Entanglement and Coherent Control Entanglement and Coherent Control

Entanglement and Coherent Control

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

Entanglement and 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.

Entanglement and 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.

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

Bichromatic “coherent control” (Chem. Phys. Lett. 126, 541 (1986)) B + A-C A + B-C E E 2 pathway a E 1 pathway b E 1 2 g 1 g Eg A-B-C

The two slit analogy: the importance of the relative phase Screen + a b + + 0 0 - + - Interference pattern

light wave a

light wave a final matter state

light wave a amplitude for absorbing light wave a

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

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

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

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

A-B + C A + B-C - is favored

A-B + C A + B-C - is favored

A-B + C A + B-C - is favored

Generation of DC current in a molecular “wire” suspended between two leads a short pulse

Need for entanglement: the control of collisions J. Gong, M. Shapiro, and P. Brumer, J. Chem. Phys. 118, 2626 (2003) H 2(j=0, k 0 ± j=2, k 2) + H 2(j=0, k 0 ± j=2, k 2) elastic _ 1 E=0. 4 cm _ 1 E=0. 04 cm + + - -

H 2(j=0, k 0 ± j=4, k 4) + H 2(j=0, k 0 ± j=4, k 4) 2 H 2( j=2, k 2) _ 1 E=0. 04 cm E=0. 004 cm + + -

Can one observer make use of entanglement? B

-n 1

Creation of variable entanglement in polyatomic molecules A B k 2 n/2 m. A k 2 n/2 m. B

How does B view the uncollapsed wavefunction?

: Control of entanglement

Coherent Control as a Disentanglement Transformation

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

pathway a pathway b

A pictorial representation Anti-symmetric - + + p wave 1 - photon absorption Symmetric (s wave) + s wave + 2 - photon absorption or + Symmetric + d wave

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

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

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

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)