Apodized Pupil Lyot Coronagraphs for Arbitrary Telescope Apertures

In the context of high dynamic range imaging, this study presents a breakthrough for the understanding of Apodized Pupil Lyot Coronagraphs, making them available for arbitrary aperture shapes. These new solutions find immediate application in current, ground-based coronagraphic studies (Gemini, VLT) and in existing instruments (AEOS Lyot Project). They also offer the possiblity of a search for an on-axis design for TPF. The unobstructed aperture case has already been solved by Aime et al. (2002) and Soummer et al. (2003). Analytical solutions with identical properties exist in the general case and, in particular, for centrally obscured apertures. Chromatic effects can be mitigated with a numerical optimization. The combination of analytical and numerical solutions enables the study of the complete parameter space (central obstruction, apodization throughput, mask size, bandwidth, and Lyot stop size).Comment: 7 pages 4 figures - ApJL, accepte

Translation-finite sets, and weakly compact derivations from \lp{1}(\Z_+) to its dual

We characterize those derivations from the convolution algebra $\ell^1({\mathbb Z}_+)$ to its dual which are weakly compact. In particular, we provide examples which are weakly compact but not compact. The characterization is combinatorial, in terms of "translation-finite" subsets of ${\mathbb Z}_+$, and we investigate how this notion relates to other notions of "smallness" for infinite subsets of ${\mathbb Z}_+$. In particular, we show that a set of strictly positive Banach density cannot be translation-finite; the proof has a Ramsey-theoretic flavour.Comment: v1: 14 pages LaTeX (preliminary). v2: 13 pages LaTeX, submitted. Some streamlining, renumbering and minor corrections. v3: appendix removed. v4: Modified appendix reinstated; 14 pages LaTeX. To appear in Bull. London Math. Soc

Persistence of a Brownian particle in a Time Dependent Potential

We investigate the persistence probability of a Brownian particle in a harmonic potential, which decays to zero at long times -- leading to an unbounded motion of the Brownian particle. We consider two functional forms for the decay of the confinement, an exponential and an algebraic decay. Analytical calculations and numerical simulations show, that for the case of the exponential relaxation, the dynamics of Brownian particle at short and long times are independent of the parameters of the relaxation. On the contrary, for the algebraic decay of the confinement, the dynamics at long times is determined by the exponent of the decay. Finally, using the two-time correlation function for the position of the Brownian particle, we construct the persistence probability for the Brownian walker in such a scenario.Comment: 7 pages, 5 figures, Accepted for publication in Phys. Rev.

Diffraction Analysis of 2-D Pupil Mapping for High-Contrast Imaging

Pupil-mapping is a technique whereby a uniformly-illuminated input pupil, such as from starlight, can be mapped into a non-uniformly illuminated exit pupil, such that the image formed from this pupil will have suppressed sidelobes, many orders of magnitude weaker than classical Airy ring intensities. Pupil mapping is therefore a candidate technique for coronagraphic imaging of extrasolar planets around nearby stars. Unlike most other high-contrast imaging techniques, pupil mapping is lossless and preserves the full angular resolution of the collecting telescope. So, it could possibly give the highest signal-to-noise ratio of any proposed single-telescope system for detecting extrasolar planets. Prior analyses based on pupil-to-pupil ray-tracing indicate that a planet fainter than 10^{-10} times its parent star, and as close as about 2 lambda/D, should be detectable. In this paper, we describe the results of careful diffraction analysis of pupil mapping systems. These results reveal a serious unresolved issue. Namely, high-contrast pupil mappings distribute light from very near the edge of the first pupil to a broad area of the second pupil and this dramatically amplifies diffraction-based edge effects resulting in a limiting attainable contrast of about 10^{-5}. We hope that by identifying this problem others will provide a solution.Comment: 23 pages, 13 figures, also posted to http://www.orfe.princeton.edu/~rvdb/tex/piaaFresnel/ms.pd

