superluminal light pulses, subluminal information transmission
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Superluminal Light Pulses, Subluminal Information Transmission. Dan Gauthier and Michael Stenner * Duke University, Department of Physics, Fitzpatrick Center for Photonics and Communication Systems Mark Neifeld * University of Arizona, Electrical and Computer - PowerPoint PPT PresentationTRANSCRIPT
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Superluminal Light Pulses,Subluminal Information Transmission
Dan Gauthier and Michael Stenner*Duke University, Department of Physics,
Fitzpatrick Center for Photonics
and Communication Systems
Mark Neifeld*University of Arizona, Electrical and Computer
Engineering, and The Optical Sciences Center
OSA Nonlinear Optics Meeting, August 6, 2004Funding from the U.S. National Science Foundation
Nature 425, 665 (2003)
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R.W. Boyd and D.J. Gauthier, "Slow and "Fast" Light, in Progress in Optics, Vol. 43, E. Wolf, Ed. (Elsevier, Amsterdam, 2002), Ch. 6, pp. 497-530.
Superluminal Light PulsesDefinition:The pulse apparently propagates in an optical medium faster than the speed of light in vacuum c.
superluminal: Linear pulse propagation (weak pulses)
superluminous: Nonlinear pulse propagation (intense pulses)
"fast" light = superluminal or superluminous
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Linear Pulse Propagation: Group Velocity
Lowest-order statement of propagation withoutdistortion
dd
0
group velocity
gg
c
n dnd
cn
different p
metamaterials, highly dispersive materials
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Variation in vg with dispersion
4 3 2 1 1 2 3 dnd
4321
1
2
3
4
Vgc
slow light
fast light
Garrett and McCumber, PRA 1, 305 (1970)
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Schematic of Pulse Propagation at Various Group Velocities
There is no causal connection between pulse peaks!
vg<c vg=c vg>c vg negative
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Superluminous Pulses
Propagate pulses through a saturable amplifier
amplifier
intense pulse
unsaturatedpulse
Basov and Letokhov, Sov. Phys. Dokl. 11, 222 (1966)
New Insight: Can also be understood in terms ofcoherent population oscillations
See next talk: FA5, Robert W. Boyd
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Fast Pulses: Linear Optics RegimeUse a single absorbing resonance
Large anomalous dispersion on resonance
(also large absorption)
Garrett and McCumber, PRA 1, 305 (1970)Chu and Wong, PRL 48, 738 (1982)Segard and Makce, Phys. Lett. 109A, 213 (1985)
Also Sommerfeld and Brillouin ~1910-1914
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Fast-light via a gain doublet
Steingberg and Chiao, PRA 49, 2071 (1994)(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
gg
c
n dnd
cn
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Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
rubidiumenergylevels
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Experimental observation of fast light
ng ~ -310 … but the fractional pulse advancement is small
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Optimize relative pulse advancement
A = tadv/tp ~ 0.1 goL ~ 0.03 gcL
Wang et al.: goL ~ 1.3 A ~ 0.13 observe ~ 0.022x narrower bandwidth than we assume
relative pulse advancement A = tadv/tp
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Setup to observe large relative pulse advancement
Tried to use bichromatic field (Wang et al. technique)
Problem: Large gain gave rise to modulation instability!! Stenner and Gauthier, PRA 67, 063801 (2003)
Solution: Dispersion Management
AOM
o
d-
d+
d-
d+
L/2 L/2
waveformgenerator
Kvapor
Kvapor
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time (ns)
-300 -200 -100 0 100 200 300
pow
er (
W)
0
2
4
6
8
10
12
pow
er (
W)
0.00.20.40.60.81.01.21.41.6
advanced vacuum
tadv=27.4 ns
Observation of "Fast" Light with LargeRelative Advancement
Stenner, Gauthier, and Neifeld, Nature 425, 665 (2003)
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Where is the information?
How fast does it travel?
