Measuring the information velocity in fast- and slow-light media

1
Measuring the information velocity infast- and
slow-light media

• 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 Optical Sciences Center

Nature 425, 665 (2003)
Institute of Optics, December 10, 2003 Funding
from the U.S. National Science Foundation
2
Outline

• Information and optical pulses
• Review of pulse propagation in dispersive media
• How fast does information travel?
• Fast light experiments
• Consequences for the special theory of
  relativity
• The information velocity
• Measuring the effects of a fast-light medium on
  the information velocity
• Measuring the effects of a slow-light medium on
  the information velocity

3
Information on Optical Pulses
4
Modern Optical Telecommunication
SystemsTransmitting information encoded on
optical fields
http//www.picosecond.com/objects/AN-12.pdf
RZ data
clock
Where is the information on the waveform?
How fast does
it travel?
5
Pulse propagation in dispersive media
"slow-light" medium
6
"Fast-Light" medium
consequences for the special theory of relativity?
7
PULSE PROPAGATION REVIEW"Slow" and "Fast" Light
R.W. Boyd and D.J. Gauthier "Slow and "Fast"
Light, in Progress in Optics, Vol. 43, E. Wolf,
Ed. (Elseiver, Amsterdam, 2002), Ch. 6, pp.
497-530.
8
Propagating Electromagnetic Waves Phase Velocity
monochromatic plane wave
phase velocity
phase
Points of constant phase move a distance Dz in a
time Dt
9
Propagating Electromagnetic Waves Group Velocity
Lowest-order statement of propagation
without distortion
10
Propagation "without distortion"
"slow" light
"fast" light
Recent experiments on fast and slow light
conducted in the regime of low distortion
11
Pulse Propagation Slow Light(Group velocity
approximation)
12
Pulse Propagation Fast Light (Group velocity
approximation)
13
Where is the information? How fast does it
travel?
14
Information Transmission An Engineering
Perspective
Starting from the work of Shannon, we know a
lot about optimizing data rates in noisy
channels No one from the engineering community
has posed the following fundamental question
What is the speed of information?
That is, how quickly can information be
transmitted between two different locations?
15
Information Transmission A physics perspective
Interest in the speed of information soon after
Einstein's publication of the special theory of
relativity in 1905 Known that optical pulses
could have a group velocity exceeding the speed
of light in vacuum (c) when propagating through
dispersive materials Conference sessions devoted
to the topic Relativity revised no information
can travel faster than c Faster-than-c
information transmission gives rise to crazy
paradoxes (e.g., an effect before its cause)
Garrison et al., Phys. Lett. A 245, 19 - 25
(1998).
16
Early Theoretical Studies of Optical "Signals"
A. Sommerfeld, Physik. Z. 8, 841 (1907) A.
Sommerfeld, Ann. Physik. 44, 177 (1914) L.
Brillouin, Ann. Physik. 44, 203 (1914) L.
Brillouin, Wave Propagation and Group Velocity,
(Academic, New York, 1960).
Sommerfeld A "signal" is an electromagnetic
wave that is zero initially. Luminal information
transmission implies that no electromagnetic
disturbance can arrive faster than the "front" of
the wave.
front
17
Primary Finding of Sommerfeld
(assumes a Lorentz-model dielectric with a single
resonance)
The front travels at c
regardless of the details of the
dielectric Physical interpretation it takes a
finite time for the polarization of the medium to
build up the first part of the field passes
straight through! This is an all-orders
calculation. The Taylor series expansion fails
to give this result!!!
18
The Sommerfeld and Brillouin Precursors
results of an asymptotic analysis (saddle-point
method)
19
Fast-Light Experiments
Fast light theory, Gaussian pulses C. G. B.
Garrett, D. E. McCumber, Phys. Rev. A 1, 305
(1970). Fast light experiments, resonant
absorbers S. Chu, S. Wong, Phys. Rev. Lett.
48, 738 (1982). B. Ségard and B. Macke, Phys.
Lett. 109, 213 (1985). A. M. Akulshin, A.
Cimmino, G. I. Opat, Quantum Electron. 32, 567
(2002). M. S. Bigelow, N. N. Lepeshkin, R. W.
Boyd, Science 301, 200 (2003)
20
Fast-light via a gain doublet
Steingberg and Chiao, PRA 49, 2071 (1994) (Wang,
Kuzmich, and Dogariu, Nature 406, 277 (2000))
21
Achieve a gain doublet using stimulated Raman
scattering with a bichromatic pump field
Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000)
22
Fast light in a laser driven potassium vapor
large anomalous dispersion
23
Some of our toys
24
Observation of large pulse advancement
tp 263 ns A 10.4
vg -0.051c ng -19.6 some pulse
compression (1.9 higher-order dispersion) H.
Cao, A. Dogariu, L. J. Wang, IEEE J. Sel. Top.
Quantum Electron. 9, 52 (2003). B. Macke, B.
Ségard, Eur. Phys. J. D 23, 125 (2003).
large fractional advancement - can distinguish
different velocities!
25
The Information Velocity
No working definition of the information
velocity The information theory community has
not considered this problem An interesting
proposal can be found in R. Y. Chiao, A.M.
Steinberg, in Progress in Optics XXXVII, Wolf,
E., Ed. (Elsevier Science, Amsterdam, 1997), p.
345.
26
Points of non-analyticity
point of non-analyticity
P
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"
27
Speed of points of non-analyticity
Spectrum falls off like a power law!
Taylor series
no longer converges even when pulse
"bandwidth" (full width at half-maximum) is
small! Subtle effect!
Chiao and Steinberg find point of
non-analyticity travels at c. Therefore, they
associate it with the information velocity.
28
Detecting points of non-analyticity
Chiao and Steinberg proposal not satisfactory
from an information-theory point of view A
point has no energy!
receiver
transmitter
Point of non-analyticity travels at vi c (Chiao
Steinberg) Detection occurs later by an
amount Dt due to noise (classical or quantum).
We call this the detection latency.
Detected information travels at less than vi,
even in vacuum!
29
Measuring the Effects of a Fast-Light Medium on
the Information Velocity
30
Information Velocity Transmit Symbols
information velocity measure time at which
symbols can first be distinguished
requested symbols
optically generated symbols
31
Send the symbols through our fast-light medium
32
Use a matched-filter to determine the
bit-error-rate (BER)
Detection for information traveling through
fast light medium is later even though group
velocity vastly exceeds c!
Ti
Determine detection times a threshold Use large
BER to minimize Dt
33
Origin of slow down?

• Slower detection time could be due to
• change in information velocity vi
• change in detection latency Dt

estimate latency using theory
34
Estimate information velocity in fast light
medium
from the model
combining experiment and model
35
Measuring the Effects of a Slow-Light Medium on
the Information Velocity
36
Slow Light via a single amplifying resonance
37
Slow Light Pulse Propagation
38
Send the symbols through our slow-light medium
vi 60 vg !!
39
Summary

• Investigate fast-light (slow-light) pulse
  propagation with large pulse advancement (delay)
• Transmit symbols to measure information velocity
• Estimate vi c
• Consistent with special theory of relativity
• Special theory of relativity may only be
• an approximation?

http//www.phy.duke.edu/research/photon/qelectron/
proj/infv/
40
What part of the waveform do you
measure? Assumes detection latency is zero.