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 OSA Nonlinear Optics Meeting, August 6, 2004 Funding from the U.S. National Science Foundation Nature 425, 665 (2003)

2 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 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

3 Linear Pulse Propagation: Group Velocity Lowest-order statement of propagation without distortion group velocity different metamaterials, highly dispersive materials

4 Variation in v g with dispersion slow light fast light Garrett and McCumber, PRA 1, 305 (1970)

5 Schematic of Pulse Propagation at Various Group Velocities There is no causal connection between pulse peaks! vg<cvg<c vg=cvg=c vg>cvg>c v g negative

6 Superluminous Pulses Propagate pulses through a saturable amplifier amplifier intense pulse unsaturated pulse 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

7 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 ~

8 Fast-light via a gain doublet 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 Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000)) rubidium energy levels

10 Experimental observation of fast light n g ~ -310 … but the fractional pulse advancement is small

11 Optimize relative pulse advancement A = t adv /t p ~ 0.1 g o L ~ 0.03 g c L Wang et al.: g o L ~ 1.3 A ~ 0.13 observe ~ x narrower bandwidth than we assume relative pulse advancement A = t adv /t p

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, (2003 ) Solution: Dispersion Management

13 Observation of "Fast" Light with Large Relative Advancement Stenner, Gauthier, and Neifeld, Nature 425, 665 (2003)

14 Where is the information? How fast does it travel?

15 Points of non-analyticity t P point of non-analyticity 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 v i = 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 v i, even in vacuum!

17 Information Velocity: Transmit Symbols information velocity: measure time at which symbols can first be distinguished

18 Send the symbols through our fast-light medium

19 Estimate information velocity in fast light medium from the model combining experiment and model

20 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 v i ~ c Consistent with special theory of relativity Demonstrates that there is no causal connection between peak of input and output pulses

21 Pulse Propagation: negative v g (Group velocity approximation) (Poynting vector always along +z direction) z vacuum

22 Send "sharp" symbols through our fast-light medium

23 Send "sharp" symbols through our slow-light medium

24 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 information traveling through fast light medium is later even though group velocity vastly exceeds c! TiTi

25 Origin of slow down? Slower detection time could be due to: change in information velocity v i change in detection latency  t estimate latency using theory