Quantum Mechanical Interaction-Free Measurements

A novel manifestation of nonlocality of quantum mechanics is presented. It is shown that it is possible to ascertain the existence of an object in a given region of space without interacting with it. The method might have practical applications for delicate quantum experiments.Comment: (revised file with no need for macro), 12, TAUP 1865-91

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.Comment: 8 pages, revtex, Title change

Nonlocal Effects of Partial Measurements and Quantum Erasure

Partial measurement turns the initial superposition not into a definite outcome but into a greater probability for it. The probability can approach 100%, yet the measurement can undergo complete quantum erasure. In the EPR setting, we prove that i) every partial measurement nonlocally creates the same partial change in the distant particle; and ii) every erasure inflicts the same erasure on the distant particle's state. This enables an EPR experiment where the nonlocal effect does not vanish after a single measurement but keeps "traveling" back and forth between particles. We study an experiment in which two distant particles are subjected to interferometry with a partial "which path" measurement. Such a measurement causes a variable amount of correlation between the particles. A new inequality is formulated for same-angle polarizations, extending Bell's inequality for different angles. The resulting nonlocality proof is highly visualizable, as it rests entirely on the interference effect. Partial measurement also gives rise to a new form of entanglement, where the particles manifest correlations of multiple polarization directions. Another novelty in that the measurement to be erased is fully observable, in contrast to prevailing erasure techniques where it can never be observed. Some profound conceptual implications of our experiment are briefly pointed out.Comment: To be published in Phys. Rev. A 63 (2001). 19 pages, 12 figures, RevTeX 3.

Control of insects in cotton

Results of two experiments at the Ord Irrigation area in 1968 indicate that farmers may be spending more than necessary to obtain economic control of cotton pests in some seasons. One experiment clearly demonstrated the relationship between low insect numbers and improved cotton yields—the second indicated that a moderate but well timed spray schedule, especially during the early part of the season, can result in more economic insect control than an intensive spray schedule

LensPerfect: Gravitational Lens Massmap Reconstructions Yielding Exact Reproduction of All Multiple Images

We present a new approach to gravitational lens massmap reconstruction. Our massmap solutions perfectly reproduce the positions, fluxes, and shears of all multiple images. And each massmap accurately recovers the underlying mass distribution to a resolution limited by the number of multiple images detected. We demonstrate our technique given a mock galaxy cluster similar to Abell 1689 which gravitationally lenses 19 mock background galaxies to produce 93 multiple images. We also explore cases in which far fewer multiple images are observed, such as four multiple images of a single galaxy. Massmap solutions are never unique, and our method makes it possible to explore an extremely flexible range of physical (and unphysical) solutions, all of which perfectly reproduce the data given. Each reconfiguration of the source galaxies produces a new massmap solution. An optimization routine is provided to find those source positions (and redshifts, within uncertainties) which produce the "most physical" massmap solution, according to a new figure of merit developed here. Our method imposes no assumptions about the slope of the radial profile nor mass following light. But unlike "non-parametric" grid-based methods, the number of free parameters we solve for is only as many as the number of observable constraints (or slightly greater if fluxes are constrained). For each set of source positions and redshifts, massmap solutions are obtained "instantly" via direct matrix inversion by smoothly interpolating the deflection field using a recently developed mathematical technique. Our LensPerfect software is straightforward and easy to use and is made publicly available via our website.Comment: 17 pages, 18 figures, accepted by ApJ. Software and full-color version of paper available at http://www.its.caltech.edu/~coe/LensPerfect

On the field dependence of the vortex core size

We argue that in clean high-$\kappa$ type II superconductors, the low temperature vortex core size (defined as the coherence length $\xi$) in high fields should decrease with increasing applied field in qualitative agreement with experimental data. Calculations are done for the Fermi sphere and cylinder (with the field parallel to the cylinder axis). The results for clean materials at T=0 can be represented as $\xi(H)/\xi(H_{c2}) = U (H/H_{c2})$ with $U$ being an universal function.Comment: 8 pages, 2 figure

The OmegaWhite Survey for Short-Period Variable Stars IV: Discovery of the warm DQ white dwarf OW J175358.85-310728.9

