Optimal states and almost optimal adaptive measurements for quantum interferometry

We derive the optimal N-photon two-mode input state for obtaining an estimate \phi of the phase difference between two arms of an interferometer. For an optimal measurement [B. C. Sanders and G. J. Milburn, Phys. Rev. Lett. 75, 2944 (1995)], it yields a variance (\Delta \phi)^2 \simeq \pi^2/N^2, compared to O(N^{-1}) or O(N^{-1/2}) for states considered by previous authors. Such a measurement cannot be realized by counting photons in the interferometer outputs. However, we introduce an adaptive measurement scheme that can be thus realized, and show that it yields a variance in \phi very close to that from an optimal measurement.Comment: 4 pages, 4 figures, journal versio

Nonclassical Fields and the Nonlinear Interferometer

We demonstrate several new results for the nonlinear interferometer, which emerge from a formalism which describes in an elegant way the output field of the nonlinear interferometer as two-mode entangled coherent states. We clarify the relationship between squeezing and entangled coherent states, since a weak nonlinear evolution produces a squeezed output, while a strong nonlinear evolution produces a two-mode, two-state entangled coherent state. In between these two extremes exist superpositions of two-mode coherent states manifesting varying degrees of entanglement for arbitrary values of the nonlinearity. The cardinality of the basis set of the entangled coherent states is finite when the ratio $\chi / \pi$ is rational, where $\chi$ is the nonlinear strength. We also show that entangled coherent states can be produced from product coherent states via a nonlinear medium without the need for the interferometric configuration. This provides an important experimental simplification in the process of creating entangled coherent states.Comment: 21 pages, 2 figure

How to perform the most accurate possible phase measurements

We present the theory of how to achieve phase measurements with the minimum possible variance in ways that are readily implementable with current experimental techniques. Measurements whose statistics have high-frequency fringes, such as those obtained from NOON states, have commensurately high information yield. However this information is also highly ambiguous because it does not distinguish between phases at the same point on different fringes. We provide schemes to eliminate this phase ambiguity in a highly efficient way, providing phase estimates with uncertainty that is within a small constant factor of the Heisenberg limit, the minimum allowed by the laws of quantum mechanics. These techniques apply to NOON state and multi-pass interferometry, as well as phase measurements in quantum computing. We have reported the experimental implementation of some of these schemes with multi-pass interferometry elsewhere. Here we present the theoretical foundation, and also present some new experimental results. There are three key innovations to the theory in this paper. First, we examine the intrinsic phase properties of the sequence of states (in multiple time modes) via the equivalent two-mode state. Second, we identify the key feature of the equivalent state that enables the optimal scaling of the intrinsic phase uncertainty to be obtained. This enables us to identify appropriate combinations of states to use. The remaining difficulty is that the ideal phase measurements to achieve this intrinic phase uncertainty are often not physically realizable. The third innovation is to solve this problem by using realizable measurements that closely approximate the optimal measurements, enabling the optimal scaling to be preserved.Comment: 23 pages, 10 figures; new general definition of resource

Dangling-bond charge qubit on a silicon surface

Two closely spaced dangling bonds positioned on a silicon surface and sharing an excess electron are revealed to be a strong candidate for a charge qubit. Based on our study of the coherent dynamics of this qubit, its extremely high tunneling rate ~ 10^14 1/s greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming a critical obstacle of charge qubit quantum computing. We investigate possible configurations of dangling bond qubits for quantum computing devices. A first-order analysis of coherent dynamics of dangling bonds shows promise in this respect.Comment: 17 pages, 3 EPS figures, 1 tabl

Chandra imaging of the X-ray core of Abell 1795

We report the discovery of a 40 arcsec long X-ray filament in the core of the cluster of galaxies A1795. The feature coincides with an Halpha+NII filament found by Cowie et al in the early 1980s and resolved into at least 2 U-band filaments by McNamara et al in the mid 1990s. The (emission-weighted) temperature of the X-ray emitting gas along the filament is 2.5-3 keV, as revealed by X-ray colour ratios. The deprojected temperature will be less. A detailed temperature map of the core of the cluster presented. The cD galaxy at the head of the filament is probably moving through or oscillating in the cluster core. The radiative cooling time of the X-ray emitting gas in the filament is about 3x10^8 yr which is similar to the age of the filament obtained from its length and velocity. This suggests that the filament is produced by cooling of the gas from the intracluster medium. The filament, much of which is well separated from the body of the cD galaxy and its radio source, is potentially of great importance in helping to understand the energy and ionization source of the optical nebulosity common in cooling flows.Comment: 5 pages, 5 figures, accepted by MNRAS, high resolution version available at http://www-xray.ast.cam.ac.uk/papers/a1795_chandra.pd

