Luz e Luz e ÁÁtomostomos comocomo ferramentasferramentas

parapara InformaInformaççãoão QuânticaQuântica

EmaranhamentoEmaranhamento MulticorMulticor

Marcelo MartinelliInst. de

Física

Lab. de Manipulação Coerente de Átomos e Luz

• “EPR” criterion [M. D. Reid, PRA 40, 913 (1989), M. D. Reid and P. D. Drummond, PRL 60, 2731 (1988) & PRA 40, 4493 (1989)]

Few words about entanglement characterization

•DGCZ separabilitycriterion:

Separability ⇒

Entanglement Test - DGCZ

•After some (simple) algebra:

Entanglement Test - DGCZ

Entanglement Test - DGCZ

p

q

p

q

p

q

p

qp1+p2 , q1+q2

p1-p2 , q1-q2

Entanglement Generation

p

q

p

q

p

q

p

q

p1+p2 , q1+q2

p1-p2 , q1-q2

non-negative eigenvalues -> Separability

• Positivity under Partial Transposition (discrete variables)

PRL 77, 1413 (1996)

Entanglement Test – Peres & Horodecki

• Continuous variables:PRL 84, 2726 (2000)

Entanglement Test - Simon

Diagonalize:

Simplectic Eigenvalues >1

Entanglement Test - Simon

Entanglement Test - Simon

Entanglement Test - Simon

p

q

p

q

p

q

p

q

p

q

p1- p2 , q1+ q2

p1+ p2 , q1- q2

• Extend DGCZ criterion to three variables

• Apply PPT to multiple partitions

Tripartite Entanglement

Covariance Matrix

Entangled fields- Vacuum (P0 < Pth, maximum entanglement)- Intense beams (P0 > Pth)

Squeezed vacuum (P0 < Pth, degenerate)Twin beams (P0 > Pth)

Pump Squeezing (P0 > Pth)

–

How can we measure the phase?

Nd:YAG

Doubling cavity532 nm

1064 nm

OPOOPO

?

Homodynedetection

Local Oscillator

1064 nm

Pump

Is it possible to perform a homodynemeasurement without a local oscillator?

And if we look for a complete characterization of the OPO, we have to measure three fields of diferent colors!

X

Y

φ

|α |

p

q

0 50 100 150 200 250

Measurement of the Field in the time domainMeasurement of the Field in the time domain

0 50 100 150 200 250

0,0 0,1 0,2 0,3 0,4 0,5

0,01

0,1

1

Frequency (Hz)

Ampl

itude

Measurement of the Field in the frequency domainMeasurement of the Field in the frequency domain

Spectrum Analyser

0 50 100 150 200 250

Measurement of the Field in the frequency domainMeasurement of the Field in the frequency domain

Amplitude

A classic field

ω

Coherent state

Squeezed state

ω0 ω0 + Ωω0 − Ω

Measurement of the Field in the frequency domainMeasurement of the Field in the frequency domain

Modulation

Phase

Phase Rotation of Noise EllipsePhase Rotation of Noise Ellipse

ain (Input)

aout (Reflection)

Optical Cavity

bin (Vacuum)

bout (Transmission)

X

Y

X

Y

Cavity detuning

Reflected Beam Amplitude Noise

Phase Rotation of Noise EllipsePhase Rotation of Noise Ellipse

Tripartite entanglement?

Set up

Quantum Correlations between pump, signal and idler for P0 > Pth

K. N. Cassemiro et al. Opt. Lett. 32, 695 (2007)

K. N. Cassemiro et al. Opt. Exp. 15, 18326 (2007)

N. B. Grosse et al. PRL 100, 243601 (2008) (degenerate case)

Three-color quantum correlationsK. N. Cassemiro et al. Opt. Lett. 32, 695 (2007)

The quest for three-color entanglement…K. N. Cassemiro et al. Opt. Exp. 15, 18326 (2007)

Noise in the reflected pump!

An open question: What is the source of the noise in the crystal?

Noise is everywhere!