We present the discovery and follow-up observations of the second known variable warm DQ white dwarf OW J175358.85-310728.9 (OW J1753-3107). OW J1753-3107 is the brightest of any of the currently known warm or hot DQ and was discovered in the OmegaWhite Survey as exhibiting optical variations on a period of 35.5452 (2) mins, with no evidence for other periods in its light curves. This period has remained constant over the last two years and a single-period sinusoidal model provides a good fit for all follow-up light curves. The spectrum consists of a very blue continuum with strong absorption lines of neutral and ionised carbon, a broad He I 4471 A line, and possibly weaker hydrogen lines. The C I lines are Zeeman split, and indicate the presence of a strong magnetic field. Using spectral Paschen-Back model descriptions, we determine that OW J1753-3107 exhibits the following physical parameters: T_eff = 15430 K, log(g) = 9.0, log(N(C)/N(He)) = -1.2, and the mean magnetic field strength is B_z =2.1 MG. This relatively low temperature and carbon abundance (compared to the expected properties of hot DQs) is similar to that seen in the other warm DQ SDSS J1036+6522. Although OW J1753-3107 appears to be a twin of SDSS J1036+6522, it exhibits a modulation on a period slightly longer than the dominant period in SDSS J1036+6522 and has a higher carbon abundance. The source of variations is uncertain, but they are believed to originate from the rotation of the magnetic white dwarf.Comment: 11 pages, 8 figures, 7 tables. Accepted for publication by MNRA

Strict detector-efficiency bounds for n-site Clauser-Horne inequalities

An analysis of detector-efficiency in many-site Clauser-Horne inequalities is presented, for the case of perfect visibility. It is shown that there is a violation of the presented n-site Clauser-Horne inequalities if and only if the efficiency is greater than n/(2n-1). Thus, for a two-site two-setting experiment there are no quantum-mechanical predictions that violate local realism unless the efficiency is greater than 2/3. Secondly, there are n-site experiments for which the quantum-mechanical predictions violate local realism whenever the efficiency exceeds 1/2.Comment: revtex, 5 pages, 1 figure (typesetting changes only

Optical Turbulence Measurements and Models for Mount John University Observatory

Site measurements were collected at Mount John University Observatory in 2005 and 2007 using a purpose-built scintillation detection and ranging system. $C_n^2(h)$ profiling indicates a weak layer located at 12 - 14 km above sea level and strong low altitude turbulence extending up to 5 km. During calm weather conditions, an additional layer was detected at 6 - 8 km above sea level. $V(h)$ profiling suggests that tropopause layer velocities are nominally 12 - 30 m/s, and near-ground velocities range between 2 -- 20 m/s, dependent on weather. Little seasonal variation was detected in either $C_n^2(h)$ and $V(h)$ profiles. The average coherence length, $r_0$, was found to be $7 \pm 1$ cm for the full profile at a wavelength of 589 nm. The average isoplanatic angle, $\theta_0$, was $1.0 \pm 0.1$ arcsec. The mean turbulence altitude, $\bar{h_0}$, was found to be $2.0\pm0.7$ km above sea level. No average in the Greenwood frequency, $f_G$, could be established due to the gaps present in the \vw\s profiles obtained. A modified Hufnagel-Valley model was developed to describe the $C_n^2(h)$ profiles at Mount John, which estimates $r_0$ at 6 cm and $\theta_0$ at 0.9 arcsec. A series of $V(h)$ models were developed, based on the Greenwood wind model with an additional peak located at low altitudes. Using the $C_n^2(h)$ model and the suggested $V(h)$ model for moderate ground wind speeds, $f_G$ is estimated at 79 Hz.Comment: 14 pages; accepted for publication in PAS

An expectation value expansion of Hermitian operators in a discrete Hilbert space

We discuss a real-valued expansion of any Hermitian operator defined in a Hilbert space of finite dimension N, where N is a prime number, or an integer power of a prime. The expansion has a direct interpretation in terms of the operator expectation values for a set of complementary bases. The expansion can be said to be the complement of the discrete Wigner function. We expect the expansion to be of use in quantum information applications since qubits typically are represented by a discrete, and finite-dimensional physical system of dimension N=2^p, where p is the number of qubits involved. As a particular example we use the expansion to prove that an intermediate measurement basis (a Breidbart basis) cannot be found if the Hilbert space dimension is 3 or 4.Comment: A mild update. In particular, I. D. Ivanovic's earlier derivation of the expansion is properly acknowledged. 16 pages, one PS figure, 1 table, written in RevTe