Gaussian-State Theory of Two-Photon Imaging

Biphoton states of signal and idler fields--obtained from spontaneous parametric downconversion (SPDC) in the low-brightness, low-flux regime--have been utilized in several quantum imaging configurations to exceed the resolution performance of conventional imagers that employ coherent-state or thermal light. Recent work--using the full Gaussian-state description of SPDC--has shown that the same resolution performance seen in quantum optical coherence tomography and the same imaging characteristics found in quantum ghost imaging can be realized by classical-state imagers that make use of phase-sensitive cross correlations. This paper extends the Gaussian-state analysis to two additional biphoton-state quantum imaging scenarios: far field diffraction-pattern imaging; and broadband thin-lens imaging. It is shown that the spatial resolution behavior in both cases is controlled by the nonzero phase-sensitive cross correlation between the signal and idler fields. Thus, the same resolution can be achieved in these two configurations with classical-state signal and idler fields possessing a nonzero phase-sensitive cross correlation.Comment: 14 pages, 5 figure

Persistence of Kardar-Parisi-Zhang Interfaces

The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18 \pm 0.08$ and $\theta_- = 1.64 \pm 0.08$. Bounds on $\theta_\pm$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar \lambda$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar \lambda = \beta + d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi

Predictability of band-limited, high-frequency, and mixed processes in the presence of ideal low-pass filters

Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of convolution integrals over future time by integrals over past time. We found that all band-limited processes are predictable in this sense, as well as high-frequency processes with zero energy at low frequencies. It follows that a process of mixed type still can be predicted if an ideal low-pass filter exists for this process.Comment: 10 page

Experimental characterization of Gaussian quantum communication channels

We present a full experimental characterization of continuous variable quantum communication channels established by shared entanglement together with local operations and classical communication. The resulting teleportation channel was fully characterized by measuring all elements of the covariance matrix of the shared two-mode squeezed Gaussian state. From the experimental data we determined the lower bound to the quantum channel capacity, the teleportation fidelity of coherent states and the logarithmic negativity and the purity of the shared state. Additionally, a positive secret key rate was obtained for two of the established channels.Comment: 9 pages, 4 figures, submitted to Physical Review

Operational interpretations of quantum discord

Quantum discord quantifies non-classical correlations going beyond the standard classification of quantum states into entangled and unentangled ones. Although it has received considerable attention, it still lacks any precise interpretation in terms of some protocol in which quantum features are relevant. Here we give quantum discord its first operational meaning in terms of entanglement consumption in an extended quantum state merging protocol. We further relate the asymmetry of quantum discord with the performance imbalance in quantum state merging and dense coding.Comment: v4: 5 pages, 1 fig. Refs added, text improved. Main results unchanged. See arXiv:1008.4135v2 for a related work. v5: close to the published versio

Multimode theory of measurement-induced non-Gaussian operation on wideband squeezed light

We present a multimode theory of non-Gaussian operation induced by an imperfect on/off-type photon detector on a splitted beam from a wideband squeezed light. The events are defined for finite time duration $T$ in the time domain. The non-Gaussian output state is measured by the homodyne detector with finite bandwidh $B$. Under this time- and band-limitation to the quantm states, we develop a formalism to evaluate the frequency mode matching between the on/off trigger channel and the conditional signal beam in the homodyne channel. Our formalism is applied to the CW and pulsed schemes. We explicitly calculate the Wigner function of the conditional non-Gaussian output state in a realistic situation. Good mode matching is achieved for BT\alt1, where the discreteness of modes becomes prominant, and only a few modes become dominant both in the on/off and the homodyne channels. If the trigger beam is projected nearly onto the single photon state in the most dominant mode in this regime, the most striking non-classical effect will be observed in the homodyne statistics. The increase of $BT$ and the dark counts degrades the non-classical effect.Comment: 20 pages, 14 figures, submitted to Phys. Rev.