From Linear Optical Quantum Computing to Heisenberg-Limited Interferometry

The working principles of linear optical quantum computing are based on photodetection, namely, projective measurements. The use of photodetection can provide efficient nonlinear interactions between photons at the single-photon level, which is technically problematic otherwise. We report an application of such a technique to prepare quantum correlations as an important resource for Heisenberg-limited optical interferometry, where the sensitivity of phase measurements can be improved beyond the usual shot-noise limit. Furthermore, using such nonlinearities, optical quantum nondemolition measurements can now be carried out at the single-photon level.Comment: 10 pages, 5 figures; Submitted to a Special Issue of J. Opt. B on "Fluctuations and Noise in Photonics and Quantum Optics" (Herman Haus Memorial Issue); v2: minor change

Measuring measurement

Measurement connects the world of quantum phenomena to the world of classical events. It plays both a passive role, observing quantum systems, and an active one, preparing quantum states and controlling them. Surprisingly - in the light of the central status of measurement in quantum mechanics - there is no general recipe for designing a detector that measures a given observable. Compounding this, the characterization of existing detectors is typically based on partial calibrations or elaborate models. Thus, experimental specification (i.e. tomography) of a detector is of fundamental and practical importance. Here, we present the realization of quantum detector tomography: we identify the optimal positive-operator-valued measure describing the detector, with no ancillary assumptions. This result completes the triad, state, process, and detector tomography, required to fully specify an experiment. We characterize an avalanche photodiode and a photon number resolving detector capable of detecting up to eight photons. This creates a new set of tools for accurately detecting and preparing non-classical light.Comment: 6 pages, 4 figures,see video abstract at http://www.quantiki.org/video_abstracts/0807244

Photon Number Statistics of Multimode Parametric Down-Conversion

We experimentally analyze the complete photon number statistics of parametric downconversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.Comment: 5 pages, 3 figure

Iron in the Sargasso Sea (Bermuda Atlantic Time-series Study region) during summer : eolian imprint, spatiotemporal variability, and ecological implications

Author Posting. © American Geophysical Union, 2005. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Global Biogeochemical Cycles 19 (2005): GB4006, doi:10.1029/2004GB002445.We report iron measurements for water column and aerosol samples collected in the Sargasso Sea during July-August 2003 (summer 2003) and April-May 2004 (spring 2004). Our data reveal a large seasonal change in the dissolved iron (dFe) concentration of surface waters in the Bermuda Atlantic Time-series Study region, from ∼1–2 nM in summer 2003, when aerosol iron concentrations were high (mean 10 nmol m−3), to ∼0.1–0.2 nM in spring 2004, when aerosol iron concentrations were low (mean 0.64 nmol m−3). During summer 2003, we observed an increase of ∼0.6 nM in surface water dFe concentrations over 13 days, presumably due to eolian iron input; an estimate of total iron deposition over this same period suggests an effective solubility of 3–30% for aerosol iron. Our summer 2003 water column profiles show potentially growth-limiting dFe concentrations (0.02–0.19 nM) coinciding with a deep chlorophyll maximum at 100–150 m depth, where phytoplankton biomass is typically dominated by Prochlorococcus during late summer.Funding for this work was provided by the U.S. National Science Foundation (OCE-0222053 to P. N. S., OCE-0222046 to T. M. C., and OCE-0241310 to D. J. M.), the U.S. National Aeronautics and Space Administration (NAG5-11265 to D. J. M.), the Australian Research Council (DP0342826 to A. R. B.), the Antarctic Climate and Ecosystems Cooperative Research Center, and the H. Unger Vetlesen Foundation

An avalanche-photodiode-based photon-number-resolving detector

Avalanche photodiodes are widely used as practical detectors of single photons.1 Although conventional devices respond to one or more photons, they cannot resolve the number in the incident pulse or short time interval. However, such photon number resolving detectors are urgently needed for applications in quantum computing,2-4 communications5 and interferometry,6 as well as for extending the applicability of quantum detection generally. Here we show that, contrary to current belief,3,4 avalanche photodiodes are capable of detecting photon number, using a technique to measure very weak avalanches at the early stage of their development. Under such conditions the output signal from the avalanche photodiode is proportional to the number of photons in the incident pulse. As a compact, mass-manufactured device, operating without cryogens and at telecom wavelengths, it offers a practical solution for photon number detection.Comment: 12 pages, 4 figure

