The effects of time delays in adaptive phase measurements

It is not possible to make measurements of the phase of an optical mode using linear optics without introducing an extra phase uncertainty. This extra phase variance is quite large for heterodyne measurements, however it is possible to reduce it to the theoretical limit of log (n) over bar (4 (n) over bar (2)) using adaptive measurements. These measurements are quite sensitive to experimental inaccuracies, especially time delays and inefficient detectors. Here it is shown that the minimum introduced phase variance when there is a time delay of tau is tau/(8 (n) over bar). This result is verified numerically, showing that the phase variance introduced approaches this limit for most of the adaptive schemes using the best final phase estimate. The main exception is the adaptive mark II scheme with simplified feedback, which is extremely sensitive to time delays. The extra phase variance due to time delays is considered for the mark I case with simplified feedback, verifying the tau /2 result obtained by Wiseman and Killip both by a more rigorous analytic technique and numerically.

Adaptive phase measurements in linear optical quantum computation

Photon counting induces an effective non-linear optical phase shift in certain states derived by linear optics from single photons. Although this non-linearity is non-deterministic, it is sufficient in principle to allow scalable linear optics quantum computation (LOQC). The most obvious way to encode a qubit optically is as a superposition of the vacuum and a single photon in one mode-so-called 'single-rail' logic. Until now this approach was thought to be prohibitively expensive (in resources) compared to 'dual-rail' logic where a qubit is stored by a photon across two modes. Here we attack this problem with real-time feedback control, which can realize a quantum-limited phase measurement on a single mode, as has been recently demonstrated experimentally. We show that with this added measurement resource, the resource requirements for single-rail LOQC are not substantially different from those of dual-rail LOQC. In particular, with adaptive phase measurements an arbitrary qubit state a alpha/0 > + beta/1 > can be prepared deterministically.

Adaptive phase measurements for narrowband squeezed beams

We have previously [Phys. Rev. A 65, 043803 (2002)] analyzed adaptive measurements for estimating the continuously varying phase of a coherent beam, and a broadband squeezed beam. A real squeezed beam must have finite photon flux N and hence can be significantly squeezed only over a limited frequency range. In this paper we analyze adaptive phase measurements of this type for a realistic model of a squeezed beam. We show that, provided it is possible to suitably choose the parameters of the beam, a mean-square phase uncertainty scaling as (N/kappa)(-5/8) is possible, where kappa is the linewidth of the beam resulting from the fluctuating phase. This is an improvement over the (N/kappa)(-1/2) scaling found previously for coherent beams. In the experimentally realistic case where there is a limit on the maximum squeezing possible, the variance will be reduced below that for coherent beams, though the scaling is unchanged.

Adaptive Phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light

We consider the task of estimating the randomly fluctuating phase of a continuous-wave beam of light. Using the theory of quantum parameter estimation, we show that this can be done more accurately when feedback is used (adaptive phase estimation) than by any scheme not involving feedback (nonadaptive phase estimation) in which the beam is measured as it arrives at the detector. Such schemes not involving feedback include all those based on heterodyne detection or instantaneous canonical phase measurements. We also demonstrate that the superior accuracy of adaptive phase estimation is present in a regime conducive to observing it experimentally.

Characterizing Greenberger-Horne-Zeilinger correlations in nondegenerate parametric oscillation via phase measurements

We present a potential realization of the Greenberger-Horne-Zeilinger all or nothing contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation. [S0031-9007(98)07671-6].

The practicality of adaptive phase estimation

Adaptive phase estimation is the process of estimating the phase of an electromagnetic field via a continually changing measurement. The measurement is varied in an attempt to optimize it at each moment. In this paper, we show that adaptive phase estimation is more accurate than nonadaptive phase estimation for continuous beams of light even when small time delays in the feedback are present. (c) 2005 Pleiades Publishing Inc.

Optimal input states and feedback for interferometric phase estimation

We derive optimal N-photon two-mode input states for interferometric phase measurements. Under canonical measurements the phase variance scales as N-2 for these states, as compared to N-1 or N-1/2 for states considered bq previous authors. We prove, that it is not possible to realize the canonical measurement by counting photons in the outputs of the interferometer, even if an adjustable auxiliary phase shift is allowed in the interferometer. However. we introduce a feedback algorithm based on Bayesian inference to control this auxiliary phase shift. This makes the measurement close to a canonical one, with a phase variance scaling slightly above N-2. With no feedback, the best result (given that the phase to be measured is completely unknown) is a scaling of N-1. For optimal input states having up to four photons, our feedback scheme is the best possible one, but for higher photon numbers more complicated schemes perform marginally better.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

