Recovery of continuous wave squeezing at low frequencies

We propose and demonstrate a system that produces squeezed vacuum using a pair of optical parametric amplifiers. This scheme allows the production of phase sidebands on the squeezed vacuum which facilitate phase locking in downstream applications. We observe strong, stably locked, continuous wave vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative resonator configuration to overcome low frequency squeezing degradation caused by the optical parametric amplifiers.Comment: 9 pages, 4 figure

Strong practical stability based robust stabilization of uncertain discrete linear repetitive processes

Repetitive processes are a distinct class of 2D systems of both theoretical and practical interest whose dynamics evolve over a subset of the positive quadrant in the 2D plane. The stability theory for these processes originally consisted of two distinct concepts termed asymptotic stability and stability along the pass respectively where the former is a necessary condition for the latter. Stability along the pass demands a bounded-input bounded-output property over the complete positive quadrant of the 2D plane and this is a very strong requirement, especially in terms of control law design. A more feasible alternative for some cases is strong practical stability, where previous work has formulated this property and obtained necessary and sufficient conditions for its existence together with Linear Matrix Inequality (LMI) based tests, which then extend to allow control law design. This paper develops considerably simpler, and hence computationally more efficient, stability tests that extend to allow control law design in the presence of uncertainty in process model

Anisotropic Magnification Distortion of the 3D Galaxy Correlation: II. Fourier and Redshift Space

In paper I of this series we discuss how magnification bias distorts the 3D correlation function by enhancing the observed correlation in the line-of-sight (LOS) orientation, especially on large scales. This lensing anisotropy is distinctive, making it possible to separately measure the galaxy-galaxy, galaxy-magnification {\it and} magnification-magnification correlations. Here we extend the discussion to the power spectrum and also to redshift space. In real space, pairs oriented close to the LOS direction are not protected against nonlinearity even if the pair separation is large; this is because nonlinear fluctuations can enter through gravitational lensing at a small transverse separation (or i.e. impact parameter). The situation in Fourier space is different: by focusing on a small wavenumber $k$, as is usually done, linearity is guaranteed because both the LOS and transverse wavenumbers must be small. This is why magnification distortion of the galaxy correlation appears less severe in Fourier space. Nonetheless, the effect is non-negligible, especially for the transverse Fourier modes, and should be taken into account in interpreting precision measurements of the galaxy power spectrum, for instance those that focus on the baryon oscillations. The lensing induced anisotropy of the power spectrum has a shape that is distinct from the more well known redshift space anisotropies due to peculiar motions and the Alcock-Paczynski effect. The lensing anisotropy is highly localized in Fourier space while redshift space distortions are more spread out. This means that one could separate the magnification bias component in real observations, implying that potentially it is possible to perform a gravitational lensing measurement without measuring galaxy shapes.Comment: 14 pages, minor revisions, as accepted for publication in Physical Review

String Organization of Field Theories: Duality and Gauge Invariance

String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invariant while expressions for single diagrams are not.Comment: 20 pages in Latex, including seven figures in postscrip

Gradient Echo Quantum Memory for Light using Two-level Atoms

We propose a quantum memory for light that is analogous to the NMR gradient echo. Our proposal is ideally perfectly efficient and provides simplifications to current 3-level quantum memory schemes based on controlled inhomogeneous broadening. Our scheme does not require auxiliary light fields. Instead the input optical pulse interacts only with two-level atoms that have linearly increasing Stark shifts. By simply reversing the sign of the atomic Stark shifts, the pulse is retrieved in the forward direction. We present analytical, numerical and experimental results of this scheme. We report experimental efficiencies of up to 15% and suggest simple realizable improvements to significantly increase the efficiency.Comment: 4 pages, 4 figure

A pseudo-spectral approach to inverse problems in interface dynamics

An improved scheme for computing coupling parameters of the Kardar-Parisi-Zhang equation from a collection of successive interface profiles, is presented. The approach hinges on a spectral representation of this equation. An appropriate discretization based on a Fourier representation, is discussed as a by-product of the above scheme. Our method is first tested on profiles generated by a one-dimensional Kardar-Parisi-Zhang equation where it is shown to reproduce the input parameters very accurately. When applied to microscopic models of growth, it provides the values of the coupling parameters associated with the corresponding continuum equations. This technique favorably compares with previous methods based on real space schemes.Comment: 12 pages, 9 figures, revtex 3.0 with epsf style, to appear in Phys. Rev.

