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Saverio Pascazio Dipartimento di Fisica , Università di 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).
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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
Quantum Zeno effect. My favorite example: spin in B field Increasing N P., Namiki, Badurek, Rauch 1993
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.
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
Simplest nontrivial example:2-dimensional projection Zeno limit
Dynamical superselection sectors Couplingor N
3 STRATEGIES to obtain Zeno subspaces Measurements (projections) Unitary kicks (“bang bang”) Continuous coupling (continuous measurement)
Continuous coupling Zeno limit
Kicks Zeno limit
What really provokes the Zeno phenomenon Zeno subspace Increasing N reminder…
levels (courtesy authors)
pulsed continuous (Schulman 1998)
The theoretician’s (simplistic) viewpoint continuous QZE pulsed QZE
QZE! recalculate although there is no bona fide “measurement…
B. Militello, A. Messina, and A. Napoli, Fortschr. Phys. 49, 1041 (2001). P. Facchi and S. Pascazio, Physical Review Letters 89, 080401 (2002). !
RF,DC flux drives Delft qubit platform high Q harmonic oscillator flux qubit SQUID readout EuroSQIP European SuperconductingQuantum Information Processor
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
? 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
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
food for thoughts sped arrow “observed” arrow
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)
Main idea Enhancement of decoherence Control of decoherence coupling K frequency N
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
It is a good thing that quantum mechanics does not depend on its foundations E.G.C. Sudarshan
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
VESTA II @ ISIS Jericha, Schwab, Jakel, Carlile, Rauch, Physica B 283, 414 (2000); Rauch, Physica B 297, 299 (2001).
Example: countering decoherence Beige, Braun, Tregenna and Knight, Phys. Rev. Lett. 85, 1762 (2000) Facchi and Pascazio, quant-ph/0202174 (Solvay conference 2002)
System-bath interaction (Gardiner & Zoller) form factor
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
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.