Critical quantum fluctuations in the degenerate parametric oscillator

We develop a systematic theory of critical quantum fluctuations in the driven parametric oscillator. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory. We show when these results agree and differ in calculations taken beyond the linearized approximation. We find that the optimal broadband noise reduction occurs just above threshold. In this region where there are large quantum fluctuations in the conjugate variance and macroscopic quantum superposition states might be expected, we find that the quantum predictions correspond very closely to the semiclassical theory.

Limits to squeezing in the degenerate optical parametric oscillator

We develop a systematic theory of quantum fluctuations in the driven optical parametric oscillator, including the region near threshold. This allows us to treat the limits imposed by nonlinearities to quantum squeezing and noise reduction in this nonequilibrium quantum phase transition. In particular, we compute the squeezing spectrum near threshold and calculate the optimum value. We find that the optimal noise reduction occurs at different driving fields, depending on the ratio of damping rates. The largest spectral noise reductions are predicted to occur with a very high-Q second-harmonic cavity. Our analytic results agree well with stochastic numerical simulations. We also compare the results obtained in the positive-P representation, as a fully quantum-mechanical calculation, with the truncated Wigner phase-space equation, also known as the semiclassical theory.

Read-only-memory-based quantum computation: Experimental explorations using nuclear magnetic resonance and future prospects

Read-only-memory-based (ROM-based) quantum computation (QC) is an alternative to oracle-based QC. It has the advantages of being less magical, and being more suited to implementing space-efficient computation (i.e., computation using the minimum number of writable qubits). Here we consider a number of small (one- and two-qubit) quantum algorithms illustrating different aspects of ROM-based QC. They are: (a) a one-qubit algorithm to solve the Deutsch problem; (b) a one-qubit binary multiplication algorithm; (c) a two-qubit controlled binary multiplication algorithm; and (d) a two-qubit ROM-based version of the Deutsch-Jozsa algorithm. For each algorithm we present experimental verification using nuclear magnetic resonance ensemble QC. The average fidelities for the implementation were in the ranges 0.9-0.97 for the one-qubit algorithms, and 0.84-0.94 for the two-qubit algorithms. We conclude with a discussion of future prospects for ROM-based quantum computation. We propose a four-qubit algorithm, using Grover's iterate, for solving a miniature real-world problem relating to the lengths of paths in a network.

Current density mapping approach for design of clinical magnetic resonance imaging magnets

Novel current density mapping (CDM) schemes are developed for the design of new actively shielded, clinical magnetic resonance imaging (MRI) magnets. This is an extended inverse method in which the entire potential solution space for the superconductors has been considered, rather than single current density layers. The solution provides an insight into the required superconducting coil pattern for a desired magnet configuration. This information is then used as an initial set of parameters for the magnet structure, and a previously developed hybrid numerical optimization technique is used to obtain the final geometry of the magnet. The CDM scheme is applied to the design of compact symmetric, asymmetric, and open architecture 1.0-1.5 T MRI magnet systems of novel geometry and utility. A new symmetric 1.0-T system that is just I m in length with a full 50-cm diameter of the active, or sensitive, volume (DSV) is detailed, as well as an asymmetric system in which a 50-cm DSV begins just 14 cm from the end of the coil structure. Finally a 1.0-T open magnet system with a full 50-cm DSV is presented. These new designs provide clinically useful homogeneous regions and have appropriately restricted stray fields but, in some of the designs, the DSV is much closer to the end of the magnet system than in conventional designs. These new designs have the potential to reduce patient claustrophobia and improve physician access to patients undergoing scans. (C) 2002 Wiley Periodicals, Inc.

Violation of multiparticle Bell inequalities for low- and high-flux parametric amplification using both vacuum and entangled input states

We show how polarization measurements on the output fields generated by parametric down conversion will reveal a violation of multiparticle Bell inequalities, in the regime of both low- and high-output intensity. In this case, each spatially separated system, upon which a measurement is performed, is comprised of more than one particle. In view of the formal analogy with spin systems, the proposal provides an opportunity to test the predictions of quantum mechanics for spatially separated higher spin states. Here the quantum behavior possible even where measurements are performed on systems of large quantum (particle) number may be demonstrated. Our proposal applies to both vacuum-state signal and idler inputs, and also to the quantum-injected parametric amplifier as studied by De Martini The effect of detector inefficiencies is included, and weaker Bell-Clauser-Horne inequalities are derived to enable realistic tests of local hidden variables with auxiliary assumptions for the multiparticle situation.

