Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed...
-
Upload
daniela-hodge -
Category
Documents
-
view
218 -
download
0
Transcript of Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed...
![Page 1: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/1.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed
microcavityM. G. Raymer, Jaewoo Noh*
Oregon Center for Optics, University of Oregon
--------------------------------------
I.A. Walmsley, K. Banaszek, Oxford Univ.
-----------------------------------------------------------------
* Inha University, Inchon, Korea
-----------------------------------------------------------------
ITR - NSF
![Page 2: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/2.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Single-Photon Wave-Packet
1
€
1 = dω ψ∫ (ω) 1 ω
Wave-Packet is a Superposition-state:
(like a one-exciton state)
![Page 3: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/3.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Interference behavior of Single-Photon Wave-Packets
At a 50/50 beamsplitter a photon transmits or reflects with 50% probabilities.
1
1
€
1 = dω ψ∫ (ω) 1 ω
Wave-Packet is a Superposition-state:
0
beam splitter
![Page 4: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/4.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Interference behavior of Single-Photon Wave-Packets
At a 50/50 beamsplitter a photon transmits or reflects with 50% probabilities.
1
0
€
1 = dω ψ∫ (ω) 1 ω
Wave-Packet is a Superposition-state:
1
beam splitter
![Page 5: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/5.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Single-Photon, Pure Wave-Packet States Interfere as Boson particles
1
1beam splitter
2
0
![Page 6: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/6.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Single-Photon, Pure Wave-Packet States Interfere as Boson particles
1
1beam splitter
0
2
![Page 7: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/7.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal
Phase-matching (momentum conservation):
rkS +
rkI =
rkP ±π / L
rkS
rkI
rkP
pumpSignal V-Pol
Idler H-Pol
Energy conservation:
ωS +ωI =ωP
red red blue
L
kz
frequency
P
VH
H-Pol
phase-matching bandwidth
![Page 8: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/8.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Correlated Photon-Pair Generation by Spontaneous Down Conversion (Hong and Mandel, 1986)
0 or 1
Monochromatic Blue Light
Red photon pairs
2nd-order Nonlinear optical crystal
ω+ω '=ωP
ωP
ω'
ω
0 or 1
Ψ 2P = dω C∫ (ω) 1SIGNAL ω 1IDLER ωP −ω
IDLER
SIGNAL
• Creation time is uncontrolled
• Correlation time ~ (bandwidth)-1
Perfect correlation of photon frequencies:
optional
![Page 9: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/9.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
1
1
Correlated Photon-Pair Measurement (Hong, Ou, Mandel, 1987)
Time difference
2 or 0
0 or 2
Red photons
Nonlinear optical crystal
Time difference
Coincidence Rate
Correlation time ~ (bandwidth)-1
Creation time uncontrolled
MC Blue light
boson behavior
![Page 10: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/10.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
1
1
trigger if n = 1
filter
Pulsed blue light
For Quantum Information Processing we need
pulsed, pure-state single-photon sources.
Create using Spontaneous Down Conversion and conditional detection:
shutter
nonlinear optical crystal
(Knill, LaFlamme, Milburn, Nature, 2001)
![Page 11: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/11.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
1
trigger if n = 1
filter
Pulsed blue light
For Quantum Information Processing we need
pulsed, pure-state single-photon sources.
Create using Spontaneous Down Conversion and conditional detection:
shutter
nonlinear optical crystal
SIGNAL
(Knill, LaFlamme, Milburn, Nature, 2001)
![Page 12: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/12.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
trigger
Pulsed Pump Spectrum has nonzero bandwidth
Ψ2P
= dω '∫ dω C∫ (ω,ω ') 1IDLER ω ' 1SIGNAL ω
Zero-Bandwidth Filter , 0
ωP
ω'
ω1IDLER '
1SIGNAL
→ dω∫ C(ω0 ,ω ) 1SIGNAL ωdetect signal
Pure-state creation at cost of vanishing data rate
![Page 13: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/13.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
1
1
1
trigger
trigger
1Time difference
Coincidence Counts
Do single photons from independent SpDC sources interfere well? Need good time and frequency correlation.
