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.

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Polarization squeezing and continuous-variable polarization entanglement

A concept of polarization entanglement for continuous variables is introduced. For this purpose the Stokes-parameter operators and the associated Poincare sphere, which describe the quantum-optical polarization properties of light, are defined and their basic properties are reviewed. The general features of the Stokes operators are illustrated by evaluation of their means and variances for a range of simple polarization states. Some of the examples show polarization squeezing, in which the variances of one or more Stokes parameters are smaller than the coherent-state value. The main object of the paper is the application of these concepts to bright squeezed light. It is shown that a light beam formed by interference of two orthogonally polarized quadrature-squeezed beams exhibits squeezing in some of the Stokes parameters. Passage of such a primary polarization-squeezed beam through suitable optical components generates a pair of polarization-entangled light beams with the nature of a two-mode squeezed state. Implementation of these schemes using the double-fiber Sagnac interferometer provides an efficient method for the generation of bright nonclassical polarization states. The important advantage of these nonclassical polarization states for quantum communication is the possibility of experimentally determining all of the relevant conjugate variables of both squeezed and entangled fields using only linear optical elements followed by direct detection.

Teleportation improvement by conditional measurements on the two-mode squeezed vacuum

We show that by making conditional measurements on the Einstein-Podolsky-Rosen (EPR) squeezed vacuum [T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000)], one can improve the efficacy of teleportation for both the position-difference, momentum-sum, and number-difference, phase-sum continuous variable teleportation protocols. We investigate the relative abilities of the standard and conditional EPR states, and show that by conditioning we can improve the fidelity of teleportation of coherent states from below to above the (F) over bar =2/3 boundary, thereby achieving unambiguously quantum teleportation.

Bayesian feedback versus Markovian feedback in a two-level atom

We compare two different approaches to the control of the dynamics of a continuously monitored open quantum system. The first is Markovian feedback, as introduced in quantum optics by Wiseman and Milburn [Phys. Rev. Lett. 70, 548 (1993)]. The second is feedback based on an estimate of the system state, developed recently by Doherty and Jacobs [Phys. Rev. A 60, 2700 (1999)]. Here we choose to call it, for brevity, Bayesian feedback. For systems with nonlinear dynamics, we expect these two methods of feedback control to give markedly different results. The simplest possible nonlinear system is a driven and damped two-level atom, so we choose this as our model system. The monitoring is taken to be homodyne detection of the atomic fluorescence, and the control is by modulating the driving. The aim of the feedback in both cases is to stabilize the internal state of the atom as close as possible to an arbitrarily chosen pure state, in the presence of inefficient detection and other forms of decoherence. Our results (obtained without recourse to stochastic simulations) prove that Bayesian feedback is never inferior, and is usually superior, to Markovian feedback. However, it would be far more difficult to implement than Markovian feedback and it loses its superiority when obvious simplifying approximations are made. It is thus not clear which form of feedback would be better in the face of inevitable experimental imperfections.

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.

The damped and coherently-driven Jaynes-Cummings model

We investigate the influence of a single-mode cavity on the Autler-Townes doublet that arises when a three-level atom is strongly driven by a laser field tuned to one of the atomic transitions and probed by a tunable, weak field coupled to the other transition. We assume that the cavity mode is coupled to the driven transition and the cavity and laser frequencies are equal to the atomic transition frequency. We find that the Autler-Townes spectrum can have one, two or three peaks depending on the relative magnitudes of the Rabi frequencies of the cavity and driving fields. We show that, in order to understand the three-peaked spectrum, it is necessary to go beyond the secular approximation, leading to interesting quantum interference effects. We find that the positions and relative intensities of the three spectral components are affected strongly by the atom-cavity coupling strength g and the cavity damping K. For an increasing g and/or decreasing K the triplet evolves into a single peak. This results in 'undressing' of the system such that the atom collapses into its ground state. We interpret the spectral features in terms of the semiclassical dressed-atom model, and also provide complementary views of the cavity effects in terms of quantum Langevin equations and the fully quantized, 'double -dressing' model.

