Causal "superluminal" effects have recently been observed and discussed in
various contexts. The question arises whether such effects could be observed
with extremely weak pulses, and what would prevent the observation of an
"optical tachyon." Aharonov, Reznik, and Stern (ARS) [Phys. Rev. Lett., vol.
81, 2190 (1998)] have argued that quantum noise will preclude the observation
of a superluminal group velocity when the pulse consists of one or a few
photons. In this paper we reconsider this question both in a general framework
and in the specific example, suggested by Chiao, Kozhekin, and Kurizki [Phys.
Rev. Lett., vol. 77, 1254 (1996)], of off-resonant, short-pulse propagation in
an optical amplifier. We derive in the case of the amplifier a signal-to-noise
ratio that is consistent with the general ARS conclusions when we impose their
criteria for distinguishing between superluminal propagation and propagation at
the speed c. However, results consistent with the semiclassical arguments of
CKK are obtained if weaker criteria are imposed, in which case the signal can
exceed the noise without being "exponentially large." We show that the quantum
fluctuations of the field considered by ARS are closely related to
superfluorescence noise. More generally we consider the implications of
unitarity for superluminal propagation and quantum noise and study, in addition
to the complete and truncated wavepackets considered by ARS, the residual
wavepacket formed by their difference. This leads to the conclusion that the
noise is mostly luminal and delayed with respect to the superluminal signal. In
the limit of a very weak incident signal pulse, the superluminal signal will be
dominated by the noise part, and the signal-to-noise ratio will therefore be
very small.Comment: 30 pages, 1 figure, eps