large data rate
filter
Pulsed blue light
filter
random delay
vanishing data rate
![Page 14: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/14.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Goal : Generation of Pure-State Photon Pairs without using Filtering
Single-photon Wave-Packet States:
1 S0 = dω ψ 0∫ (ω) 1 Sω
1 I0 = dω φ0∫ (ω) 1 I ω
signal
idler
Ψ2P
= dω '∫ dω C∫ (ω,ω ') 1IDLER ω ' 1SIGNAL ω
= 1I 0⊗ 1
S 0
€
C(ω,ω ') = ψ 0 (ω) × φ0 (ω ')Want :
(no entanglement)
![Page 15: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/15.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Decomposition of field into Discrete Wave-Packet Modes. (Law, Walmsley, Eberly, PRL, 2000)
Ψ = vac + dω'∫ dω C∫ (ω,ω' ) 1 Sω 1 Iω'
Ψ = vac + λ jj
∑ 1 Sj ⊗ 1 I j
1 S j = dω ψ j∫ (ω) 1 Sω
1 I j = dω φ j∫ (ω) 1 Iω
Single-photon Wave-Packet States:
(Schmidt Decomposition)
![Page 16: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/16.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
The Schmidt Wave-Packet Modes are perfectly correlated.
But typically it is difficult to measure, or separate, the Schmidt Modes.
Ψ = vac + λ jj
∑ 1 Sj ⊗ 1 I j
Mode Amplitude Functions: Mode spectra overlap.
No perfect filters exist, in time and/or frequency.
frequency
€
CS1(ω)
€
CS 2(ω)
€
CS 3(ω)
filter
1 S j = dω ψ j∫ (ω) 1 Sω 1 I j = dω φ j∫ (ω) 1 Iω
![Page 17: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/17.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Why does the state generally NOT factor?
€
Ψ2P
= dω'∫ dω C∫ (ω,ω ') 1SIGNAL ω 1IDLER ω '
≠ 1S 0⊗ 1
I 0
€
€
'
€
C(ω,ω ')
need to engineer the state to make it factor
Energy conservation and phase matching typically lead to frequency correlation
![Page 18: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/18.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Spontaneous Parametric Down Conversion inside a Single-Transverse-Mode
Optical Cavity
rkS
rkI
rkP
pump
Nonlinear optical crystal with wave-guide
1 mm
DOES NOT WORK
the problem:
cavity FSR ~ 1/L
phase-matching BW ~ 10/L
![Page 19: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/19.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Spontaneous Parametric Down Conversion inside a Distributed-Feedback Cavity
4 mm
0.2 mm cavity
second-order nonlinear-optical crystal
pump
H-PolH-Pol idler
V-Pol signal
4 mm
Linear-index Distributed-Bragg Reflectors (DBR)
Linear-index wave-guide
• large FSR = c /(2x0.2 mm)
• small phase-matching BW:
~ 10 c /(4 mm)
![Page 20: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/20.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
0 =800 nm KG = 25206/mm
n/n ~ 6x10-4 ( = 2/mm)
4 mm
DBR 99% mirror
SIMPLIFIED MODEL: Half-DBR Cavity
Reflectivity
frequency/1015
DBR band gap
0.2 mm cavity
cavity mode
![Page 21: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/21.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Quantum Generation in a Dielectric-Structured Cavity: Phenomenological Treatment
∂x2E(x, t) −∂t
2D(x, t) = J(x, t) = χ NL Ep (x, t)E * (x, t)Signal Source Pump
Frequency Domain:
∂x
2 + ε (x,ω ) ω 2⎡⎣ ⎤⎦%E(x,ω ) = %J(x,ω )
∂x2 + ε (x,ω )ω 2⎡⎣ ⎤⎦u(x,ω ) = 0 (modes)
space and frequency dependent electric permeability:
ε(x,ω ) = ε (x)n2 (ω )
![Page 22: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/22.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
€
x
internal Signal, Idler modes
pump fieldinteraction
€
˜ E S (x,ω)
€
˜ E S (x,ω) = ˜ E VAC (x,ω) + uout(x,ω) dω'∫ C(ω,ω') ˆ a I†(ω')
0 L
€
C(ω,ω') = χ NL dx '0
L
∫ ˜ E p (x ' ,ω +ω') uS *(x ' ,ω)uI * (x' ,ω')
€
˜ E p
two-photon amplitude
![Page 23: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/23.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Heisenberg Picture Schrodinger Picture
Ψ = vac + dω'∫ dω C∫ (ω,ω' ) 1 Sω 1 Iω'
€
C(ω,ω ') = α p (ω + ω') Φ(ω,ω ')
Amplitude for Photon Pair Production:
€
Φ(ω,ω') = χ NL dx '0
L
∫ uP (x ' ,ω +ω')uS *(x ' ,ω)uI * (x ' ,ω')
pump spectrum
Cavity Phase-Matching
