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arXiv:quant-ph/9805040 · OptSp

Optical Tachyons in Parametric Amplifiers: How Fast Can Quantum Information Travel?

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

Published May 14, 1998• 5 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.quant-ph/9805040

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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.
We theoretically analyze wave packet transmission through a phase-conjugating mirror and show that the transmission of a suitably chosen input pulse is superluminal, i.e. the peak of the pulse emerges from the mirror before the time it takes to travel the same distance in vacuum. This pulse reshaping effect can be attributed directly to the dispersion relation in the nonlinear medium constituting the mirror. Thus, for the first time a connection is laid between optical phase conjugation and superluminal behavior. In view of its additional amplifying ability, a phase-conjugating mirror is a most promising candidate for an experimental observation of tachyonic signatures.
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.