2,6,,9-trioxabicyclo[3.3.1]nona-3,7-dienes and 2,4,6,8-tetraoxaadamantanes: Novel chiral spacer units in macrocyclic polyethers

The unusual chiral heterocyclic systems, trioxabicyclo[3.3.1]nona-3,7-dienes (bridged bisdioxines), are incorporated as novel spacer molecules into macrocyclic polyether ring systems of various sizes (8, 9 as well as 11-15) by cyclocondensation reaction of the! bisacid chloride 4b or bisesters 6,7 and 10, with several ethylene glycols. The 2:2 macrocycles 12-14 are obtained in approximately 50:50 mixtures of diastereomers. These conclusions are mainly based on HPLC data presented in Table I as well as X-ray analyses of (1R,5R)-8c (space group Pbca, a = 10.163(3) Angstrom, b = 18.999(4) Angstrom, c = 36.187(10) Angstrom, V = 6987(3) Angstrom(3), Z = 8, d(calc) = 1.218 g cm(-3), 6974 reflections, R = 0.0553.), mesolrac-11 (space group P (1) over bar, a = 10.472(5) Angstrom, b = 16.390(5) Angstrom, c = 17.211(5) Angstrom, alpha = 98.69(2)degrees, beta = 93.04(2)degrees, gamma = 98.52(2)degrees, V = 2879.3(18) Angstrom(3), Z = 2, d(calc) = 1.173 g cm(-3), 11,162 reflections, R = 0.0945) and meso-12 (space group P2(1)/c, a = 9.927(2), b = 18.166(3), c = 17.820(3) Angstrom, beta = 96.590(10)degrees, V = 3192.3(10)Angstrom(3), Z = 4, D-c = 1.109 g cm(-3), 3490 reflections, R = 0.0646). The 1:1 macrocycles 8b,c are also formed by intramolecular transesterification of the open-chain bisesters 7b,c and their formation is favored by the use of metal ions as templates. The bridged bisdioxine moieties in 8b and 12 are converted into the corresponding chiral tetra-oxaadamantane spacers to afford macrocycles 16 and 17. Preliminary metal ion complexation studies with selected species (8c, 11-14) were also performed.

The influence of cis/trans isomerism on the physical properties of a cyano-bridged dinuclear mixed valence complex

The cyano-bridged complexes cis-[L14CoIIINCFeII(CN)5]– and cis-[L14CoIIINCFeIII(CN)5] (L14= 6-methyl-1,4,8,11-tetraazacyclotetradecan-6-amine) are prepared and characterised spectroscopically, electrochemically and structurally: Na{cis-[L14CoIIINCFeII(CN)5]}·9H2O, monoclinic space group P21/c, a= 14.758(3), b= 10.496(1), c= 19.359(3) , = 92.00(2)°, Z= 4; cis-[L14CoIIINCFeIII(CN)5]·4H2O, orthorhombic space group P212121, a= 9.492(1), b= 14.709(2), c= 18.760(3) , Z= 4. In both complexes, the pendant amine is cis to the bridging cyanide ligand. An analysis of the metal-to-metal charge transfer (MMCT) transition in these systems with Hush theory has been carried out. This has revealed that the change in the configuration of the macrocycle both decreases the redox isomer energy difference (E1/2) and increases the reorganisational energy () of the cis-[L14CoIIINCFeII(CN)5]– complex with respect to the trans-[L14CoIIINCFeII(CN)5]– complex, the result being that both isomers display an MMCT transition of similar energy. The variation in redox isomer energy differences of the configurational isomers has been related to strain energy differences by molecular mechanics analysis of the [CoL14Cl]2+/+ precursor complexes.

Three-dimensional space-borne synthetic aperture radar (SAR) imaging with multiple pass processing

Three-dimensional (3D) synthetic aperture radar (SAR) imaging via multiple-pass processing is an extension of interferometric SAR imaging. It exploits more than two flight passes to achieve a desired resolution in elevation. In this paper, a novel approach is developed to reconstruct a 3D space-borne SAR image with multiple-pass processing. It involves image registration, phase correction and elevational imaging. An image model matching is developed for multiple image registration, an eigenvector method is proposed for the phase correction and the elevational imaging is conducted using a Fourier transform or a super-resolution method for enhancement of elevational resolution. 3D SAR images are obtained by processing simulated data and real data from the first European Remote Sensing satellite (ERS-1) with the proposed approaches.

Calorimetric demonstration of the potential of molecular crowding to emulate the effect of an allosteric activator on pyruvate kinase kinetics

A method based on isothermal calorimetry is described for the direct kinetic assay of pyruvate kinase. In agreement with earlier findings based on the standard coupled assay system for this enzyme in the presence of a fixed ADP concentration, the essentially rectangular hyperbolic dependence of initial velocity upon phosphoenolpyruvate concentration is rendered sigmoidal by the allosteric inhibitor phenylalanine. This effect of phenylalanine can be countered by including a high concentration of a space- filling osmolyte such as proline in the reaction mixtures. This investigation thus affords a dramatic example that illustrates the need to consider potential consequences of thermodynamic nonideality on the kinetics of enzyme reactions in crowded molecular environments such as the cell cytoplasm.

Calculation of resonances and product state distributions for the unimolecular dissociation of H2S

Resonance phenomena associated with the unimolecular dissociation of H2S --> SH + H have been investigated quantum mechanically by the Lanczos homogeneous filter diagonalization method using a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). Resonance energies, widths (rates), and product state distributions have been obtained. Both dissociation rates and product state distributions of SH show, strong fluctuations, indicating that the dissociation of H2S is essentially irregular. Statistical analysis of neighboring level spacing and width distributions also confirms this behavior. The dissociation rates and product state distributions are compared to the predictions of quantum phase space theory.