Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Entanglement of Macroscopic Ensembles(Schroedinger’s Cat)

Team:Alex Heifetz (Graduate Student)Dr. Ashish Agarwal (Post-Doc)Prof. Prem Kumar (Collaborator)Prof. Philip Hemmer (Texas A&M; collaborator)Prof. Saxena (Visitor)

Supported By:DARPA, NSF

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

ENS 1

ENS 2

DET 1

DET 2

|g>

|e>

BS

LASER

21212

1GEEG DET 1

GENERATING ENSEMBLE ENTANGLEMENT

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

|g>

|e>

1 0

1 0

C

L

ADVANTAGE OF THE MACROSCOPIC APPROACH

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

• Field + Atom + Cavity

e

b

a

e

b

a

Laser Field

Cavity Mode 0 or 11

2

System

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Wavefunction

• cavitylaseratomsystem

where

1)(0)(

! where)()(

)()()(

10

2

0

2

tctc

en

bntbt

etcbtcatc

cavity

n

nn

nlaser

ebaatom

• Initial condition before the interaction

0)0(,1)0( i.e. 0

)0()0(

,0)0(,0)0(,1)0( i.e.

10

cc

nb

ccca

cavity

nlaser

ebaatom

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Number states

Light in state 1)()( 1 ntAntA nnn

other.each ostrongly t couple and degeneratenearly are

01 and 11 ,0 states the,,,When 21 nenbna

01 11 0 11110 neccAnbccAnaccA bnbnann

10 1 101 ccnAnAecbcac nneban

1,n 2,1

a

e

b

.0 Initially n

na

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

. , , ,

where

0

0~

)1(

)1(

)1(0

0~

20

20

10

10

00

0

0

1

100

021

01

bebeaeaebeae

e

e

b

a

ererV

gV

gn

g

nH

n

ngn

gn

nnH

0na

11nb

01ne

Hamiltoniann0na 11nb 01ne

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Time evolution

bbbb

baaa

Cng

Cg

CC

Cng

Cn

CC

neng

0020

0020

00

iii

,iii

evolution thefrom decoupled is 01 state the,,When

,2

,2

20

1

20

1

g

g

nn

ng

nR002

)(41

11 ng

If we design the system such that

then time evolution reduces to

)(41

,

,i

11 n

n

n gH

C

CH

C

C

nnR

Rn

I

b

aI

b

a

0na 11nb

nR

aC bC

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

01na 12nb

0na 11nb

nR

1

nR

01na 1nb

1

nR

Laser in state

0

)(n

n ntb

Coherent State

1

1

• Photon distribution)(NP

pN

NpN

• Coupling constant

Rp

R

Ngngn

0000 22

• Wavefunction

1)sin(0)cos(

e)(

1

121

btiat RR

ti

nnsystem

a

0a 1b

RpN

20

1 2

1pN

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Classical Laser Field

pNCavity Mode 0 or 1e

b

a

1

0g

0a 1b

pNg01

Result

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Interaction time

Single

PhotonDetector

1i0

pulse 2π

4π

thatso Choose

21

01

ba

Ng p

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

BBBBAAAABAtotal

BBBBB

AAAAA

baba

ba

ba

1i01i0

1i0

1i0

21

21

21

Set-up for Entanglement generation

Laser

BB

A

A

D1

D2

AA1,0

BB1,0

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Entangled Atomic States

BABA

BABABA

BABABABA

BABABABA

BABABABABABABABA

abba

abba

abba

abba

bbabbaaa

00

0000

0110

11011000

2i

2i

2i

21

2i

21

Conditional click in Either D1 Or D2

Photon Annihilation in Detector

Projected Atomic State

=

Bb

BaA

b

Aa

Atom A Atom B

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Single

PhotonDetector

aN

a

a

a

a

a

a

N

ii

a

N

N

N

Na

N

BAEnsemble

BN

baaa

abaa

aaba

aaabN

B

aaaaA

BcAc

1

321

321

321

321

321

1

..........

...................................

...................................

..........

..........

..........1

..........

11

0

10

1

aN

ii

aBA

BA

cavityEnsemble

BN

CAC

BCAC

0a 1b

R

0A

R

11

B 12

B 1aN

B

RR

Many Particle System

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Collective Enhancement

Ra

N

ii

a

Ri

N

BHAN

BHA

BHA

a

1

1~01

1~0

1~0

Collective enhancement factor

1)sin(0)cos( BtNiAtN RaRa

1i0

pulse 2π

4π

thatso Choose

21 BA

N Ra

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Laser

BB

A

A

D1

D2

Entanglement of atomic ensembles

BABAABABBA

Conditional on detector click, Atomic ensembles are Entangled:

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Atomic Ensemble: 87Rb

Laser Field

Raman signal 1 2

F=2

F=16.8347 GHz

P3/2

2

1

F=2 P3/2 F=1 P3/2

6.8347 GHz 6.8347 GHz

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Raman Spectroscopy Set-up

Argon ionLaser

Ti-SapphireLaser

Rb Heat- Pipe Oven

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

Rubidium Raman Laser

Argon ionLaser

Ti-SapphireLaser

Rb Heat Pipe Oven

PZT

Spectrum Analyzer

s

p

pOC

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science

TRAPPING OF LIGHT IN A Pr:YSO CRYSTAL

Center for Photonic Communication and Computing McCormick School of Engineering and Applied Science“Observation of Ultraslow and Stored Light Pulses in a Solid,” A. V. Turukhin, V.S. Sudarshanam, M.S. Shahriar, J.A. Musser, B.S. Ham, and P.R. Hemmer, Phys. Rev. Lett. 88, 023602 (2002).

TRAPPING OF LIGHT IN A Pr:YSO CRYSTAL