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Points of non-analyticity
t
Ppoint of non-analyticity
knowledge of the leading part of the pulse cannot be usedto infer knowledge after the point of non-analyticity
new information is available because of the "surprise"
Chiao and Steinberg find point of non-analyticitytravels at c. Therefore, they associate it with theinformation velocity.
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Detecting points of non-analyticityChiao and Steinberg proposal not satisfactory from aninformation-theory point of view: A point has no energy!
transmitter receiver
Point of non-analyticity travels at vi = c (Chiao & Steinberg)
Detection occurs later by an amount t due to noise (classical or quantum). We call this the detection latency.
Detected information travels at less than vi, even in vacuum!
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time (ns)
-300 -200 -100 0 100 200 300
optic
al p
ulse
am
plitu
de (a
.u.)
0.0
0.5
1.0
1.5
"1"
"0"
Information Velocity: Transmit Symbols
information velocity: measure time at which symbols can first be distinguished
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time (ns)
-300 -200 -100 0 100 200 300
optic
al p
ulse
am
plitu
de (a
.u.)
0.0
0.5
1.0
1.5
advanced
vacuum
"1"
"0"
time (ns)
-60 -40 -20 00.6
0.8
1.0
1.2
1.4
1.6
1.8
Y D
ata
0.2
0.4
0.6
0.8
1.0
1.2
vacuum
advanced
A
B
advanced
Send the symbolsthrough our fast-lightmedium
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Estimate information velocity in fast light medium
t t nsadv vac b g12 05. .
i adv c, ( . . ) 0 4 05
from the model
combining experiment and model
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Summary• Generate "fast" light pulses using highly dispersive materials, metamaterials, saturation• Investigate fast-light pulse propagation with large pulse advancement (need large gain path length)• Transmit symbols to measure information velocity
• Estimate vi ~ c
• Consistent with special theory of relativity• Demonstrates that there is no causal connection between peak of input and output pulses
http://www.phy.duke.edu/research/photon/qelectron/proj/infv/
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Pulse Propagation: negative vg
(Group velocity approximation)
(Poynting vector always along +z direction)
z
vacuum vacuum
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time (ns)
-12 -10 -8 -6 -4 -2 0 20.7
0.8
0.9
1.0
1.1
1.2
1.3
Y D
ata
0.7
0.8
0.9
1.0
1.1
1.2
1.3 time (ns)-300 -200 -100 0 100 200 300
optic
al p
ulse
am
plitu
de (a
.u.)
0.0
0.5
1.0
1.5
2.0
2.5
advanced
vacuum
"1"
"0"
vacuum advanced
a
b
advanced
Send "sharp" symbolsthrough our fast-lightmedium
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time (ns)
-14 -12 -10 -8 -6 -4 -20.7
0.8
0.9
1.0
1.1
1.2
Y D
ata
0.7
0.8
0.9
1.0
1.1
1.2 time (ns)-300 -200 -100 0 100 200 300
optic
al p
ulse
am
plitu
de (a
.u.)
0.0
0.5
1.0
1.5
2.0
2.5
delayed
vacuum
"1"
"0"
vacuum
delayed
a
b
delayed
Send "sharp" symbolsthrough our slow-lightmedium
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-40 -30 -20 -10 0
BE
R
10-4
10-3
10-2
10-1
100
vacuum
advanced
A
final observation time (ns)
Matched-filter to determine the bit-error-rate (BER)
Determine detection times using a threshold BER
Use large threshold BER to minimize t
Detection for informationtraveling through fastlight medium is later eventhough group velocityvastly exceeds c!
Ti
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final observation time (ns)
0 2 4 6 8 10
BE
R
10-4
10-3
10-2
10-1
100
advanced
vacuum
B
Origin of slow down?
Slower detection time could be due to:• change in information velocity vi
• change in detection latency t
T L L t tii adv i vac
adv vac FHG
IKJ
, ,
b gestimate latencyusing theory