Optimal quantum measurements for phase-shift estimation in optical interferometry

Quantum information theory, applied to optical interferometry, yields a 1/n scaling of phase uncertainty Delta phi independent of the applied phase shift phi, where n is the number of photons in the interferometer. This 1/n scaling is achieved provided that the output state is subjected to an optimal phase measurement. We establish this scaling law for both passive (linear) and active (nonlinear) interferometers and identify the coefficient of proportionality. Whereas a highly nonclassical state is required to achieve optimal scaling for passive interferometry, a classical input state yields a 1/n scaling of phase uncertainty for active interferometry.

Bed shear stress measurements in dam break and swash flows

A novel shear plate was used to make direct bed shear stress measurements in laboratory dam break and swash flows on smooth, fixed, impermeable beds. The pressure gradient due to the slope of the fluid free-surface across the plate was measured using pressure transducers. Surface elevation was measured at five locations using acoustic displacement sensors. Flow velocity was measured using an Acoustic-Doppler Velocimeter and calculated using the ANUGA inundation model. The measured bed shear stress at the dam break fluid tip for an initially dry, horizontal bed was close to twice that estimated using steady flow theory. The temporal variation of swash bed shear stress showed a large peak in landward directed stress at the uprush tip, followed by a rapid decay throughout the uprush flow interior. The peak seaward directed stress during the backwash phase was less than half that measured in the uprush. Close to the still water line, in the region of bore collapse and at the time of initial uprush, favourable pressure gradients were measured. In the lower swash region predominately weak adverse pressure gradients were measured.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

Homodyne measurements on a Bose-Einstein condensate

We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.

X-ray absorption and phase contrast imaging to study the interplay between plant roots and soil structure

Plant performance is, at least partly, linked to the location of roots with respect to soil structure features and the micro-environment surrounding roots. Measurements of root distributions from intact samples, using optical microscopy and field tracings have been partially successful but are imprecise and labour-intensive. Theoretically, X-ray computed micro-tomography represents an ideal solution for non-invasive imaging of plant roots and soil structure. However, before it becomes fast enough and affordable or easily accessible, there is still a need for a diagnostic tool to investigate root/soil interplay. Here, a method for detection of undisturbed plant roots and their immediate physical environment is presented. X-ray absorption and phase contrast imaging are combined to produce projection images of soil sections from which root distributions and soil structure can be analyzed. The clarity of roots on the X-ray film is sufficient to allow manual tracing on an acetate sheet fixed over the film. In its current version, the method suffers limitations mainly related to (i) the degree of subjectivity associated with manual tracing and (ii) the difficulty of separating live and dead roots. The method represents a simple and relatively inexpensive way to detect and quantify roots from intact samples and has scope for further improvements. In this paper, the main steps of the method, sampling, image acquisition and image processing are documented. The potential use of the method in an agronomic perspective is illustrated using surface and sub-surface soil samples from a controlled wheat trial. Quantitative characterization of root attributes, e.g. radius, length density, branching intensity and the complex interplay between roots and soil structure, is presented and discussed.

Experimental study of phase equilibria in the systems Fe-Zn-O and Fe-Zn-Si-O at metallic iron saturation

The reported experimental work on the systems Fe-Zn-O and Fe-Zn-Si-O in equilibrium with metallic iron is part of a wider research program that combines experimental and thermodynamic computer modeling techniques to characterize zinc/lead industrial slags and sinters in the system PbO-ZnO-SiO2-CaO-FeO-Fe2O3. Extensive experimental,investigations using high-temperature equilibration and quenching techniques followed by electron probe X-ray microanalysis (EPMA) were carried out. Special experimental; procedures were developed to enable accurate measurements in these ZnO-containing systems to be performed in equilibrium with metallic iron; The systems Fe-Zn-O and FeZn-Si-O were experimentally investigated in equilibrium with metallic iron in the temperature ranges 900 degreesC to 1200 degreesC (1173 to 1473 K) and from 1000 degreesC to 1350 degreesC (1273 to 1623 K), respectively. The liquidus surface in the system Fe-Zn-Si-O in equilibrium with metallic iron was characterized in the composition ranges 0 to 33 wt pet ZnO and 0 to 40 wt pet SiO2. The wustite (Fe,Zn)O, zincite (Zn,Fe)O, willemite (Zn,Fe)(2)SiO4, arid fayalite: (Fe,Zn)(2)SiO4 solid solutions in equilibrium with metallic iron were measured.