1
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
Nature 425, 665 (2003)
OSA Nonlinear Optics Meeting, August 6, 2004
Funding from the U.S. National Science Foundation
2
Superluminal Light Pulses
Definition:
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
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.
3
Linear Pulse Propagation: Group Velocity
Lowest-order statement
of propagation without
distortion
dφ
=0
dω
different
υp
group velocity
c
=
υg =
dn ng
n +ω
dω
c
metamaterials, highly dispersive materials
4
Variation in vg with dispersion
Vg
ÅÅÅÅÅÅÅÅÅ
c
4
3
2
slow light
1
-4
-3
-2
-1
-1
-2
-3
fast light
-4
Garrett and McCumber, PRA 1, 305 (1970)
1
2
dn
w ÅÅÅÅÅÅÅÅÅ
dw
3
5
Schematic of Pulse Propagation at
Various Group Velocities
vg<c
vg=c
vg>c
vg negative
There is no causal connection between pulse peaks!
6
Superluminous Pulses
Propagate pulses through a saturable amplifier
unsaturated
pulse
intense pulse
amplifier
Basov and Letokhov, Sov. Phys. Dokl. 11, 222 (1966)
New Insight: Can also be understood in terms of
coherent population oscillations
See next talk: FA5, Robert W. Boyd
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Fast Pulses: Linear Optics Regime
Use 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
8
Fast-light via a gain doublet
c
c
υg =
=
dn ng
n +ω
dω
Steingberg and Chiao, PRA 49, 2071 (1994)
(Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
9
Achieve a gain doublet using stimulated Raman
scattering with a bichromatic pump field
rubidium
energy
levels
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
10
Experimental observation of fast light
ng ~ -310
… but the fractional pulse advancement is small
11
Optimize relative pulse advancement
relative pulse advancement A = tadv/tp
A = tadv/tp ~ 0.1 goL
~ 0.03 gcL
Wang et al.: goL ~ 1.3 A ~ 0.13 observe ~ 0.02
2x narrower bandwidth than we assume
12
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
ωd+
ωdAOM
ωo
L/2
L/2
K
vapor
K
vapor
waveform
generator
ωd-
ωd+
13
12
10
power (µW)
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
tadv=27.4 ns
8
advanced
6
vacuum
4
2
0
-300
-200
-100
0
100
200
time (ns)
Stenner, Gauthier, and Neifeld, Nature 425, 665 (2003)
300
power (µW)
Observation of "Fast" Light with Large
Relative Advancement
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Where is the information?
How fast does it travel?
15
Points of non-analyticity
P
point of non-analyticity
t
knowledge of the leading part of the pulse cannot be used
to infer knowledge after the point of non-analyticity
new information is available because of the "surprise"
Chiao and Steinberg find point of non-analyticity
travels at c. Therefore, they associate it with the
information velocity.
16
Detecting points of non-analyticity
Chiao and Steinberg proposal not satisfactory from an
information-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!
17
Information Velocity: Transmit Symbols
optical pulse amplitude (a.u.)
information velocity: measure time at which symbols can first be distinguished
1.5
"1"
1.0
0.5
"0"
0.0
-300
-200
-100
0
time (ns)
100
200
300
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A
1.5
"1"
Y Data
optical pulse amplitude (a.u.)
1.0
0.5
advanced
advanced
"0"
vacuum
0.0
-300
-200
-100
0
100
200
time (ns)
1.2
Send the symbols
through our fast-light
medium
B
1.8
advanced
1.6
1.0
1.4
0.8
1.2
0.6
1.0
0.4
0.2
-60
300
0.8
vacuum
0.6
-40
-20
time (ns)
0
19
Estimate information velocity in fast light medium
from the model
b∆t
adv
g
− ∆t vac ≈ 12
. ± 0.5 ns
combining experiment and model
υ i ,adv = (0.4 ± 0.5)c
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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)
vacuum
vacuum
z
(Poynting vector always along +z direction)
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2.5 a
"1"
advanced
2.0
Y Data
optical pulse amplitude (a.u.)
1.5
Send "sharp" symbols
through our fast-light
medium
advanced
1.0
0.5
vacuum
0.0
-300 -200 -100
1.3
1.2
"0"
0
100
200
300
time (ns)
1.3
b
1.2
1.1
1.1
1.0
1.0
0.9
0.9
0.8
advanced
vacuum
0.8
0.7
0.7
-12 -10
-8
-6
-4
time (ns)
-2
0
2
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2.5
a
delayed
Y Data
optical pulse amplitude (a.u.)
1.5
vacuum
1.0
"0"
0.5
delayed
0.0
-300 -200 -100
1.2
Send "sharp" symbols
through our slow-light
medium
"1"
2.0
0
100
200
300
time (ns)
1.2
b
1.1
1.1
vacuum
1.0
1.0
0.9
0.9
0.8
0.7
-14
delayed
0.8
0.7
-12
-10
-8
-6
time (ns)
-4
-2
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Matched-filter to determine the bit-error-rate (BER)
100
advanced
BER
10-1
Detection for information
traveling through fast
light medium is later even
though group velocity
vastly exceeds c!
Ti
10-2
vacuum
10-3
10-4
A
-40
-30
-20
-10
0
final observation time (ns)
Determine detection times using a threshold BER
Use large threshold BER to minimize ∆t
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Origin of slow down?
Slower detection time could be due to:
• change in information velocity vi
• change in detection latency ∆t
F
L
T =G
Hυ
−
i
i ,adv
L
υ i ,vac
I + b ∆t
JK
adv
− ∆t vac
100
advanced
10-1
BER
estimate latency
using theory
g
10-2
vacuum
10-3
B
10-4
0
2
4
6
final observation time (ns)
8
10