pump mode internal Signal, Idler modes
![Page 24: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/24.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Type-II Collinear Spontaneous Parametric Down Conversion in a second-order nonlinear, birefringent crystal
Phase-matching (momentum conservation):
rkS +
rkI =
rkP ±π / L
rkS
rkI
rkP
pumpSignal
Idler
Energy conservation:
ωS +ωI =ωP
red red blue
L
k
frequency
P
VH
H-PolH-Pol
V-Pol
phase-matching bandwidth
![Page 25: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/25.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
P
I
S
0 kS kI kP
S = I = P/2
Birefringent Nonlinear Crystal, Collinear, Type-II, Bulk Phase Matched, with Double-
Period Grating:
KGS/2 KGI/2
kS + kI = kP
KTP -->
![Page 26: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/26.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
0 L
• grating index contrast • crystal length L = 4 mm, giving G L = 8• cavity length ~ 0.2mm• signal and idler fields are phase matched at degeneracy wavelength S I = 800 nm • pump wavelength = 400 nm• pump pulse duration 10 ps
n / n = 5 ×10−4
KTP Crystal with Double Gratings
95% mirror
![Page 27: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/27.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.Two-Photon Amplitude C(, ’)
’ ’
No Grating, No Cavity
’ ’
Two Gratingszo
om
in
Two Gratings
with Cavity
![Page 28: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/28.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.Two-Photon Amplitude C(, ’)
’ ’
’
’
Two Gratings with Cavity
x Pump Spectrum zoom
in
(hi res)
![Page 29: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/29.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
€
C(ω,ω ') = χ NL dx '0
L
∫ ˜ E p (x ' ,ω +ω') uS * (x ' ,ω)uI * (x ',ω')
Schmidt-Mode Decomposition
Schmidt-mode eigenvalues for different values of cavity-mirror reflectivity ρ2ρ2 j=1 j=2 j=3 j=4 j=50.95 0.951 0.0196 0.0196 0.0044 0.00440.99 0.998 0.0007 0.0007 0.0002 0.0002
Ψ = vac + dω'∫ dω C∫ (ω,ω' ) 1 Sω 1 Iω'
Ψ = vac + λ jj
∑ 1 Sj ⊗ 1 I j
1 S j = dω ψ j∫ (ω) 1 Sω 1 I j = dω φ j∫ (ω) 1 Iω
![Page 30: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/30.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
First Four Schmidt Modes
for 95% Cavity Mirror
j=1 j=2
j=4j=3
frequency frequency
amplitude
DBR
![Page 31: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/31.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
Unfiltered Measurement-Induced Wave-function Collapse
• For cavity-mirror reflectivity = 0.99, the central peak contains 99% of the probability for photon pair creation, without any external filtering before detection.
• If any idler photon is detected, then the signal photon will be in the first Schmidt mode with 99% probability.
• Promising for high-rate production of pure-state, controlled single-photon wave packets.
![Page 32: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/32.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
CONCLUSIONS & DIRECTIONS:
• Spontaneous Down Conversion can be controlled by modifying the density of states of vacuum modes using distributed cavity structures.
• One can engineer the vacuum to create single-photon pairs in well defined, pure-state wave packets, with no spectral no spectral entanglemententanglement.
• In the absence of detector filtering, detection of one of the pair leaves the other in a pure single-photon state.
• Waveguide development at Optoelectronics Research Center (Uni-Southampton, Peter Smith)
![Page 33: Pure-state, single-photon wave-packet generation by parametric down conversion in a distributed microcavity M. G. Raymer, Jaewoo Noh* Oregon Center for.](https://reader036.fdocuments.us/reader036/viewer/2022062423/56649e9f5503460f94ba2312/html5/thumbnails/33.jpg)
QuickTime™ and aPhoto - JPEG decompressor
are needed to see this picture.
cavity 1
cavity 2
beamsplitter
photon pairweak single-mode squeezed
Alternative Scheme: Single-mode squeezers combined at a beam splitter