Entanglement and Coherent Control

Entanglement and Coherent Control

Coherent Control. objectives: Control of future events.

Tools: Use quantum interference between material waves.

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.

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.

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

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

A-B-C

B + A-C A + B-C

E1

E2

E1

E2

E

Eg

2g

1g

pathway a pathway b

Interferencepattern

+

+

+

+

-

-

-

-

0

0

Screen

a

b

The two slit analogy: the importance of the relative phase

light wave a

light wave a

final matter state

light wave a

amplitude forabsorbing light wave a

light wave a

light wave b

phaseshift

amplitude forabsorbinglight wave a

light wave a

light wave b

phaseshift

amplitude for absorbinglight wave a

amplitude forabsorbing light wave b

light wave a

light wave b

phaseshift

amplitude forabsorbinglight wave a

amplitude forabsorbinglight wave b

interfere

A-B + C

A + B-Cthe “screen” ofrelative phases

The key to control is that the interference patterns of different outcomesbe shifted in phase.

- 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

0 / 2

2 2

2(( ) ,

2)

iH

dH

m dV U x tx

x

2( / )

0 |x|>0.1 nm( )

-0.5 eV |x|<0.1 n

( , ) sin sin 2 (

m

)

( ) t

U x t x t t f t

t

x

f

V

e

-200 -100 0 100 200

-0.5

-0.4

-0.3

-0.2

-0.1

0

x [A]

V(x

) [eV

]

=0.1; t= 3 10-2 [au]=150 nstep=100; N

T=2000;

(x,t=0)=0(x)

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

a short pulse

H2(j=0,k0 ± j=2,k2) + H2(j=0,k0 ± j=2,k2) elastic

Need for entanglement: the control of collisions

J. Gong, M. Shapiro, and P. Brumer, J. Chem. Phys. 118, 2626 (2003)

+ +

--

E=0.4cm_

1

E=0.04cm_

1

H2(j=0,k0 ± j=4,k4) + H2(j=0,k0 ± j=4,k4)

2H2( j=2,k2)

E=0.04cm_

1 E=0.004cm_

1

++

--

Can one observer make use of entanglement?

B

n1-

Creation of variable entanglement in polyatomic molecules

A B

k2n/2mA

k2n/2mB

How does B view the uncollapsed wavefunction?

Control of entanglement

:

Coherent Control as a Disentanglement Transformation

/

/

pathway a

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

pathway a pathway b

- ++

1- photon absorption

+2- photon absorption

+

-++

-

Symmetric (s wave)

Symmetric

Anti-symmetric

or

p wave

s wave

d wave

A pictorial representation

+-

- +

+

+

(forward current)

pathway a

pathway b

+-

- +

+

+- +

+

-

- +

(forward current)

pathway a

(backward current)

pathway b

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

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)

Acknowledgments