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arXiv:0805.1315 · New Journal of Physics

Apparent superluminal advancement of a single photon far beyond its coherence length

S. Cialdi, Ilario Boscolo, F. Castelli, V. Petrillo

Published Feb 20, 2009• 4 citations
arXivHTMLPDF

Abstract

We present experimental results relative to superluminal propagation based on a single photon traversing an optical system, called 4f-system, which acts singularly on the photon's spectral component phases. A single photon is created by a CW laser light down{conversion process. The introduction of a linear spectral phase function will lead to the shift of the photon peak far beyond the coherence length of the photon itself (an apparent superluminal propagation of the photon). Superluminal group velocity detection is done by interferometric measurement of the temporal shifted photon with its correlated untouched reference. The observed superluminal photon propagation complies with causality. The operation of the optical system allows to enlighten the origin of the apparent superluminal photon velocity. The experiment foresees a superluminal effect with single photon wavepackets.

DOI
10.1088/1367-2630/11/2/023036

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We present experimental results relative to superluminal propagation based on a single photon traversing an optical system, called 4f-system, which acts singularly on the photon's spectral component phases. A single photon is created by a CW laser light down{conversion process. The introduction of a linear spectral phase function will lead to the shift of the photon peak far beyond the coherence length of the photon itself (an apparent superluminal propagation of the photon). Superluminal group velocity detection is done by interferometric measurement of the temporal shifted photon with its correlated untouched reference. The observed superluminal photon propagation complies with causality. The operation of the optical system allows to enlighten the origin of the apparent superluminal photon velocity. The experiment foresees a superluminal effect with single photon wavepackets.
An explanation for superluminal phenomena based on wave-particle duality of photons is suggested. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As a photon propagates as a wave train in vacuum, its velocity is just the speed of light. When it tunnels through a barrier as a particle, its wave function collapses and it will travel faster than light. Superluminal motion can occur only within the coherence length and the time constrained by uncertainty principle. A massive particle cannot be superluminal during the tunneling process. So superluminality does not violate causality. As for the superluminal and negative group velocities in anomalously dispersive medium, they are merely reshaping effect of the pulse, and they will become subluminal at large distances. A couple of experiments are proposed to test the superluminal phenomena.
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.
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.
We study the propagation of single photons through an atomic vapour cell where group velocity exceeds the velocity of light in vacuum. The mechanism behind this phenomenon is a result of interference of Fourier components due to the dispersive properties of the medium. By considering the distinction between group velocity and information velocity and its implications for special relativity, we show that fast single photons do not violate the principle of relativistic causality. To produce fast single photons, we fine-tune the emission of a single GaAs quantum dot to the 87 Rb D2 atomic transition, where a spectrally narrow region of anomalous dispersion enables a group velocity of vg = 1.21c at room temperature. It is shown that our current configuration does not allow the detection of fast single photons by means of a time resolved measurement of the exciton lifetime. Instead, we propose an alternative detection scheme based on single photon interference, where the peak of the fringe visibility is shifted forward in time by t = -0.4167⌧c (where ⌧c denotes the coherence time of the photon).
It says in the report1^11 by Wang et al. that a negative group velocity u=−c/310u=-c/310u=−c/310 is obtained and that a pulse advancement shift 62-ns is measured. The authors claim that the negative group velocity is associated with superluminal light propagation and that the pulse advancement is not at odds with causality or special relativity. However, it is shown here that their conclusions above are not true. Furthermore, I give some suggestion concerning a re-definition of group-velocity and a new explanation in special relativity of causality.
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.