Quantum Zeno subspaces

1. SaverioPascazio DipartimentodiFisica, Universitàdi Bari, Italy Quantum Zeno subspaces M. Asorey (Zaragoza) G. Badurek (Vienna) P. Facchi (Bari) R. Fazio (Pisa) V. Gorini (Como) H. Hradil (Olomouc) D. Lidar (Toronto) V.I. Man’ko (Moscow) G. Marmo (Napoli) M. Namiki (Waseda) H. Nakazato (Waseda) I. Ohba (Waseda) H. Rauch (Vienna) A. Scardicchio (Princeton) L. S. Schulman (Clarkson) E. C. G. Sudarshan (Texas) J. Perina (Olomouc) J. Rehacek (Olomouc) S. Tasaki (Waseda) K. Yuasa (Bari) Palermo CEWQO 2007

2. Quantum Zeno effect. My favorite example: spin in B field Increasing N P., Namiki, Badurek, Rauch 1993

3. History: 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 around 488 BC, and at the age of 40 accompanied Parmenides to Athens. The flying arrow is at rest. At any given moment it is in a portion of space equal to its own length, and therefore is at rest at that moment. So, it is at rest at all moments. The sum of an infinite number of these positions of rest is not a motion.

4. Raphael’s School of Athens (Vatican Museums)

5. Quantum Zeno effect ..…. P P P P P P U U U U Quantum Zeno effect: repeated observation in succession inhibit transitions outside Note: P notnecessarily1-Dimensional Beskow & Nilsson 1967von Neumann 1932 Misra and Sudarshan 1977

6. Simplest nontrivial example:2-dimensional projection Zeno limit

7. Dynamical superselection sectors Couplingor N

8. Zeno subspaces

9. 3 STRATEGIES to obtain Zeno subspaces Measurements (projections) Unitary kicks (“bang bang”) Continuous coupling (continuous measurement)

10. Continuous coupling Zeno limit

11. Kicks Zeno limit

12. What really provokes the Zeno phenomenon Zeno subspace Increasing N reminder…

13. levels (courtesy authors)

14. pulsed continuous (Schulman 1998)

15. The theoretician’s (simplistic) viewpoint continuous QZE pulsed QZE

16. Analysis (Cohen-Tannoudji…) ?

17. QZE! recalculate although there is no bona fide “measurement…

18. @ lowest order in dissipation

19. Control of a qubit!

20. B. Militello, A. Messina, and A. Napoli, Fortschr. Phys. 49, 1041 (2001). P. Facchi and S. Pascazio, Physical Review Letters 89, 080401 (2002). !

21. RF,DC flux drives Delft qubit platform high Q harmonic oscillator flux qubit SQUID readout EuroSQIP European SuperconductingQuantum Information Processor

22. high Q harmonic oscillator Flux qubits osc osc osc osc Coupling between JJ qubits and photons TU Delft: Photons in Josephson resonators I. Chiorecu et al.. Nature 431, 159 (2004) Sideband physics Yale: Photons in stripline resonators A. Wallraff et al. Nature 431, 162 (2004) Goal: Hardware integration with microwave/optical quantum communication Photons typically coupled through guiding circuitry Use microwave transmission lines / cascaded quantum oscillator systems for transferring microwave photons Use interface to Ion traps for accessing the optical world Use other frequency conversion techniques known from optics Superconducting qubits can be entangled with microwave photons in transmission lines through high-Q cavities in all designs

23. ? 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 2003Gustavson 2004

24. W Example: free particle in D dimensions How does the particle move inside W? Does it leak out? Free particle in a box with perfectly reflecting hard walls …although there is NO wall! Facchi, Pascazio, Scardicchio, Schulman 2002Facchi, Marmo, Pascazio, Scardicchio, Sudarshan 2003

25. food for thoughts sped arrow “observed” arrow

26. How frequent or strongmust be the coupling? QZE Kofman and Kurizki, Nature 405, 546 (2000)Facchi, Nakazato and Pascazio, Phys. Rev. Lett. 86, 2699 (2001) The Devil in the gaps: Timescales UNDISTURBED IZE ExperimentFischer, Gutièrrez-Medina and Raizen, Phys. Rev. Lett. 87, 040402 (2001) Wilkinson, Bharucha, Fischer, Madison, Morrow, Niu, Sundaram, and Raizen, Nature 387, 575 (1997); Koshino, Shimizu, Phys. Rev. Lett. 92, 030401 (2004)

27. Main idea Enhancement of decoherence Control of decoherence coupling K frequency N

28. Outlook • Applications • Control of decoherence. Engineering of Zeno subspaces • Constrained dynamics. • Open problems • Infinite dimensional • Algebra of observables (Marmo, Asorey, Facchi, Sudarshan) It is a good thing that quantum mechanics does not depend on its foundations E.G.C. Sudarshan

29. It is a good thing that quantum mechanics does not depend on its foundations E.G.C. Sudarshan

30. S. Pascazio Quantum Zeno effect and inverse Zeno effect in “Quantum Interferometry,” edited by F. De Martini et al. (VCH Publishing Group, Weinheim, 1996) p. 525

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

32. Example: countering decoherence Beige, Braun, Tregenna and Knight, Phys. Rev. Lett. 85, 1762 (2000) Facchi and Pascazio, quant-ph/0202174 (Solvay conference 2002)

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

34. Polynomial and exponential case

35. 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

36. Comparison

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

38. Sketch of proof W By using asymptotic analysis one proves that such a basis exists andis just the eigenbasis of the free particle in W with Dirichlet b.c.

39. Asymptotics t  0