Simulations of thermal Bose fields in the classical limit

We demonstrate that the time-dependent projected Gross-Pitaevskii equation (GPE) derived earlier [M. J. Davis, R. J. Ballagh, and K. Burnett, J. Phys. B 34, 4487 (2001)] can represent the highly occupied modes of a homogeneous, partially-condensed Bose gas. Contrary to the often held belief that the GPE is valid only at zero temperature, we find that this equation will evolve randomized initial wave functions to a state describing thermal equilibrium. In the case of small interaction strengths or low temperatures, our numerical results can be compared to the predictions of Bogoliubov theory and its perturbative extensions. This demonstrates the validity of the GPE in these limits and allows us to assign a temperature to the simulations unambiguously. However, the GPE method is nonperturbative, and we believe it can be used to describe the thermal properties of a Bose gas even when Bogoliubov theory fails. We suggest a different technique to measure the temperature of our simulations in these circumstances. Using this approach we determine the dependence of the condensate fraction and specific heat on temperature for several interaction strengths, and observe the appearance of vortex networks. Interesting behavior near the critical point is observed and discussed.

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.

The radiation chemistry of ultem at 77 K as revealed by ESR spectroscopy

Radical formation in ultem following gamma-radiolysis has been reassessed, and the G(R*) values at different temperatures have been determined by ESR spectroscopy. The radical assignment and radical reactivity have been re-examined by photobleaching and thermal annealing studies. Photobleachable radical anions were found to comprise approximate to40% of the total number of radicals formed on radiolysis at 77 K. Spectral subtraction methods, ESR spectral simulations, measurement of g-values and the hyperfine splitting constants were used to identify the other radical intermediates. The principal chain scission radicals are formed due to scission of the main-chain at (i) the ether linkage, (ii) the isopropylidene group and (iii) the imide ring in the main chain. The side chain methyl groups of the isopropylidine units also lose hydrogen to form methylene radicals. The five-line spectrum observed to decay in the temperature range 370-430 K, which has not been assigned previously, has been identified as being characteristic of a di-substituted benzyl radical. (C) 2002 Elsevier Science Ltd. All rights reserved.

From molecular complexes to zwitterions and final products. Reactions between C3O2 and amines

The formation of molecular complexes (prereactive intermediates) between C3O2 and amines (ammonia, dimethylamine, trimethylamine, and 4-(dimethylamino)pyridine) as well as the subsequent transformation of the complexes into C3O2-amine zwitterions in cryogenic matrixes (ca. 40 K) has been observed. In the case of dimethylamine, the formation of tetramethylmalonamide has also been documented. Calculations using density functional theory (B3LYP/6-31G(2d, p)) are used to assign all above species and are in excellent agreement with the IR spectra.

A real symmetric Lanczos subspace implementation of quantum scattering using boundary inhomogeneities

We present an efficient and robust method for calculating state-to-state reaction probabilities utilising the Lanczos algorithm for a real symmetric Hamiltonian. The method recasts the time-independent Artificial Boundary Inhomogeneity technique recently introduced by Jang and Light (J. Chem. Phys. 102 (1995) 3262) into a tridiagonal (Lanczos) representation. The calculation proceeds at the cost of a single Lanczos propagation for each boundary inhomogeneity function and yields all state-to-state probabilities (elastic, inelastic and reactive) over an arbitrary energy range. The method is applied to the collinear H + H-2 reaction and the results demonstrate it is accurate and efficient in comparison with previous calculations. (C) 2002 Elsevier Science B.V. All rights reserved.

Efficient time-independent wave packet scattering calculations within a Lanczos subspace: H+O-2 (J=0) state-to-state reaction probabilities

An efficient Lanczos subspace method has been devised for calculating state-to-state reaction probabilities. The method recasts the time-independent wave packet Lippmann-Schwinger equation [Kouri , Chem. Phys. Lett. 203, 166 (1993)] inside a tridiagonal (Lanczos) representation in which action of the causal Green's operator is affected easily with a QR algorithm. The method is designed to yield all state-to-state reaction probabilities from a given reactant-channel wave packet using a single Lanczos subspace; the spectral properties of the tridiagonal Hamiltonian allow calculations to be undertaken at arbitrary energies within the spectral range of the initial wave packet. The method is applied to a H+O-2 system (J=0), and the results indicate the approach is accurate and stable. (C) 2002 American Institute of Physics.

Lanczos subspace time-independent wave packet calculations of S(D-1)+H-2 reactive scattering

In this paper. we present the results of quantum dynamical simulations of the S (D-1) + H-2 insertion reaction on a newly developed potential energy surface (J. Chem. Phys. 2001, 114, 320). State-to-state reaction probabilities. product state distributions, and initial-state resolved cumulative reaction probabilities from a given incoming reactant channel are obtained from a time-independent wave packet analysis, performed within a single Lanczos subspace. Integral reaction cross sections are then estimated by J-shifting method and compared with the results from molecular beam experiment and QCT calculations.