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Classical and Quantum Precision with
Broadband Down-Converted Light
Avi Pe’er
Dept. of Physics and BINA center for Nano-Technology,
Bar Ilan University, Ramat-Gan 52900, ISRAEL
email: [email protected]
Outline


Coherence properties of broadband down conversion and SFG
(sum frequency generation).
Experiments:
Low power – Quantum Behavior

High power - Super precision in phase measurement with SFG

Conclusions
Parametric Conversion
Non-linear
crystal
Signal
Pump
Non-linear
crystal
Idler
Up conversion
Idler
Down conversion
Energy conservation
s i   p
As    A  p   
*
i
Signal
Up conversion (SFG)
Momentum conservation (phase matching)
  
k s  ki  k p
The Signal and Idler are Complex
Conjugates
Parametric Conversion II
Many options for pair production
3-waves mixing
p
s
i
 p   s  i
4-waves mixing
p
p
s
i
2 p  s  i
Attractive in-fiber
pump
Non linear
fiber
idler
signal
Broadband Phase Matching
Co-Linear Phase Matching:
s ns   i ni    p n p 
Broad phase matching around
the degeneracy point.
The broadband FWM
Ultra
- zero dispersion
Broadbroad
– degenerate
type I
-20
740nm
0.8
0.4
Power [dbm]
Phase mi smatch cm-1
Phase mi smatch cm-1
-30
0.2
0.6
0
0.4
-0.2
630nm
-40
-50
-60
-0.4
0.2
-70
-0.6
0
-0.8
-80
1.50E+015
1.04 1.05
1.08 1.09
1.2
1.4 1.06
1.6 1.07 1.8
2
micron
λ micron
2.00E+015
2.50E+015
Frequency [Hz]
3.00E+015
3.50E+015
What is non-Classical ?
The signal – idler correlation To the last photon!

A major effect at the single-photon level

What about high-power ?
Time-Energy Entangled Photons
The two-photon Wavefunction
  ts , ti   0 Es ts  Ei ti  
 p  5 MHz
SIGNAL (cw)
PUMP (cw)
1
2
ts  ti 
(2)
IDLER (cw)
  30nm  10THz
1  p  0.2 s
t s  ti
1   100 fs
Time-Energy Entangled Photons
SIGNAL (CW)
Gate
CW PUMP
(2)
IDLER (CW)
The time DIFFERENCE between the photons behaves as an ultrashort pulse
Coincidence Detection by SFG
Signal (CW)
Delay
CW pump
(2)
(2)
Delay
Idler (CW)
 104  105 s 1
 10 9
 10 4 s 1
How High can ‘Low Power’ be ?
(How many ‘single photons’ can arrive in one second ?)
1
1
1






 max    1013 s-1  2 W !!
Analysis
The input flux of photon pairs:
  n
For SFG with a continuously-pumped, broadband down-converted light :
I SFG   nn  1   n   n
2
2
2
2
Coherent contribution
(Entangled pairs)
The Experimental Setup
Computer
Beam
dump
Pump
532nm
PP-KTP
Down-converting
crystal
Fourier
plane
IR detector
PP-KTP
SFG
crystal
SPCM
~40,000 s-1
Intensity Dependence of Quantum SFG
 n 2  n
 n
 n2T 2
“Nonlinear Interactions with an Ultrahigh Flux of Broadband Entangled Photons”,
Phys. Rev. Lett. 94, 043602 (2005)
Phase measurement
Optical phase estimation is THE tool for
precision measurement
!
Length
Time
Frequency
Mach-Zehnder interferometer
e i
B1
A2
B2
 
 
 A cos    A sin  
B1  A1 sin
B2
A1

2
 A2 cos

1
2

2

2
2
With one input
 
cos  
B1  I1 sin 2
2
B2  I1
2
2

2

2
A variable beam splitter !
What are the limits
e
A1
1.0
i
B1
0.8
0.6
B2
0.4
0.2
2
1. When does the first photon
appear in output 1 ?
1
 
N
SQL !
4
6
8
10
12
2. But what about the linear range ?
Quantum noise !!
Beam splitter noise
If we ask a photon ‘which way?’
It will randomly answer
Fluctuations !
(Splitting noise)
SQL !
1
 ~
N
Schemes to overcome SQL
Number N  N
1
2
correlation
1  2
Phase
correlation
Correlated beams
(Holland & Burnett 1993) …
 0
Detector 1
N
−
N
Detector 2
Number
near-correlation
1
 
N
Heisenberg sensitivity for first photon of relative intensity noise
Heisenberg detection
Pump
LO
a1
Homodyne
LO

a1ei
b1
c1
d1
c2
d2
 0
Squeezing
a2
b2
a2
Interferometer stage
Detection stage
Conclusions




Broadband down conversion – a combination of two
worlds - Ultrashort temporal resolution with CW
spectral resolution.
A non-linear interaction with entangled photons Demonstration of non-classicality at low power
Robust, ultrafast detection of squeezing using the
quantum properties of up-conversion
Heisenberg scaled phase measurement with
broadband down conversion and up conversion
Semi classical model
A1
n
B1
B2
2
B1,2 
A1
2
2
 Re  nA1 
‘vacuum fluctuations’
penetrate through the unused port
Only one quadrature of the ‘noise’ is important → Squeeze it
!
(Caves, 1981) +
…
Squeezed light
Vacuum
Squeezed vacuum
2
M
2M
p
p
q
q
Measuring squeezing
φ
LO
ω
Up
conversion
Homodyne detection
2ω
Down
conversion
Squeezing
_
1.Loss –
The quantum resource (number correlation) is very fragile
2.Need ideal detectors
(100% efficient).
3. Bandwidth
Photo detectors are limited to several GHz at most.
Ultrafast squeezing detection !
φ
LO
2ω
Down
conversion
ω
Up
conversion
Squeezing
SFG detection
_
What happens if we up-convert the
down-converted…
Non-Linear
Crystal
(a) Squeezed state (M=3)
(b) Squeezed input (M=10)
squeezed beam
(photon pairs) ω
2
Up conversion
2ω
M
2M
ADC  q  ip
p
q
(c) UC state (M=3)
AUC  Ain2
p
q
(c) UC state (M=10)
Q  iP  q 2  p 2  i 2 pq
NOT squeezed
P  2qp
Q  M2
Q  q2  p2
P  2qp
Q  M2
Q  q2  p2
Ultrafast
squeezing detector
Why is it good?
1. Loss –
Still sensitive to input loss
2. NO Need for ideal detectors
(Up conversion efficiency not critical).
3. ‘Unlimited’ bandwidth
(Up to 100THz).
Two-photon Interactions with BPDC
Rate of TPA (SFG)
At   real
RTP t   A2 t 
A   A*  p   
RTP     dA A   
When    p
RTP  p    d A    dt At 
2
2
Ultrashort pulse !

Temporal resolution of a transform-limited pulse

Spectral resolution of single frequency CW
Experimental Setup
Computer
Pump
Signal
Idler
4D5/2,1/2
Idler
~ 1270
nm
Signal
~ 870
nm
Digital
oscilloscope
PMT
Delay line
Rb cell
516.65
nm
5S1/2
Experimental Results
Temporal resolution of 23 fs,
5 orders of magnitude
Below the duration of the light (3 ns).
Spectral resolution as of the pump (0.04nm)
3 orders of magnitude
Below the bandwidth of the light
(~100nm each beam)
Phys. Rev. Lett. 93, 023005 (2004).
What is non-Classical ?
The signal – idler correlation exceeds shot-noise
The Down converted field is pure real !

A major effect at the single-photon level

What about high-power ?