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Physical Review A

Velocity of detectable information in faster-than-light pulses

Ahmed H. Dorrah, Mo Mojahedi

Published Sep 16, 2014• 7 citations
Publisher

Abstract

The velocity of detectable information (signal velocity) in a medium capable of supporting abnormal (superluminal or negative) group velocities is calculated. This is carried out by tracking the time instant at which the signal-to-noise ratio (SNR) at the detector output reaches a predetermined threshold while considering the total classical and quantum noise of the channel in addition to the detector noise. Furthermore, the method of steepest descent is incorporated to systematically study various forms of pulse reshaping associated with superluminal propagation and its effect on SNR. By studying the behavior of SNR as a function of both space and time, the present analysis predicts the existence of a cutoff distance beyond which signal velocity of a superluminal pulse is delayed as compared to a companion pulse traveling the same distance in vacuum. Finally, the interplay between the relative strength of the medium-generated noise and the detector noise and its effect on signal velocity is discussed.

DOI
10.1103/physreva.90.033822

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The velocity of detectable information (signal velocity) in a medium capable of supporting abnormal (superluminal or negative) group velocities is calculated. This is carried out by tracking the time instant at which the signal-to-noise ratio (SNR) at the detector output reaches a predetermined threshold while considering the total classical and quantum noise of the channel in addition to the detector noise. Furthermore, the method of steepest descent is incorporated to systematically study various forms of pulse reshaping associated with superluminal propagation and its effect on SNR. By studying the behavior of SNR as a function of both space and time, the present analysis predicts the existence of a cutoff distance beyond which signal velocity of a superluminal pulse is delayed as compared to a companion pulse traveling the same distance in vacuum. Finally, the interplay between the relative strength of the medium-generated noise and the detector noise and its effect on signal velocity is discussed.
Energy exchange between an electromagnetic pulse and dispersive media may result in complicated, yet interesting, phenomena in which the group velocity becomes abnormal (i.e., superluminal or negative). For such cases, signal velocity (velocity of detectable information) remains debatable. In this chapter, we present a systematic study that can be applied to pulse propagation in any dispersive medium in order to quantify the detectable information content and calculate its speed, while accounting for pulse reshaping effects and noise generated in the medium and the detector. Accordingly, we present an operational context within which the constraints of superluminal signaling and its potential applications are shown. We provide scenarios in which the signal velocity is evaluated in microwave circuits with negative group delays and extend the method to include optical pulses in inverted media as well. Such analysis explores the fundamental limitations and capabilities of a broad range of superluminal signaling applications.
Spectral reshaping and nonuniform phase delay associated with an electromagnetic pulse propagating in a temporally dispersive medium may lead to interesting observations in which the group velocity becomes superluminal or even negative. In such cases, the finite bandwidth of the superluminal region implies the inevitable existence of a cutoff distance beyond which a superluminal pulse becomes subluminal. In this paper, we derive a closed-form analytic expression to estimate this cutoff distance in abnormal dispersive media with gain. Moreover, the method of steepest descent is used to track the time-frequency dynamics associated with the evolution of the center of mass of a superluminal pulse to the subluminal regime. This evolution takes place at longer propagation depths as a result of the subluminal components affecting the behavior of the pulse. Finally, the analysis presents the fundamental limitations of superluminal propagation in light of factors such as the medium depth, pulse width, and the medium dispersion strength.
Abstract This paper considers the question of superluminal (or negative) group velocities of signals in dispersive media, as well as negative group delay times of signals passing through linear filters. It is shown that information can be transmitted only with the help of jumps in the time dependence of a function or its derivatives and, therefore, the information propagation velocity in any (including dispersive, absorbing, or amplifying) medium exactly coincides with the speed of light in vacuum. As for the group velocity of a wave packet, it is only the propagation velocity of its infinitely differentiable envelope, by means of which the transmission of information, strictly speaking, is impossible. Therefore, in regions with anomalous dispersion, the group velocity can be superluminal or negative without violating the “light limitation” of the theory of relativity or the principle of causality. Examples of situations in which superluminal or negative group velocity occurs are given.
In this Rapid Communication, we experimentally demonstrate that the signal velocity, defined as the earliest time when a signal is detected above the realistic noise floor, may be altered by a region of anomalous dispersion. We encode information in the spatial degree of freedom of an optical pulse so that the imprinted information is not limited by the frequency bandwidth of the region of anomalous dispersion. We then show that the combination of superluminal pulse propagation and realistic detectors with nonideal quantum efficiency leads to a speed-up of the earliest experimentally obtainable arrival time of the transmitted signal even with the overall pulse experiencing unity gain. This speed-up is reliant upon nonideal detectors and losses, as perfect detection efficiency would result in the speed of information being equal to the speed of light in vacuum, regardless of the group velocity of the optical pulses.