Compensation of relector antenna surface distortion using an array feed

The dimensional stability of the surface of a large reflector antenna is important when high gain or low sidelobe performance is desired. If the surface is distorted due to thermal or structural reasons, antenna performance can be improved through the use of an array feed. The design of the array feed and its relation to the surface distortion are examined. The sensitivity of antenna performance to changing surface parameters for fixed feed array geometries is also studied. This allows determination of the limits of usefulness for feed array compensation

Microlensing of gamma ray bursts by stars and MACHOs

The microlensing interpretation of the optical afterglow of GRB 000301C seems naively surprising, since a simple estimate of the stellar microlensing rate gives less than one in four hundred for a flat Omega_Lambda=0.7 cosmology, whereas one event was seen in about thirty afterglows. Considering baryonic MACHOs making up half of the baryons in the universe, the microlensing probability per burst can be roughly 5% for a GRB at redshift z=2. We explore two effects that may enhance the probability of observing microlensed gamma-ray burst afterglows: binary lenses and double magnification bias. We find that the consideration of binary lenses can increase the rate only at the ~15% level. On the other hand, because gamma-ray bursts for which afterglow observations exist are typically selected based on fluxes at widely separated wavebands which are not necessarily well correlated (e.g. localization in X-ray, afterglow in optical/infrared), magnification bias can operate at an enhanced level compared to the usual single-bias case. We find that existing estimates of the slope of the luminosity function of gamma-ray bursts, while as yet quite uncertain, point to enhancement factors of more than three above the simple estimates of the microlensing rate. We find that the probability to observe at least one microlensing event in the sample of 27 measured afterglows can be 3-4% for stellar lenses, or as much as 25 Omega_lens for baryonic MACHOs. We note that the probability to observe at least one event over the available sample of afterglows is significant only if a large fraction of the baryons in the universe are condensed in stellar-mass objects. (ABRIDGED)Comment: 22 pages, 4 figures, 2 table

Extremely Small Sizes for Faint z~2-8 Galaxies in the Hubble Frontier Fields: A Key Input For Establishing their Volume Density and UV Emissivity

We provide the first observational constraints on the sizes of the faintest galaxies lensed by the Hubble Frontier Fields (HFF) clusters. Ionizing radiation from faint galaxies likely drives cosmic reionization, and the HFF initiative provides a key opportunity to find such galaxies. Yet, we cannot really assess their ionizing emissivity without a robust measurement of their sizes, since this is key to quantifying both their prevalence and the faint-end slope to the UV luminosity function. Here we provide the first such size constraints with 2 new techniques. The first utilizes the fact that the detectability of highly-magnified galaxies as a function of shear is very dependent on a galaxy's size. Only the most compact galaxies will remain detectable in regions of high shear (vs. a larger detectable size range for low shear), a phenomenon we carefully quantify using simulations. Remarkably, however, no correlation is found between the surface density of faint galaxies and the predicted shear, using 87 faint high-magnification mu>10 z~2-8 galaxies seen behind the first 4 HFF clusters. This can only be the case if such faint (~-15 mag) galaxies have significantly smaller sizes than luminous galaxies. We constrain their half-light radii to be <~30 mas (<160-240 pc). As a 2nd size probe, we rotate and stack 26 faint high-magnification sources along the major shear axis. Less elongation is found than even for objects with an intrinsic half-light radius of 10 mas. Together these results indicate that extremely faint z~2-8 galaxies have near point-source profiles in the HFF dataset (half-light radii conservatively <30 mas and likely 5-10 mas). These results suggest smaller completeness corrections and hence much lower volume densities for faint z~2-8 galaxies and shallower faint-end slopes than have been derived in many recent studies (by factors of ~2-3 and by dalpha>~0.1-0.3).Comment: 19 pages, 15 figures, 3 tables, accepted for publication in Ap