Rev. A 71, 022302 (2005)

34. Measurements

35. Measurements (small times)

36. “Kicks”

37. kicks (small times)

38. Continuous coupling

39. (strong) continuous coupling

40. Comparison

41. Comparison (small times 1/N -- strong coupling K)

42. Remarkable differences Zeno control (non-unitary) “bang bang” control (kicks) (unitary) control via continuous coupling (unitary) For unitary controls feels the “tail” of the form factor

43. (partial) CONCLUSIONS • BEST strategy: kicks/continuous rather than measurements • GAIN: factor 10 • Hopefully: more to come • Qdots, cavities, JJ