FRISNO 2013, Ein Gedi
Measuring the Wave-Function
of Broadband Bi-Photons
Yaakov Shaked, Roey Pomeranz, Avi Pe’er
Rafi Vered, Lena Kirjner, Michael Rosenbluh
Physics Dept. and BINA center for nanotechnology, Bar Ilan University
$$
ISF, EU-IRG,
Kahn Foundation
How to make a Ti:Sapphire laser tap-dance –
Posters M17, T23
Outline
 Why

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 contrast
FWM – Observe the entire quantum-toclassical transition
Time-Energy Entangled Photons
pump
p
non linear
crystal
signal
s
p
i
idler
s  i   p
s  i  ?
The two-photon state (monochromatic pump)
  0    d g ( ) 1
Entanglement
g ( )
0 
,10 


Time-Energy Correlation
  (1   ) 0    d g ( ) 1
uncertainty
relation
p / 2 
,1 p / 2 
t s  ti  ? t s  ti  1 
1
2
ts  ti 
the two-photon
wave function
(monochromatic pump)
1  10 fs

(ts , ti )  G(ts  ti )
t s  ti
Ultra-Broadband bi-Photons
Zero Dispersion !
PPKTP
Pump
880nm
DC Sp ectrum
Spectral Intensity [a.u]
8
7
6
5
4
3
“Single cycle”
bi-photons
2
1
110
130
150
170
190
210
230
Angular Frequency (T Hz)
250
Why ultra-broad photon pairs ?
Because there are so many of them !
1


1


1


max    1014 pairs/ s  12W
Standard detection does not work
Need new schemes !
Measuring entanglement - HOM
1
BS
2
Limitations:
 Phase sensitivity, but no phase
measurement
 Only for indistinguishable photons
 Not directly applicable for collinear
configuration
Measuring entanglement - SFG
Computer
Beam
dump
IR
detector
Pump
532nm
Down-converting
crystal
SPCM
up-converting
crystal
PRL 94, 043602 (2005) , PRL 94, 073601 (2005)
Efficient two-photon interaction

I SFG  2 n  n2
Limitations:
 Phase sensitivity, but no phase
measurement
 Very low SFG efficiency ! (10-8)

Quantum two-photon interference
What if we let the pump pass ?
“Frustrated Two-Photon Creation via Interference" , T. J. Herzog, J. G.
Rarity, H. Weinfurt & A. Zeilinger, Phys. Rev. Lett. 72, 629-632 (1993).
CCD
camera
Pump laser
(880nm)
Crystal 2
Crystal 1
300
Pump
power meter
250
Intensity [Arb]
200
150
60%
60%
100
50
SFG efficiency = 60%
Inherent phase stability !
0
100
150
200
Freq. [THz]
250
Reconstruct the spectral phase
20
300
15
200
10
100
5
0
100
150
200
250
 Phase mismatch
 Dispersion from the dielectric mirrors
What is non-classical ?
Classical fringe contrast
A
Pump laser
(880nm)
e gz  e  gz
F  gz
 tanhgz 
 gz
e e
B
Crystal 2
Crystal 1
A
B
CCD
camera
Pump
power meter
Measure of the
two-photon purity
Now to FWM…
Four Waves Mixing
Down conversion
pump
non linear
crystal
pump
non linear fiber
signal
idler
idler
energy
conservation
p
momentum
conservation
(phase matching)
signal
s
i

ki

ks

kp
ωi
2ωp
ki
ωs
ks
2kp
The Experiment
6ps
PCF
Dispersive
window
Ti:S Laser (6ps)
Spontaneously generated
signal-idler (ASE)
Spectrometer
Pump from supercontinnum generation!
Different
filterINCOHERENT – No comb
Unique regime compared to CW – High gain
Can cover the full Quantum-Classical
transition
Rafi Z. Vered, Michael Rosenbluh, and Avi Pe’er,
“Two-photon correlation of broadband-amplified spontaneous fourwave mixing”, Phys. Rev. A 86, 043837 (2012)
FWM and TWM – Differences…
Four Waves Mixing
Down conversion

As  iAp A*i e ik  z
z

Ai  iAp A s* e ik  z
z


2

As  i 2 Ap As  Ap2 A*i e ik  z
z
2

Ai  i 2 Ap Ai  Ap2 A s* e ik  z
z
Rescale equations

Bs  iAp2, 0 B e
z
i  k  2

Bi  iAp2, 0 B s*e 
z
Bs ,i  As ,i e
2
i  k  2 Ap  z
*


i
Ap
2
 z


2
 2 i Ap z
Generalized phase
mismatch
  k  2 Ap
2


FWM Gain Solution
Signal/idler solution
Bs ,i  bs ,i e g  z e
g   Ap
2
4
 i 2
z
 2

4
g   k   Ap
2
k 2

4
Ap z, t   Ap z  0, t e
Similar to 3-waves,
but…
Ap
2
  0 
2
i Ap z
k
2
Gain only when Δk<0 !
Gain also when Δκ≠0 !
Correlation ?
Threshold pump intensity !
FWM results (Fresh)
At zero dispersion - 784nm (Δk≈0)
1
Classical
0.9
0.8
0.7
0.6
0.5
Threshold0.4
0.3
?
0.2
0.1
1
1
0
0.8
0.4 0.9
0.8
0.7
0.7
0.6
0.6
0.9
0
0.2
0.6
0.8
1
0.5
Full Quantum-classical
transition !
0.4
0.3
788nm
786nm
0.2
0.5
0.4
0.3
0.2
0.1
0.1
0
0
0
0.2
0.4
0.6
0.8
1
0
0.2
0.4
0.6
0.8
1
Conclusions
A source of collinear “single cycle” bi-photons
 Huge ‘Homodyne’ Gain in two-photon efficiency
(~40%) with pump inserted into the 2nd crystal
 Holographic measurement of the spectral phase of
the bi-photons by pairwise interference
 Fringe 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 needed
 Many things we don’t understand yet…
