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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

g

g

c

ndnd

cn

different p

metamaterials, highly dispersive materials

4

Variation in vg with dispersion

4 3 2 1 1 2 3dnd

4

3

2

1

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 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

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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))

g

g

c

ndnd

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-analyticity

Chiao 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

1.3time (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

1.2time (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

TL L

t tii adv i vac

adv vac FHG

IKJ

, ,

b g

estimate latencyusing theory