Luz e Átomos como ferramentas para Informação Quântica...
Transcript of Luz e Átomos como ferramentas para Informação Quântica...
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
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
• Extend DGCZ criterion to three variables
• Apply PPT to multiple partitions
Tripartite Entanglement
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
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)
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)
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 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
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
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