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Quantum Optics Journal of the European Optical Society Part B

Atomic coherence effects which produce superluminal (but causal) propagation of wavepackets

R. Y. Chiao

Published Aug 1, 1994• 18 citations
Publisher

Abstract

Analytic, limited-bandwidth signals, e.g. Gaussian wavepackets, whose frequencies lie in a transparent spectral window far below the resonance of an amplifying atomic medium, can propagate with phase, group, energy and 'signal' velocities (as defined by Sommerfeld and Brillouin) all exceeding the vacuum speed of light c. This 'superluminal' propagation may occur without significant distortion or gain. The front velocity, however, is not superluminal, and therefore Einstein causality is not violated. Applications will be discussed, including the possibility of using superluminal atomic coherence in condensed matter (e.g. macroscopic mass currents in superfluid helium which arise from vortex motions) for efficient gravitational antennae.

DOI
10.1088/0954-8998/6/4/013

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Chinese Physics Letters•May 1, 2004•3 citations
Analytic, limited-bandwidth signals, e.g. Gaussian wavepackets, whose frequencies lie in a transparent spectral window far below the resonance of an amplifying atomic medium, can propagate with phase, group, energy and 'signal' velocities (as defined by Sommerfeld and Brillouin) all exceeding the vacuum speed of light c. This 'superluminal' propagation may occur without significant distortion or gain. The front velocity, however, is not superluminal, and therefore Einstein causality is not violated. Applications will be discussed, including the possibility of using superluminal atomic coherence in condensed matter (e.g. macroscopic mass currents in superfluid helium which arise from vortex motions) for efficient gravitational antennae.
In the region between two lines of a doublet of an inverted medium, there exists a point of zero group-velocity dispersion, where highly superluminal effects may be observable without significant gain, loss, distortion, or broadening. The results of this group-velocity analysis hold for sufficiently narrow-band, analytic pulses, and do not constitute a violation of causality, although the group, ``signal,'' and energy velocities as defined by Sommerfeld and Brillouin may all exceed c or even become negative. No sharp disturbance in the pulse (a real signal) could propagate faster than light, but the scheme offers an unusual noiseless amplification scheme for the leading edge of a pulse, both at the classical and at the single-photon level.
Summary form only given. It is well known that the group velocity v/sub g/ of a light pulse can exceed c in an anomalously dispersive medium. As discussed many years ago by Sommerfeld and Brillouin, a group velocity greater than c does not violate causality because it is not the velocity of information transmission. They noted that the "frontal velocity," the velocity at which an infinitely sharp step-function-like disturbance of the light intensity propagates, can serve as a velocity of information transfer. We suggest here an operational definition of the signal velocity and apply it to the recently observed superluminal propagation of a light pulse in a gain medium.
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 a dispersive medium, different monochromatic modes of light have different phase velocities. Under special circumstances, a superposition of these modes results in an interesting effect wherein the group velocity (the velocity at which the peak of the wavepacket propagates) could be greater than c or even negative although the phase velocities of the modes are all less than c . Can this superluminal group velocity be used for information transfer? We show here that the `superluminal' effect is due to a coherent optical wave superposition effect. Whatever the velocity of the `peak', the whole pulse cannot travel with a speed greater than the fastest phase velocity of its component modes. Thus the maximum speed for information transfer, which involves the sending of a finite pulse, cannot be greater than the maximum phase velocity in the medium.