Quantum limitations on superluminal propagation

Unstable systems such as media with inverted atomic population have been shown to allow the propagation of analytic wavepackets with group velocity faster than that of light, without violating causality. We illuminate the important role played by unstable modes in this propagation, and show that the quantum fluctuations of these modes, and their unitary time evolution, impose severe restrictions on the observation of superluminal phenomena.Comment: RevTeX 4 page

Physical mechanism of superluminal traversal time: interference between multiple finite wave packets

The mechanism of superluminal traversal time through a potential well or potential barrier is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier. In the case of potential-well traveling that is classically allowed, each of the successively transmitted constituents is delayed by a subluminal time. When the thickness of the well is much smaller in comparision with a characteristic length of the incident wave packet, the reshaped wave packet in transmission maintains the profile of the incident wave packet. In the case of potential-barrier tunneling that is classically forbidden, though each of the successively transmitted constituents is delayed by a time that is independent of the barrier thickness, the interference between multiple transmitted constituents explains the barrier-thickness dependence of the traversal time for thin barriers and its barrier-thickness independence for thick barriers. This manifests the nature of Hartman effect.Comment: 9 pages, 3 figures, Some comments and suggestions are appreciate

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

Effective photon-photon interaction in a two-dimensional "photon fluid"

We formulate an effective theory for the atom-mediated photon-photon interactions in a two-dimensional ``photon fluid'' confined in a Fabry-Perot resonator. With the atoms modelled by a collection of anharmonic Lorentz oscillators, the effective interaction is evaluated to second order in the coupling constant (the anharmonicity parameter). The interaction has the form of a renormalized two-dimensional delta-function potential, with the renormalization scale determined by the physical parameters of the system, such as density of atoms and the detuning of the photons relative to the resonance frequency of the atoms. For realistic values of the parameters, the perturbation series has to be resummed, and the effective interaction becomes independent of the ``bare'' strength of the anharmonic term. The resulting expression for the non-linear Kerr susceptibility, is parametrically equal to the one found earlier for a dilute gas of two-level atoms. Using our result for the effective interaction parameter, we derive conditions for the formation of a photon fluid, both for Rydberg atoms in a microwave cavity and for alkali atoms in an optical cavity.Comment: 25 pages (revtex4), including 2 figure

Weak-wave advancement in nearly collinear four-wave mixing

We identify a new four-wave mixing process in which two nearly collinear pump beams produce phase-dependent gain into a weak bisector signal beam in a self-defocusing Kerr medium. Phase matching is achieved by weak-wave advancement caused by cross-phase modulation between the pump and signal beams. We relate this process to the inverse of spatial modulational instability and suggest a time-domain analog.Comment: 7 pages, 3 figure

Optical frequency waveguide Patent

Self-generating optical frequency waveguid

Photonic crystal polarizers and polarizing beam splitters

We have experimentally demonstrated polarizers and polarizing beam splitters based on microwave-scale two-dimensional photonic crystals. Using polarized microwaves within certain frequency bands, we have observed a squared-sinusoid (Malus) transmission law when using the photonic crystal as a polarizer. The photonic crystal also functions as a polarizing beamsplitter; in this configuration it can be engineered to split incident polarizations in either order, making it more versatile than conventional, Brewster-angle beamsplitters.Comment: 7 pages, 3 figures, published Journal Applied Physics 93, 9429 (2003

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