Quantum Zeno subspaces

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Quantum Zeno subspaces
Saverio Pascazio Dipartimento di Fisica,
Università di Bari, Italy
M. Asorey (Zaragoza) G. Badurek (Vienna) P.
Facchi (Bari) R. Fazio (Pisa) V. Gorini (Como) H.
Hradil (Olomouc) D. Lidar (Toronto) V.I. Manko
(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

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Quantum Zeno effect. My favorite example spin
in B field
P., Namiki, Badurek, Rauch 1993
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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.
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Raphaels School of Athens (Vatican Museums)
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Quantum Zeno effect
Note P notnecessarily1-Dimensional
Beskow Nilsson 1967von Neumann 1932
Misra and Sudarshan 1977
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Simplest nontrivial example2-dimensional
projection
Zeno limit
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Dynamical superselection sectors
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Zeno subspaces
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3 STRATEGIES to obtain Zeno subspaces
Measurements (projections)
Unitary kicks (bang bang)
Continuous coupling (continuous measurement)
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Continuous coupling
Zeno limit
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Kicks
Zeno limit
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What really provokes the Zeno phenomenon
reminder
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levels
(courtesy authors)
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pulsed
continuous
(Schulman 1998)
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The theoreticians (simplistic) viewpoint
continuous QZE
pulsed QZE
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Analysis (Cohen-Tannoudji)
?
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recalculate
QZE!
although there is no bona fide measurement
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_at_ lowest order in dissipation
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Control of a qubit!
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B. Militello, A. Messina, and A. Napoli,
Fortschr. Phys. 49, 1041 (2001). P. Facchi and
S. Pascazio, Physical Review Letters 89, 080401
(2002).
!
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EuroSQIP European SuperconductingQuantum
Information Processor

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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
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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 2003Gustavson 2004

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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
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food for thoughts
sped arrow
observed arrow
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The Devil in the gaps Timescales
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)
UNDISTURBED
IZE
Experiment Fischer, 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)
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Main idea
Enhancement of decoherence
Control of decoherence
coupling K frequency N
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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
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It is a good thing that quantum mechanics does
not depend on its foundations E.G.C. Sudarshan
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• 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

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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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Example countering decoherence
Beige, Braun, Tregenna and Knight, Phys. Rev.
Lett. 85, 1762 (2000)
Facchi and Pascazio, quant-ph/0202174 (Solvay
conference 2002)
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System-bath interaction (Gardiner Zoller)
form factor
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Polynomial and exponential case
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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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Comparison
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Comparison (small times 1/N -- strong coupling K)
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Sketch of proof
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.
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Asymptotics t ? 0