Decoherence of Quantum-Enhanced Timing Accuracy

Quantum enhancement of optical pulse timing accuracy is investigated in the Heisenberg picture. Effects of optical loss, group-velocity dispersion, and Kerr nonlinearity on the position and momentum of an optical pulse are studied via Heisenberg equations of motion. Using the developed formalism, the impact of decoherence by optical loss on the use of adiabatic soliton control for beating the timing standard quantum limit [Tsang, Phys. Rev. Lett. 97, 023902 (2006)] is analyzed theoretically and numerically. The analysis shows that an appreciable enhancement can be achieved using current technology, despite an increase in timing jitter mainly due to the Gordon-Haus effect. The decoherence effect of optical loss on the transmission of quantum-enhanced timing information is also studied, in order to identify situations in which the enhancement is able to survive.Comment: 12 pages, 4 figures, submitte

Determination of the Aspect-ratio Distribution of Gold Nanorods in a Colloidal Solution using UV-visible absorption spectroscopy

Knowledge of the distribution of the aspect ratios (ARs) in a chemically-synthesized colloidal solution of Gold Nano Rods (GNRs) is an important measure in determining the quality of synthesis, and consequently the performance of the GNRs generated for various applications. In this work, an algorithm has been developed based on the Bellman Principle of Optimality to readily determine the AR distribution of synthesized GNRs in colloidal solutions. This is achieved by theoretically fitting the longitudinal plasmon resonance of GNRs obtained by UV-visible spectroscopy. The AR distribution obtained from the use of the algorithm developed have shown good agreement with those theoretically generated one as well as with the previously reported results. After bench-marking, the algorithm has been applied to determine the mean and standard deviation of the AR distribution of two GNRs solutions synthesized and examined in this work. The comparison with experimentally derived results from the use of expensive Transmission Electron Microscopic images and Dynamic Light Scattering technique shows that the algorithm developed offers a fast and thus potentially cost-effective solution to determine the quality of the synthesized GNRs specifically needed for many potential applications for the advanced sensor systems

Darboux transformation for two component derivative nonlinear Schr\"odinger equation

In this paper, we consider the two component derivative nonlinear Schr\"{o}dinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a compact representation for the $N-$soliton solutions.Comment: 12 pages, 2 figure

Emission of correlated photon pairs from superluminal perturbations in dispersive media

We develop a perturbative theory that describes a superluminal refractive perturbation propagating in a dispersive medium and the subsequent excitation of the quantum vacuum zero-point fluctuations. We find a process similar to the anomalous Doppler effect: photons are emitted in correlated pairs and mainly within a Cerenkov-like cone, one on the forward and the other in backward directions. The number of photon pairs emitted from the perturbation increases strongly with the degree of superluminality and under realizable experimental conditions, it can reach up to ~0.01 photons per pulse. Moreover, it is in principle possible to engineer the host medium so as to modify the effective group refractive index. In the presence of "fast light" media, e.g. a with group index smaller than unity, a further ~10x enhancement may be achieved and the photon emission spectrum is characterized by two sharp peaks that, in future experiments would clearly identify the correlated emission of photon pairs.Comment: 9 pages, 7 figure

Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet

Potential scattering problems governed by the time-dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have the Gaussian-type envelope, which differs from the soliton solution. The potential is chosen to be a box or well type. We estimate the dependences of reflectance and transmittance on the width of the potential and compare these results with those given by the stationary Schr\"odinger equation. We attribute the behaviors of these quantities to the limitation on the width of the nonlinear wave packet. The coupling constant and the width of the potential play an important role in the distribution of the waves appearing in the final state of scattering.Comment: 18 pages, 12 figures; added 2 figure

Lattice dynamics of mixed semiconductors (Be,Zn)Se from first-principles calculations

Vibration properties of Zn(1-x)Be(x)Se, a mixed II-VI semiconductor haracterized by a high contrast in elastic properties of its pure constituents, ZnSe and BeSe, are simulated by first-principles calculations of electronic structure, lattice relaxation and frozen phonons. The calculations within the local density approximation has been done with the Siesta method, using norm-conserving pseudopotentials and localized basis functions; the benchmark calculations for pure endsystems were moreover done also by all-electron WIEN2k code. An immediate motivation for the study was to analyze, at the microscopic level, the appearance of anomalous phonon modes early detected in Raman spectra in the intermediate region (20 to 80%) of ZnBe concentration. This was early discussed on the basis of a percolation phenomenon, i.e., the result of the formation of wall-to-wall --Be--Se-- chains throughout the crystal. The presence of such chains was explicitly allowed in our simulation and indeed brought about a softening and splitting off of particular modes, in accordance with experimental observation, due to a relative elongation of Be--Se bonds along the chain as compared to those involving isolated Be atoms. The variation of force constants with interatomic distances shows common trends in relative independence on the short-range order.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Controlling pulse propagation in optical fibers through nonlinearity and dispersion management

In case of the nonlinear Schr\"odinger equation with designed group velocity dispersion, variable nonlinearity and gain/loss; we analytically demonstrate the phenomenon of chirp reversal crucial for pulse reproduction. Two different scenarios are exhibited, where the pulses experience identical dispersion profiles, but show entirely different propagation behavior. Exact expressions for dynamical quasi-solitons and soliton bound-states relevant for fiber communication are also exhibited.Comment: 4 pages, 5 eps figure

Noise resistance of adiabatic quantum computation using random matrix theory

Besides the traditional circuit-based model of quantum computation, several quantum algorithms based on a continuous-time Hamiltonian evolution have recently been introduced, including for instance continuous-time quantum walk algorithms as well as adiabatic quantum algorithms. Unfortunately, very little is known today on the behavior of these Hamiltonian algorithms in the presence of noise. Here, we perform a fully analytical study of the resistance to noise of these algorithms using perturbation theory combined with a theoretical noise model based on random matrices drawn from the Gaussian Orthogonal Ensemble, whose elements vary in time and form a stationary random process.Comment: 9 pages, 3 figure