1. Measuring the information velocity in fast- 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. Where is the information on the waveform? How fast does it travel?
Modern Optical Telecommunication Systems: Transmitting information encoded on optical fields
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

8. Propagating Electromagnetic Waves: Phase Velocity
monochromatic plane wave E z
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
group velocity

10. Propagation "without distortion"
pulse bandwidth not too large
"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, (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)
vg has no meaning when vg >c
precursors very small
Sommerfeld:
signal velocity vs depends on detector sensitivity
Brillouin: vs c when vg >c
vs= vg when vg >c

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 = c 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!
transmitter
receiver
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?

40. What part of the
waveform do you
measure?
Assumes detection
latency is zero.