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

Quantum Nonlocality in Two-Photon Experiments at Berkeley

We review some of our experiments performed over the past few years on two-photon interference. These include a test of Bell's inequalities, a study of the complementarity principle, an application of EPR correlations for dispersion-free time-measurements, and an experiment to demonstrate the superluminal nature of the tunneling process. The nonlocal character of the quantum world is brought out clearly by these experiments. As we explain, however, quantum nonlocality is not inconsistent with Einstein causality.Comment: 16 pages including 24 figure

A comparison between matter wave and light wave interferometers for the detection of gravitational waves

We calculate and compare the response of light wave interferometers and matter wave interferometers to gravitational waves. We find that metric matter wave interferometers will not challenge kilometric light wave interferometers such as Virgo or LIGO, but could be a good candidate for the detection of very low frequency gravitational waves

Signal velocity, causality, and quantum noise in superluminal light pulse propagation

We consider pulse propagation in a linear anomalously dispersive medium where the group velocity exceeds the speed of light in vacuum (c) or even becomes negative. A signal velocity is defined operationally based on the optical signal-to-noise ratio, and is computed for cases appropriate to the recent experiment where such a negative group velocity was observed. It is found that quantum fluctuations limit the signal velocity to values less than c.Comment: 4 Journal pages, 3 figure

Efficient Reactive Brownian Dynamics

We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are closer than a chosen reactive distance. In our Doi model, we ensure that the microscopic reaction rules for various association and disassociation reactions are consistent with detailed balance (time reversibility) at thermodynamic equilibrium. The SRBD algorithm uses Strang splitting in time to separate reaction and diffusion, and solves both the diffusion-only and reaction-only subproblems exactly, even at high packing densities. To efficiently process reactions without uncontrolled approximations, SRBD employs an event-driven algorithm that processes reactions in a time-ordered sequence over the duration of the time step. A grid of cells with size larger than all of the reactive distances is used to schedule and process the reactions, but unlike traditional grid-based methods such as Reaction-Diffusion Master Equation (RDME) algorithms, the results of SRBD are statistically independent of the size of the grid used to accelerate the processing of reactions. We use the SRBD algorithm to compute the effective macroscopic reaction rate for both reaction- and diffusion-limited irreversible association in three dimensions. We also study long-time tails in the time correlation functions for reversible association at thermodynamic equilibrium. Finally, we compare different particle and continuum methods on a model exhibiting a Turing-like instability and pattern formation. We find that for models in which particles diffuse off lattice, such as the Doi model, reactions lead to a spurious enhancement of the effective diffusion coefficients.Comment: To appear in J. Chem. Phy

Theory of vortex lattice effects on STM spectra in d-wave superconductors

Theory of scanning tunneling spectroscopy of low energy quasiparticle (QP) states in vortex lattices of d-wave superconductors is developed taking account of the effects caused by an extremely large extension of QP wavefunctions in the nodal directions and the band structure in the QP spectrum. The oscillatory structures in STM spectra, which correspond to van Hove singularities are analysed. Theoretical calculations carried out for finite temperatures and scattering rates are compared with recent experimental data for high temperature cuprates.Comment: 4 pages, 3 eps figures, M2S-HTSC-VI conference paper, using Elsevier style espcrc2.st

Manifestation of classical wave delays in a fully quantized model of the scattering of a single photon

We consider a fully quantized model of spontaneous emission, scattering, and absorption, and study propagation of a single photon from an emitting atom to a detector atom both with and without an intervening scatterer. We find an exact quantum analog to the classical complex analytic signal of an electromagnetic wave scattered by a medium of charged oscillators. This quantum signal exhibits classical phase delays. We define a time of detection which, in the appropriate limits, exactly matches the predictions of a classically defined delay for light propagating through a medium of charged oscillators. The fully quantized model provides a simple, unambiguous, and causal interpretation of delays that seemingly imply speeds greater than c in the region of anomalous dispersion.Comment: 18 pages, 4 figures, revised for clarity, typos corrrecte

Angle Dependence of the Transverse Thermal Conductivity in YBa2_2Cu3_3O7_7 single crystals: Doppler Effect vs. Andreev scattering

We have measured the transverse thermal conductivity $\kappa_{xy}$ of twinned and untwinned YBa$_2$Cu$_3$O$_7$ single crystals as a function of angle $\theta$ between the magnetic field applied parallel to the CuO$_2$ planes and the heat current direction, at different magnetic fields and temperatures. For both crystals we observed a clear twofold variation in the field-angle dependence of $\kappa_{xy}(\theta) = - \kappa^0_{xy}(T,B) \sin(2\theta)$. We have found that the oscillation amplitude $\kappa^0_{xy}$ depends on temperature and magnetic field. Our results show that $\kappa^0_{xy} = a B \ln(1/(bB))$ with the temperature- and sample-dependent parameters $a$ and $b$. We discuss our results in terms of Andreev scattering of quasiparticles by vortices and a recently proposed theory based on the Doppler shift in the quasiparticle spectrum.Comment: 5 pages, 4 figure

Quasiparticle-quasiparticle Scattering in High Tc Superconductors

The quasiparticle lifetime and the related transport relaxation times are the fundamental quantities which must be known in order to obtain a description of the transport properties of the high T_c superconductors. Studies of these quantities have been undertaken previously for the d-wave, high T_c superconductors for the case of temperature-independent elastic impurity scattering. However, much less is known about the temperature-dependent inelastic scattering. Here we give a detailed description of the characteristics of the temperature-dependent quasiparticle-quasiparticle scattering in d-wave superconductors, and find that this process gives a natural explanation of the rapid variation with temperature of the electrical transport relaxation rate.Comment: 4 page

Time-resolved broadband analysis of slow-light propagation and superluminal transmission of electromagnetic waves in three-dimensional photonic crystals

A time-resolved analysis of the amplitude and phase of THz pulses propagating through three-dimensional photonic crystals is presented. Single-cycle pulses of THz radiation allow measurements over a wide frequency range, spanning more than an octave below, at and above the bandgap of strongly dispersive photonic crystals. Transmission data provide evidence for slow group velocities at the photonic band edges and for superluminal transmission at frequencies in the gap. Our experimental results are in good agreement with finite-difference-time-domain simulations.Comment: 7 pages, 11 figure