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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
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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 Nature 425, 665 (2003) OSA Nonlinear Optics Meeting, August 6, 2004 Funding from the U.S. National Science Foundation
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.
different metamaterials, highly dispersive materials Linear Pulse Propagation: Group Velocity Lowest-order statement of propagation without distortion group velocity
Variation in vg with dispersion slow light fast light Garrett and McCumber, PRA 1, 305 (1970)
Schematic of Pulse Propagation at Various Group Velocities vg<c vg=c vg negative vg>c There is no causal connection between pulse peaks!
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
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
Fast-light via a gain doublet Steingberg and Chiao, PRA 49, 2071 (1994) (Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
Achieve a gain doublet using stimulated Raman scattering with a bichromatic pump field rubidium energy levels Wang, Kuzmich, and Dogariu, Nature 406, 277 (2000))
Experimental observation of fast light ng ~ -310 … but the fractional pulse advancement is small
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
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
Observation of "Fast" Light with LargeRelative Advancement Stenner, Gauthier, and Neifeld, Nature 425, 665 (2003)
Where is the information? How fast does it travel?
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" Chiao and Steinberg find point of non-analyticity travels at c. Therefore, they associate it with the information velocity.
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!
Information Velocity: Transmit Symbols information velocity: measure time at which symbols can first be distinguished
Send the symbols through our fast-light medium
Estimate information velocity in fast light medium from the model combining experiment and model
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/
Pulse Propagation: negative vg (Group velocity approximation) vacuum vacuum z (Poynting vector always along +z direction)
Send "sharp" symbols through our fast-light medium
Send "sharp" symbols through our slow-light medium
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 using a threshold BER Use large threshold BER to minimize Dt
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