Download Poster 4

November 3-4, 2003
Optical-Fiber Entanglement Sources: Theoretical
progress and development of associated
technologies
Xiaoying Li, Paul Voss, Jun Chen, Sarah Dugan, and Prem Kumar
Center for Photonic Communication and Computing
Northwestern University, Evanston, IL 60208-3118
Our Motivation
• Provide theoretical understanding for optimization of
polarization entanglement purity
– Model Raman effect (noninstantaneous nonlinear
response)
– Model pulsed pump with realistic signal/idler filters
• Cascaded four wave mixing in PPLN waveguide:
alternate source of polarization entangled photons
• Develop photon counting technology
2
Cause of Uncorrelated Photons in the Fiber
λp = 1530nm, λ0 = 1535±2nm
40
30
1545.3nm
20
1515nm
10
0
0
5
10
3
1545.3nm
2
1
1515nm
0
15
0
*107
Pump photons/pulse
λp = 1534nm, λ0 = 1537±2nm
*103 4
Single counts(1s)
Single counts(5s)
*103
50
100
200
300
Length of DSF (m)
It is Raman Scattering! S
RS
∝
P
p
L
DSF
800
Theory curve for two
independent sources
Coin(5s)
600
Improvements are possible!
Suppress Raman scattering and
optimize FWM:
400
• Optimize signal / idler wavelengths
• Optimize filter bandwidth
• Decrease temperature, although not
desirable
200
0
0
20
40
Single A(5s)
60
*103
3
400
χ(3) Nonlinear Response
• Noninstantaneous response
due to back action of nuclei on
electronic Kerr nonlinearity
• Nonlinear coefficient
from
parallel Raman power gain profile
(Dougherty, 94),
power gain peak magnitude
for DSF (Taylor, 01),
Kramers-Kronig transform gives
from
,
and from H(0) for DSF (Taylor, 94).
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Quantum Model of FWM plus Raman Effect
L. Boivin, F. X. Kärtner, and H. A. Haus, Phys. Rev. Lett. 73, 240 (1994).
J. H. Shapiro and L. Boivin, Opt. Lett. 20, 925 (1995).
• Envelope propagation for continuous-time temporal modes
• After Fourier Transform, undepleted pump approximation,
only looking at three modes
5
FWM plus Raman solution
•
Voss and Kumar, to appear in Opt. Lett.
Solution is
where
and
and Noise Figure is:
6
Excellent Agreement with Several Experiments
• Addition of Raman noise can be treated analytically
• Matches PIA noise figure data with no fitting parameters
• Theory ok for twin beam noise reduction (TBNR) at low gains
• At G>2, need Raman + higher order FWM theory for TBNR
7
Classical Equations of FWM: Start of pulsed theory
•
Degenerate FWM
•
Non-degenerate FWM
•
Heisenberg Equation of Motion
8
Interaction Hamiltonian for FWM in Optical Fibers
• Hamiltonian for Degenerate FWM
• Hamiltonian for Non-degenerate FWM
where
9
Standard Approach: Pulsed fields
•
Electric Fields of Pump, Signal and Idler
•
First-Order Perturbation
•
Two-photon State
10
Coincidence Counting
• Biphoton Amplitude
• Coincidence Counting Rate
• Gaussian Filter Approximation
• Analytical Expression for Coincidence Counting Rate
11
Effect of filter bandwidth and filter frequency shift
60000
50000
Experimental Data
Theoretical Prediction
CC/sec
40000
30000
20000
10000
0
0
0.5
1
1.5
2
2.5
3
3.5
Pump Peak Power [W]
14000
Coincidence
Counts sec
12000
4000
CC/sec
10000
8000
3000
6000
2000
4000
1000
2000
0
0
0.5
1
1.5
2
2.5
-1 ´ 10
Filter Bandwidth [nm]
12
-8
-5 ´ 10
-9
5´ 10
-9
1´ 10
-8
Dl
Cascaded Four-Wave Mixing
•Cascaded χ(2) process -- pump
generates second harmonic which
pumps down-conversion
•Leading to mode-matched source
of entangled photons
Pump source:
20kHz, 10ns into 1542nm
GS DFB
90/10
FPCs
FC
1531nm
PBS
2ω Det.