Quantum walks in higher dimensions

We analyze the quantum walk in higher spatial dimensions and compare classical and quantum spreading as a function of time. Tensor products of Hadamard transformations and the discrete Fourier transform arise as natural extensions of the quantum coin toss in the one-dimensional walk simulation, and other illustrative transformations are also investigated. We find that entanglement between the dimensions serves to reduce the rate of spread of the quantum walk. The classical limit is obtained by introducing a random phase variable.Comment: 6 pages, 6 figures, published versio

Use of Hawaii Analog Sites for Lunar Science and In-Situ Resource Utilization

In-Situ Resource Utilization (ISRU) and lunar science share similar objectives with respect to analyzing and characterizing the physical, mineral, and volatile materials and resources at sites of robotic and human exploration. To help mature and stress instruments, technologies, and hardware and to evaluate operations and procedures, space agencies have utilized demonstrations at analog sites on Earth before use in future missions. The US National Aeronautics and Space Administration (NASA), the Canadian Space Agency (CSA), and the German Space Agency (DLR) have utilized an analog site on the slope of Mauna Kea on the Big Island of Hawaii to test ISRU and lunar science hardware and operations in two previously held analog field tests. NASA and CSA are currently planning on a 3rd analog field test to be held in June, 2012 in Hawaii that will expand upon the successes from the previous two field tests

The Littlewood-Gowers problem

We show that if A is a subset of Z/pZ (p a prime) of density bounded away from 0 and 1 then the A(Z/pZ)-norm (that is the l^1-norm of the Fourier transform) of the characterstic function of A is bounded below by an absolute constant times (log p)^{1/2 - \epsilon} as p tends to infinity. This improves on the exponent 1/3 in recent work of Green and Konyagin.Comment: 31 pp. Corrected typos. Updated references

Spectroscopy of Blue Stragglers and Turnoff Stars in M67 (NGC 2682)

We have analyzed high-resolution spectra of relatively cool blue stragglers and main sequence turnoff stars in the old open cluster M67 (NGC 2682). We attempt to identify blue stragglers whose spectra are least contaminated by binary effects (contamination by a binary companion or absorption by circumstellar material). These ``best'' stragglers have metallicities ([Fe/H] = -0.05) and abundance ratios of the blue stragglers are not significantly different from those of the turnoff stars. Based on arguments from hydrodynamical models of stellar collisions, we assert that the current upper limits for the lithium abundances of all blue stragglers observed in M67 (by us and others) are consistent with no mixing during the formation process, assuming pre-main sequence and main sequence depletion patterns observed for M67 main sequence stars. We discuss composition signatures that could more definitively distinguish between blue straggler formation mechanisms in open cluster stars. We confirm the spectroscopic detection of a binary companion to the straggler S 1082. From our spectra, we measure a projected rotational speed of 90+/-20 km/sec for the secondary, and find that its radial velocity varies with a peak-to-peak amplitude of ~ 25 km/sec. Because the radial velocities do not vary with a period corresponding to the partial eclipses in the system, we believe this system is currently undergoing mass transfer. In addition we present evidence that S 984 is a true blue straggler (and not an unresolved pair). If this can be proven, our detection of lithium may indicate a collisional origin.Comment: 20 pages, 4 figures, to appear in October 2000 A

Molecular Gas in the Powerful Radio Nucleus of the Ultraluminous Infrared Galaxy PKS 1345+12

Millimeter CO(1-0) interferometry and high resolution, Hubble Space Telescope (HST) 1.1, 1.6, and 2.2 micron imaging of the radio compact galaxy PKS 1345+12 are presented. With an infrared luminosity of 2x10^{12} L_sun, PKS 1345+12 is a prime candidate for studying the link between the ultraluminous infrared galaxy phenomenon and radio galaxies. These new observations probe the molecular gas distribution and obscured nuclear regions of PKS 1345+12 and provide morphological support for the idea that the radio activity in powerful radio galaxies is triggered by the merger of gas rich galaxies. Two nuclei separated by 2" (4.0 kpc) are observed in the near-infrared; the extended southeastern nucleus has colors consistent with reddened starlight, and the compact northwestern nucleus has extremely red colors indicative of an optical quasar with a warm dust component. Further, the molecular gas, 3mm continuum, and radio emission are coincident with the redder nucleus, confirming that the northwestern nucleus is the site of the AGN and that the molecular gas is the likely fuel source.Comment: LaTex, 5 pages with 1 postscript and 1 jpg figure, ApJ Letters, in press (August 20, 1999