Effetto Zenone quantistico e controllo della decoerenza

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Effetto Zenone quantisticoe controllo della
decoerenza
Paolo Facchi Dipartimento di Matematica,
Università di Bari

• Milano, 23 marzo 2007

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Quantum Zeno effect fundamentals
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QZE fundamentals
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Theorem
Misra and Sudarshan, J. Math. Phys. 18, 756 (1977)
Quantum Zeno paradox an observed particle does
not evolve.
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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.
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Example spin
Peres, Am. J. Phys. 48, 931 (1980)
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Neutron spin
Pascazio, Namiki, Badurek, Rauch, Phys. Lett. A
169, 155 (1993)
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History
von Neumann,1932 Beskow and Nilsson,1967 Khalfin
1968 Friedman 1972 Misra and Sudarshan, 1977
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)
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VESTA II _at_ ISIS
Jericha, Schwab, Jakel, Carlile, Rauch, Physica B
283, 414 (2000) Rauch, Physica B 297, 299
(2001).
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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.

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What really provokes Zeno
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Incomplete measurements
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Nonselective measurements
P. F. and Pascazio, Phys. Rev. Lett. 89, 080401
(2002)
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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 decouplingBang-bang control
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Continuous coupling
P. F. and Pascazio, Phys. Rev. Lett. 89, 080401
(2002)
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Dynamical superselection sectors
Quantum Zeno subspaces
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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
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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
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Different manifestations of the same physical
phenomenon
Measurements à la von Neumann (projections)
Unitary kicks (bang-bang control)
Continuous coupling
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Projections
Zeno limit
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Kicks
Zeno limit
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Continuous coupling
Simonius 1978 Harris Stodolsky 1982
Zeno limit
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Main objective understand and suppress
decoherence

• 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)

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)
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Relevant timescales
NOTICE
How frequent or strongmust be the coupling?
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)
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Main idea
?
Enhancement of decoherence
Control of decoherence
coupling K frequency N
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The problem
Unstable systems
?
Unstable systems and Inverse Zeno
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Framework
decoherence
Liouvillian
Hilbert spaces
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Framework (contd)
initial state of total system
evolved state of system
Decoherence if
not unitarily equivalent to
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Computational subspace
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System-bath interaction (Gardiner Zoller)
form factor
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Polynomial and exponential case
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Form factors
Full line exponential dashed line polynomial
form factor.
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Controlled Dynamics
important !!
control(protection)
enhancement
P.F., Tasaki, Pascazio, Nakazato,Tokuse, Lidar,
Phys. Rev. A 71, 022302 (2005)
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Measurements
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Measurements (small times)
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Kicks
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kicks (small times)
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Continuous coupling
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(strong) continuous coupling
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Comparison
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Comparison (small times 1/N -- strong coupling K)
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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
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(partial) CONCLUSIONS

• BEST strategy kicks/continuous rather than
  measurements
• GAIN factor 10
• Hopefully more to come
• Qdots, cavities, JJ