Dichroic
FC
oscilliscope
13
Det.
Tunable
BPF (idl)
Waveguide
Signal Source:
Tunable diode
laser (Santac)
Idler power vs. pump second-harmonic
Coincidence counting with conversion
14
10GHz
Amplitude
modulator
Pump
1551nm
DFB
Variable
Attenuator
WG1, gen.
FPC
Grating2
WG2, conv.
•The two waveguides have
10GHz BERT
similar modes, so coupling is
10MHz
100ps,
easier
clock
10MHz
•Use one pump for both
processes – improve coupling,
signal and idler need 20nm
separation
•Pump requirements are same as
earlier signal – pulsed, 100ps,
<0.2nm – but now also <10kHz
InGaAs/InP
•First (shorter) waveguide has
PCM
larger BW, may have to filter
WDM
unconverted light
•Detection efficiency is the
average of the two detectors
(~45%)
•Coordinate coincidence
measurements between Si
DAQ
detector and InGaAs/InP detector
card
Dichroic
Grating1
Si
PCM
14 MHz InGaAs/InP APD Photon Counters
• Highest rate operation to date
Detectors
• Possible because of room temperature
operation
• Good suppression of afterpulses
• Relatively high dark count rate
Avalanche pulse
Fast
amplifiers
A/D
Digital
thresholding
logic
• Previous system limited to <1 MHz
because of:
• Delay Generator DG535 rate limit (1 MHz)
• Data Acquisition card (NI PCI6010E)
• Avtech Pulse Generator rate limit (1 MHz)
• Upgrade includes
• Delay line based on phase shifter at 14 MHz
• Avtech Pulse Generator (25 MHz)
• Fast A/D to sample photocurrent (AD9033)
• Digital thresholding for auto-recalibration and
programmability
• NI PCI5102 data acquisition (20 MHz)
15
Optical Clock
Detection
& Recovery
Adjustable Delay
Line
14 MHz results: Bias Scanned
• Threshold constant
• APD A scanned
from 48.8 to 51.2 V.
• APD B scanned
from 49.4 to 51.0 V.
• Scanned in 200 mV
increments.
• 800 ps, 12 V gate
16
14 MHz results: decision threshold scanned
• Decision threshold scanned for
each bias
• 800 ps, 12 V gate
• Q.E. ~ 10-15% for dark count
probability of 0.2%
• Fluctuations due to timing drift
in phase shifting circuit
• Conclusion: Most bias
settings equivalent
• Conclusion: threshold
scanning or bias scanning are
roughly equivalent
17
Threshold determination
capacitive
“ringing”
light + dark count distribution
Note: 1 ns capacitive
“ringing” slowed down by
100 MHz bandwidth of
amplifier
dark counts
capacitive
“ringing”
dark count distribution
• Dark and light counts have different
voltage distributions
light + dark
counts
• Similar to PMT
• There is an optimum threshold level
18
Afterpulsing at room temperature
• 1 ns, 10 V gate
Bias:
49 V asterisks
50 V squares
51 V circles
• Afterpulsing
increases with
bias voltage
(larger breakdown
currents fill
more trapping
centers)
• Afterpulsing prob
≈ dark count rate
at 50 V bias,
14 MHz operation
19
Accomplishments and Work in Progress
• Observed polarization entanglement / biphoton
interference
• Violation of Bell’s inequalities demonstrated
• Observation of polarization entanglement over long
distances (25/50 km)
• Continuing studies on background photons
• Coincidence counting in the 800 nm region
• Progress on high-rate photon counting
• Progress in quantum frequency conversion using
PPLN waveguides
20