0 5 10 15 20 25 30 35 40

1.0

1.5

2.0

2.5

3.0N

oise

(nor

mal

ized

to S

QL)

Reflected Power (mW)

-8 -4 0 4 8

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Cavity Detuning (normalized to bandwidth)

-1

0

1

Ana

lisys

Cav

ity R

efle

ctan

ce

N

oise

(nor

mal

ized

to S

QL)

0 1 2 3 4 5 6 7

1.0

1.2

1.4

1.6

1.8

Noi

se (n

orm

aliz

ed to

SQ

L)

Transmitted Power (mW)

∆2p1

∆2q1

∆2p2

∆2q2

0 5 10 15 20 250.0

0.2

0.4

0.6

0.8

Transmitted Power - mode 1 (1064 nm) 13.5mW 8.3mW

Cov

aria

nce

(SQ

L un

its)

Reflected Power - mode 0 (mW)0 1 2 3 4 5 6 7

0.0

0.2

0.4

0.6

0.8

Cor

rela

tion

(nor

mal

ized

to S

QL)

Reflected Power - mode 0 (532 nm) 62 mW 39 mW

Transmitted Power - mode 1 (mW)

ω0

Is the noise inside the crystal… as a random modulationof the refractive index?

X

Y

φ

|α |

ω0 ω0

Grosse et al. PRL 100 243601(2008)

GAWBS?

Or phonon scattering?

260 280 300 320 340 360 3800.0

0.2

0.4

0.6

0.8

1.0

Cou

plin

g co

effic

ient

η00

(1/W

)

Temperature (K)

Way to go

1.0 1.1 1.2 1.3 1.4 1.5 1.6

-1

0

1

2

3

4

Cov

aria

nce

(SQ

L un

its)

Pin/Pth

q0q0 q1q1 q2q2 q0q1 q1q2 q2q0

1.0 1.1 1.2 1.3 1.4 1.5 1.6

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cov

aria

nce

(SQ

L un

its)

Pin/Pth

p0p0 p1p1 p2p2 p0p1 p1p2 p2p0

1.0 1.1 1.2 1.3 1.4 1.5 1.6

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Cov

aria

nce

(SQ

L)

Pin/Pth

p0p0 p1p1 p2p2 p0p1 p1p2 p2p0

1.0 1.1 1.2 1.3 1.4 1.5 1.6

-1

0

1

2

3

4

Cov

aria

nce

(SQ

L)

Pin/Pth

q0q0 q1q1 q2q2 q0q1 q1q2 q2q0

The effect of losses

The problem of decoherenceIs the main problem for an eventual quantum computer, operating over many entangled qubits.

What is the limit for this entanglement?

Interaction with the environment!

Why producing and keeping them is a hard task?

Decoherence: as if the environment where continuously measuring the system!

Famous example: Schrödinger Cat Paradox (1935).

Also an entangled state

No more “surprises”?Disentanglement for a Bipartite & Gaussian state

Scenario (1): robust entanglement

Scenario (2):disentanglement

Disentanglement for a simpler model:Attenuation on a single beam

Tighter conditions for transmission of quantum entanglement!

Duan (optimized)

What’s next?The sideband problem: non-unitary purity for unitary operations?Are we missing something in our S(Ω) measurement?

YES WE ARE!

S(Ω) includes information in the complex part

(ignored up to the moment).

And represents a pair of sidebands!

V is not 6 x 6, it is 12 x 12 (2 quadratures of 2

sidebands of 3 modes)

And we are measuring it right now!

More to More to followfollow: use : use thethe OPO as a OPO as a coloredcolored entanglingentangling tooltool

Teleportation

Teleportation

|ψout>

Multicolor Teleportation

p

q

PMAM

g +

q

|ψin>Charlie

Alice

Bob

Light – Matter Interaction

Ti:Sapphire PBSOPO

Crystal

FR

Analysis

Atoms

Felippe Barbosa Antônio Sales Jonatas César

Alencar Faria Luciano Cruz Paulo Valente

Mikael Lassen (MPI) Alessandro Villar

Katiúscia Cassemiro Kaled Dechoum A. Zelaquett Khoury

Claude Fabre (LKB) Marcelo Martinelli Paulo Nussenzveig

Raiders of the Lost Entanglement

Paulo Nussenzveig (1996)

Marcelo Martinelli (2004)

Alessandro Villar (Post-doc)

Márcio Heráclyto (Post-doc)

Antônio Sales (PhD – MSc 2008)

Felippe Barbosa (PhD – MSc 2008)

Hans Marin Torres (MSc)

Flávio Moraes (MSc)

Paula Meirelles (PhD)

Laboratório de Manipulação Coerente de Átomos e Luz