Electro-Optic Modulation of Single Photons

We use the Stokes photon of a biphoton pair to set the time origin for electro-optic modulation of the wave function of the anti-Stokes photon thereby allowing arbitrary phase and amplitude modulation. We demonstrate conditional single-photon wave functions composed of several pulses, or instead, having gaussian or exponential shapes

Sub-wavelength imaging at infrared frequencies using an array of metallic nanorods

We demonstrate that an array of metallic nanorods enables sub-wavelength (near-field) imaging at infrared frequencies. Using an homogenization approach, it is theoretically proved that under certain conditions the incoming radiation can be transmitted by the array of nanorods over a significant distance with fairly low attenuation. The propagation mechanism does not involve a resonance of material parameters and thus the resolution is not strongly affected by material losses and has wide bandwidth. The sub-wavelength imaging with $\lambda/10$ resolution by silver rods at 30 THz is demonstrated numerically using full-wave electromagnetic simulator.Comment: 12 pages, 16 figures, submitted to PR

Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

Quantum critical transport, duality, and M-theory

We consider charge transport properties of 2+1 dimensional conformal field theories at non-zero temperature. For theories with only Abelian U(1) charges, we describe the action of particle-vortex duality on the hydrodynamic-to-collisionless crossover function: this leads to powerful functional constraints for self-dual theories. For the n=8 supersymmetric, SU(N) Yang-Mills theory at the conformal fixed point, exact hydrodynamic-to-collisionless crossover functions of the SO(8) R-currents can be obtained in the large N limit by applying the AdS/CFT correspondence to M-theory. In the gravity theory, fluctuating currents are mapped to fluctuating gauge fields in the background of a black hole in 3+1 dimensional anti-de Sitter space. The electromagnetic self-duality of the 3+1 dimensional theory implies that the correlators of the R-currents obey a functional constraint similar to that found from particle-vortex duality in 2+1 dimensional Abelian theories. Thus the 2+1 dimensional, superconformal Yang Mills theory obeys a "holographic self duality" in the large N limit, and perhaps more generally.Comment: 35 pages, 4 figures; (v2) New appendix on CFT2, corrected normalization of gauge field action, added ref

Third order superintegrable systems separating in polar coordinates

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function

Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential

We consider dynamics of Bose-Einstein condensates with long-range attractive interaction proportional to $1/r^b$ and arbitrary angular dependence. It is shown exactly that collapse of Bose-Einstein condensate without contact interactions is possible only for $b\ge 2$. Case $b=2$ is critical and requires number of particles to exceed critical value to allow collapse. Critical collapse in that case is strong one trapping into collapsing region a finite number of particles. Case $b>2$ is supercritical with expected weak collapse which traps rapidly decreasing number of particles during approach to collapse. For $b<2$ singularity at $r=0$ is not strong enough to allow collapse but attractive $1/r^b$ interaction admits stable self-trapping even in absence of external trapping potential

Superintegrable systems with spin and second-order integrals of motion

We investigate a quantum nonrelativistic system describing the interaction of two particles with spin 1/2 and spin 0, respectively. We assume that the Hamiltonian is rotationally invariant and parity conserving and identify all such systems which allow additional integrals of motion that are second order matrix polynomials in the momenta. These integrals are assumed to be scalars, pseudoscalars, vectors or axial vectors. Among the superintegrable systems obtained, we mention a generalization of the Coulomb potential with scalar potential $V_0=\frac{\alpha}{r}+\frac{3\hbar^2}{8r^2}$ and spin orbital one $V_1=\frac{\hbar}{2r^2}$.Comment: 32 page

Gauge-invariant electromagnetic response of a chiral px+ipy superconductor

We present a gauge-invariant theory of the electromagnetic response of a chiral px+ipy superconductor in the clean limit. Due to the spontaneously broken time-reversal symmetry, the effective action of the system contains an anomalous term not present in conventional superconductors. As a result, the electromagnetic charge and current responses contain anomalous terms, which depend explicitly on the chirality of the superconducting order parameter. These terms lead to a number of unusual effects, such as coupling of the transverse currents to the collective plasma oscillations and a possibility of inducing the charge density by the magnetic field perpendicular to the conducting planes. We calculate the antisymmetric part of the conductivity tensor (the intrinsic Hall conductivity) and show that it depends on the wave vector of the electromagnetic field. We also show that the Mermin-Muzikar magnetization current and the Hall conductivity are strongly suppressed at high frequencies. Finally, we discuss implications of the theory to the experiments in Sr2RuO4.Comment: 22 pages, 4 figures, final version as published in PR