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Europhysics Letters (EPL)

Tachyons and information transfer in quantized parametric amplifiers

Gershon Kurizki, Alexander E. Kozhekin, Abraham G. Kofman

Published Jun 1, 1998• 16 citations
Publisher

Abstract

We show that the injection of spectrally narrow probe wave packets into quantized parametrically amplifying media can give rise to transient tachyonic wave packets. Remarkably, their quantum information, albeit causal, is confined to times corresponding to superluminal velocities, which is advantageous for communications. These phenomena are explicitly analyzed for stimulated Raman scattering, parametric down-conversion and four-wave mixing.

DOI
10.1209/epl/i1998-00280-2

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We show that the injection of spectrally narrow probe wave packets into quantized parametrically amplifying media can give rise to transient tachyonic wave packets. Remarkably, their quantum information, albeit causal, is confined to times corresponding to superluminal velocities, which is advantageous for communications. These phenomena are explicitly analyzed for stimulated Raman scattering, parametric down-conversion and four-wave mixing.
We show that optical tachyonic dispersion corresponding to superluminal (faster than-light) group velocities characterizes parametrically amplifying media. The turn-on of parametric amplification in finite media, followed by illumination by spectrally narrow probe wavepackets, can give rise to transient tachyonic wavepackets. In the stable (sub-threshold) operating regime of an optical phase conjugator it is possible to transmit probe pulses with a superluminally advanced peak, whereas conjugate reflection is always subluminal. In the unstable (above-threshold) regime, superluminal response occurs both in reflection and in transmission, at times preceding the onset of exponential growth due to the instability. Remarkably, the quantum information transmitted by probe or conjugate pulses, albeit causal, is confined to times corresponding to superluminal velocities. These phenomena are explicitly analyzed for four-wave mixing, stimulated Raman scattering and parametric downconversion.
Experiments at Berkeley and elsewhere which show that the process of tunneling is apparently superluminal will be reviewed. Conflicting theories for the tunneling time will be compared with experiment. The tunneling particle in the Berkeley experiments was the photon. The measurement of the tunneling time utilized a two-photon light source (spontaneous parametric down-conversion), a Hong-Ou-Mandel interferometer, and a coincidence counter of photon pairs. The tunnel barrier consisted of a photonic-bandgap medium excited at midgap. We find that the peak of a tunneling single-photon wave packet appeared on the far side of the barrier 1.47 ± 0.21 fs earlier than the peak of a wave packet which traveled an equal distance in air. Group velocities which exceed c can also occur in transparent media with inverted atomic populations. Tachyon-like excitations, i.e., collective normal modes of atoms coupled to electromagnetic radiation which possess tachyon-like dispersion relations, occur in these media. However, relativistic causality is not violated by any of these superluminal phenomena.
An analytical treatment of a propagating wave packet incident on a transient barrier reveals a counterintuitive quantum mechanical effect in which, for a particular time interval, the time-varying transmission probability {\it exceeds} (`superarrival') that for the free propagation of the wave packet. It is found that the speed with which the information about the barrier perturbation propagates across the wave packet can exceed the group velocity of the wave packet. An interesting implication of this effect regarding information transfer is analyzed by showing one-to-one correspondence between the strength of the barrier and the magnitude of `superarrival'.