Signal velocity and quantum fluctuation in superluminal light pulse propagation
Pulse propagation with a superluminal group velocity is a rather counterintuitive phenomenon that at first might appear to violate the special theory of relativity’s pillar statement that no signal can be transmitted faster than c. However, it has been argued by Sommerfeld and Brillouin  and discussed later in a series of works by Chiao et al. ( and references therein) that the faster-than-c propagation is perfectly in accord with special relativity. The reason, they noted, is that the signal velocity should be properly defined as the velocity of a step-function-like signal, not that of a smooth pulse. While this argument is certainly a correct one, it is based on the classical wave theory. On the other hand, the phenomenon of gain-assisted superluminal pulse propagation  can be studied in the situations when a pulse consists of only a few photons, or when the number of photons is large, but the sensitivity of the light detection system is at or better than the shot photon noise level. In both situations, quantum mechanical treatment of both the light and the medium is necessary to provide a meaningful description of the system’s dynamics. Here we report the results of such a study .
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