Ground states of two-dimensional ±\pmJ Edwards-Anderson spin glasses

We present an exact algorithm for finding all the ground states of the two-dimensional Edwards-Anderson $\pm J$ spin glass and characterize its performance. We investigate how the ground states change with increasing system size and and with increasing antiferromagnetic bond ratio $x$. We find that that some system properties have very large and strongly non-Gaussian variations between realizations.Comment: 15 pages, 21 figures, 2 tables, uses revtex4 macro

Generating droplets in two-dimensional Ising spin glasses by using matching algorithms

We study the behavior of droplets for two dimensional Ising spin glasses with Gaussian interactions. We use an exact matching algorithm which enables study of systems with linear dimension L up to 240, which is larger than is possible with other approaches. But the method only allows certain classes of droplets to be generated. We study single-bond, cross and a category of fixed volume droplets as well as first excitations. By comparison with similar or equivalent droplets generated in previous works, the advantages but also the limitations of this approach are revealed. In particular we have studied the scaling behavior of the droplet energies and droplet sizes. In most cases, a crossover of the data can be observed such that for large sizes the behavior is compatible with the one-exponent scenario of the droplet theory. Only for the case of first excitations, no clear conclusion can be reached, probably because even with the matching approach the accessible system sizes are still too small.Comment: 11 pages, 16 figures, revte

Avalanche Photo-Detection for High Data Rate Applications

Avalanche photo detection is commonly used in applications which require single photon sensitivity. We examine the limits of using avalanche photo diodes (APD) for characterising photon statistics at high data rates. To identify the regime of linear APD operation we employ a ps-pulsed diode laser with variable repetition rates between 0.5MHz and 80MHz. We modify the mean optical power of the coherent pulses by applying different levels of well-calibrated attenuation. The linearity at high repetition rates is limited by the APD dead time and a non-linear response arises at higher photon-numbers due to multiphoton events. Assuming Poissonian input light statistics we ascertain the effective mean photon-number of the incident light with high accuracy. Time multiplexed detectors (TMD) allow to accomplish photon- number resolution by photon chopping. This detection setup extends the linear response function to higher photon-numbers and statistical methods may be used to compensate for non-linearity. We investigated this effect, compare it to the single APD case and show the validity of the convolution treatment in the TMD data analysis.Comment: 16 pages, 5 figure

Sharp Trace Hardy-Sobolev-Maz'ya Inequalities and the Fractional Laplacian

In this work we establish trace Hardy and trace Hardy-Sobolev-Maz'ya inequalities with best Hardy constants, for domains satisfying suitable geometric assumptions such as mean convexity or convexity. We then use them to produce fractional Hardy-Sobolev-Maz'ya inequalities with best Hardy constants for various fractional Laplacians. In the case where the domain is the half space our results cover the full range of the exponent $s \in (0,1)$ of the fractional Laplacians. We answer in particular an open problem raised by Frank and Seiringer \cite{FS}.Comment: 42 page

Mineralogy of Vera Rubin Ridge in Gale Crater from the Mars Science Laboratory CheMin instrument

Gale crater was selected as the landing site for the Mars Science Laboratory Curiosity rover because of orbital evidence for a variety of secondary minerals in the lower slopes of Aeolis Mons (aka Mount Sharp) that indicate changes in aqueous conditions over time. Distinct units demonstrate orbital spectral signatures of hematite, phyllosilicate (smectite), and sulfate minerals, which suggest that ancient aqueous environments in Gale crater varied in oxidation potential, pH, and water activity. Vera Rubin ridge (VRR) is the first of these units identified from orbit to have been studied by Curiosity. Orbital near-infrared data from VRR show a strong band at 860 nm indicative of hematite. Before Curiosity arrived at VRR, the hypotheses to explain the formation of hematite included (1) precipitation at a redox interface where aqueous Fe2+ was oxidized to Fe3+, and (2) acidic alteration of olivine in oxic fluids. Studying the composition and sedimentology of the rocks on VRR allow us to test and refine these hypotheses and flesh out the depositional and diagenetic history of the ridge. Here, we focus on the mineralogical results of four rock powders drilled from and immediately below VRR as determined by CheMin