Entanglement and Coherent Control

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• Entanglement and Coherent Control

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• Entanglement and Coherent Control

Coherent Control. objectives Control of future
events. Tools Use quantum interference between
material waves.
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• Entanglement and Coherent Control

Coherent Control. objectives Control of future
events. Tools Use quantum interference between
material waves. We access the same final state
using more than one pathway. Lacking the which
way information these pathways interfere.
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• Entanglement and Coherent Control

Coherent Control. objectives Control of future
events. Tools Use quantum interference between
material waves. We access the same final state
using more than one pathway. Lacking the which
way information these pathways interfere.
Interference is not enough. In order to achieve
control we need to tune this interference,
and this is done
with photons.
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• Bichromatic coherent control (Chem. Phys.
  Lett. 126, 541 (1986))

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• Bichromatic coherent control (Chem. Phys.
  Lett. 126, 541 (1986))

A-B-C
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The two slit analogy the importance of the
relative phase
Screen
Interference pattern
a
b

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light wave a

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final matter state
light wave a

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light wave a
amplitude for absorbing light wave a

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phase shift

light wave a
amplitude for absorbing light wave a
light wave b
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phase shift

light wave a
amplitude for absorbing light wave a
light wave b
amplitude for absorbing light wave b
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phase shift

light wave a
amplitude for absorbing light wave a
interfere
light wave b
amplitude for absorbing light wave b
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The key to control is that the interference
patterns of different outcomes be shifted in
phase.
A-B C
the screen of relative phases

A B-C
- is favored
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A-B C

A B-C
- is favored
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A-B C

A B-C
- is favored
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A-B C

A B-C
- is favored
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Generation of DC current in a molecular wire
suspended between two leads
a short pulse
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Need for entanglement the control of collisions

J. Gong, M. Shapiro, and P. Brumer, J. Chem.
Phys. 118, 2626 (2003)
H2(j0,k0 j2,k2) H2(j0,k0 j2,k2) elastic

E0.4cm_1
E0.04cm_1


-
-
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Can one observer make use of entanglement?
B
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-
n1
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Creation of variable entanglement in polyatomic
molecules
A
B

k2n/2mB
k2n/2mA
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How does B view the uncollapsed wavefunction?
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Control of entanglement
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Coherent Control as a Disentanglement
Transformation

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/
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A second objective to control of the direction
of electronic motion. The
generation of current without voltage!

pathway a
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pathway b
pathway a
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A pictorial representation

p wave
s wave
d wave
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(forward current)
-


pathway a
pathway b
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(backward current)
(forward current)
-
-



-

pathway a

-
pathway b
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E. Dupont, P.B. Corkum, H.C. Liu, M. Buchanan,
and Z.R. Wasilewski, Phys. Rev. Lett. 74, 3596
(1995)
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Acknowledgments

• Theory
• Ioannis Thanopulos (Univ. of British
  Columbia)
• Einat Frishman (Univ. of British
  Columbia)
• Petr Kral (Univ. Illinois
  at Chicago)
• Dvira Segal
  (Weizmann )
• Paul Brumer (University of
  Toronto)
• Jiangbin Gong (University of
  Toronto)
• John Hepburn (University of
  British Columbia)
• Experiment
• Qun Zhang (Weizmann, now at Univ. of British
  Columbia)
• Alexander Shnitman (Weizmann) , Mark Keil (BGU)