Quantum Noise and Superluminal Propagation

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

Vacuum field energy and spontaneous emission in anomalously dispersive cavities

Anomalously dispersive cavities, particularly white light cavities, may have larger bandwidth to finesse ratios than their normally dispersive counterparts. Partly for this reason, their use has been proposed for use in LIGO-like gravity wave detectors and in ring-laser gyroscopes. In this paper we analyze the quantum noise associated with anomalously dispersive cavity modes. The vacuum field energy associated with a particular cavity mode is proportional to the cavity-averaged group velocity of that mode. For anomalously dispersive cavities with group index values between 1 and 0, this means that the total vacuum field energy associated with a particular cavity mode must exceed $\hbar \omega/2$. For white light cavities in particular, the group index approaches zero and the vacuum field energy of a particular spatial mode may be significantly enhanced. We predict enhanced spontaneous emission rates into anomalously dispersive cavity modes and broadened laser linewidths when the linewidth of intracavity emitters is broader than the cavity linewidth.Comment: 9 pages, 4 figure

Simultaneous arrival of information in absorbing wave guides

We demonstrate that the temporal peak generated by specific electromagnetic pulses may arrive at different positions simultaneously in an absorbing wave guide. The effect can be used for triggering several devices all at once at unknown distances from the sender or generally to transmit information so that it arrives at the same time to receivers at different, unknown locations. This simultaneity cannot be realized by the standard transmission methods

Microwave measurements of the photonic bandgap in a two-dimensional photonic crystal slab

We have measured the photonic bandgap in the transmission of microwaves through a two-dimensional photonic crystal slab. The structure was constructed by cementing acrylic rods in a hexagonal closed-packed array to form rectangular stacks. We find a bandgap centered at approximately 11 GHz, whose depth, width and center frequency vary with the number of layers in the slab, angle of incidence and microwave polarization.Comment: 8 pages, 3 figures, submitted to Journal of Applied Physic

Temporal variability of the telluric sodium layer

The temporal variability of the telluric sodium layer is investigated by analyzing 28 nights of data obtained with the Colorado State University LIDAR experiment. The mean height power spectrum of the sodium layer was found to be well fit by a power law over the observed range of frequencies, 10 microhertz to 4 millhertz. The best fitting power law was found to be 10^\beta \nu^\alpha, with \alpha = -1.79 +/- 0.02 and \beta = 1.12 +/- 0.40. Applications to wavefront sensing require knowledge of the behavior of the sodium layer at kHz frequencies. Direct measurements at these frequencies do not exist. Extrapolation from low-frequency behavior to high frequencies suggests that this variability may be a significant source of error for laser-guide-star adaptive optics on large-aperture telescopes.Comment: 3 pages, 3 figures, accepted for publication in Optics Letter

Relativistic Tunneling Through Two Successive Barriers

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in the context of nonrelativistic tunneling as well as in its electromagnetic counterparts, and which is often associated with the possibility of superluminal velocities in the tunneling process. We discuss the behavior of both the phase (or group) tunneling time and the dwell time, and show that in the limit of opaque barriers the relativistic theory also allows the emergence of the Generalized Hartman Effect. We compare our results with the nonrelativistic ones and discuss their interpretation.Comment: 7 pages, 3 figures. Revised version, with a new appendix added. Slightly changes in the styles and captions of Figures 1 and 2. To appear in Physical Review