Measuring the Wave-FunctionMeasuring the Wave-Function of Broadband Bi-Photons of Broadband Bi-PhotonsYaakov Shaked, Roey Pomeranz, Avi Pe’er

Rafi Vered, Lena Kirjner, Michael Rosenbluh

Physics Dept. and BINA center for nanotechnology, Bar Ilan University

FRISNO 2013, Ein Gedi

$$ ISF, EU-IRG, Kahn

FoundationHow to make a Ti:Sapphire laser tap-dance

– Posters M17, T23

OutlineOutlineWhy ultra broadband photon pairs?Measuring time-energy entanglement

◦HOM interference◦SFG correlation

Measuring the two-photon phase with quantum pairwise interference

Non-classical nature – Fringe contrastFWM – Observe the entire quantum-to-

classical transition

Time-Energy Entangled Time-Energy Entangled Photons Photons

? is pis

00

1,1)(0 gd

Entanglement

The two-photon state (monochromatic pump)

non linear crystalpump signal

idler

pp

s

i

)(g

the two-photon wave function

(monochromatic pump)

? is tt 1is tt

Time-Energy CorrelationTime-Energy Correlation

)(),( isis ttGtt

2/2/

1,1)(0)1(pp

gd

uncertainty relation

is tt 21

is tt

fs101

Ultra-Broadband bi-Ultra-Broadband bi-PhotonsPhotons

PPKTPPump880nm

CCD

Zero Dispersion !

110 130 150 170 190 210 230 250

1

2

3

4

5

6

7

8

DC Spectrum

Angular Frequency (THz)

Spe

ctra

l Int

ensi

ty [

a.u]

“Single cycle” bi-photons

Why ultra-broad photon Why ultra-broad photon pairs ?pairs ?

1

1

1

Because there are so many of them !

Wspairs 12/1014max

Standard detection does not work

Need new schemes !

Measuring entanglement - Measuring entanglement - HOMHOM

Limitations: Phase sensitivity, but no phase

measurement Only for indistinguishable photons Not directly applicable for collinear

configuration

1

2BS

Measuring entanglement - Measuring entanglement - SFGSFG

Down-convertingcrystal

up-convertingcrystal

Pump 532nm

IR detector

SPCM

Beam dump

Computer

PRL 94, 043602 (2005) , PRL 94, 073601 (2005)

Limitations: Phase sensitivity, but no phase

measurement Very low SFG efficiency ! (10-8)

Efficient two-photon interaction 22 nnISFG

60%

100 150 200 250

0

50

100

150

200

250

300

Freq. [THz]

Quantum two-photon Quantum two-photon interferenceinterferenceWhat if we let the pump pass ?

CCD camera

Pump laser (880nm)

Pump power meter

Crystal 1 Crystal 2

SFG efficiency = 60%

Inherent phase stability !

“Frustrated Two-Photon Creation via Interference" , T. J. Herzog, J. G. Rarity, H. Weinfurt & A. Zeilinger, Phys. Rev. Lett. 72, 629-632 (1993).

60%

Reconstruct the spectral Reconstruct the spectral phasephase

100 150 200 250

5

10

15

20

100 150 200 250

0

100

200

300

Phase mismatch Dispersion from the dielectric mirrors

What is non-classical ?What is non-classical ?

CCD camera

Pump laser (880nm)

A

B

Pump power meter

Crystal 1 Crystal 2

A

B

gzee

eeF

gzgz

gzgz

tanh

Classical fringe contrast

Measure of the

two-photon purity

Now to FWM…Now to FWM…

Down conversion

ps

ienergy conservation

momentum conservation(phase matching) pk

sk

ik

non linear crystal

pump signalidler

Four Waves Mixingnon linear

fiberpump signal

idler

2ωp

ωi

ωs

2kp

ki ks

The ExperimentThe ExperimentTi:S Laser (6ps)

PCF

Rafi Z. Vered, Michael Rosenbluh, and Avi Pe’er, “Two-photon correlation of broadband-amplified spontaneous four-wave mixing”, Phys. Rev. A 86, 043837 (2012)

Pump filter

Spectrometer

Dispersive window

Spontaneously generated signal-idler

(ASE)Different from supercontinnum

generation! INCOHERENT – No comb

Unique regime compared to CW – High gain

Can cover the full Quantum-Classical transition

6ps

FWM and TWM – FWM and TWM – Differences…Differences…

Down conversion Four Waves Mixing

zkispi

zkiips

eAAiAz

eAAiAz

*

*

zki

spipi

zkiipsps

eAAAAiAz

eAAAAiAz

*22

*22

2

2

zAki

spi

zAki

ips

p

p

eBAiBz

eBAiBz

2

2

2*2

0,

2*2

0,

Rescale equations zAi

isispeAB

22

,,

22 pAk

Generalized phase mismatch

FWM Gain SolutionFWM Gain SolutionSignal/idler solution

zizgisis eebB 2

,,

zAi

pppetzAtzA

2

,0,

Gain only when Δk<0 !

4

242 pAg

4

22 k

Akg p

Similar to 3-waves, but…

Gain also when Δκ≠0 ! Correlation ?

2

02 k

Ap

Threshold pump intensity !

Full Quantum-classical transition !

FWM results (Fresh)FWM results (Fresh)At zero dispersion - 784nm (Δk≈0)

786nm 788nm

Threshold?

Classical

ConclusionsConclusionsA source of collinear “single cycle” bi-photons Huge ‘Homodyne’ Gain in two-photon efficiency

(~40%) with pump inserted into the 2nd crystalHolographic measurement of the spectral phase

of the bi-photons by pairwise interferenceFringe contrast is a quantum signature –

“Measure quantum correlation by trying to undo it…”Observation of the entire classical-quantum

transition with FWM in fiber Inherently stable collinear interferometer –

No locking neededMany things we don’t understand yet…