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.

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.

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.

Entanglement creation using quantum interrogation

We present some applications of high-efficiency quantum interrogation (interaction-free measurement) for the creation of entangled states of separate atoms and of separate photons. The quantum interrogation of a quantum object in a superposition of object-in and object-out leaves the object and probe in an entangled state. The probe can then be further entangled with other objects in subsequent quantum interrogations. By then projecting out those cases in which the probe is left in a particular final state, the quantum objects can themselves be left in various entangled states. In this way, we show how to generate two-, three-, and higher-qubit entanglement between atoms and between photons. The effect of finite efficiency for the quantum interrogation is delineated for the various schemes.

Temperature dependence of polaronic transport through single molecules and quantum dots

Motivated by recent experiments on electric transport through single molecules and quantum dots, we investigate a model for transport that allows for significant coupling between the electrons and a boson mode isolated on the molecule or dot. We focus our attention on the temperature-dependent properties of the transport. In the Holstein picture for polaronic transport in molecular crystals the temperature dependence of the conductivity exhibits a crossover from coherent (band) to incoherent (hopping) transport. Here, the temperature dependence of the differential conductance on resonance does not show such a crossover, but is mostly determined by the lifetime of the resonant level on the molecule or dot.

Quantum correlated twin atomic beams via photodissociation of a molecular Bose-Einstein condensate

We study the process of photodissociation of a molecular Bose-Einstein condensate as a potential source of strongly correlated twin atomic beams. We show that the two beams can possess nearly perfect quantum squeezing in their relative numbers.

GH treatment in adults with chronic liver disease: A randomized, double-blind, placebo-controlled, cross-over study

Patients with chronic liver disease (CLD) are catabolic and GH-resistant. The effects of supraphysiological recombinant human GH (rhGH; 0.2 IU.kg(-1).d(-1)) treatment in adults with CLD were assessed in a randomized, double-blind, placebo-controlled cross-over trial (4-wk dietary run-in, 4-wk treatment, and 2-wk wash-out phases). Nine adults with mild- to moderate-severity CLD participated (median age, 49 yr; three males and six females; Child's classification A in six and B in three). Biopsy-proven etiologies were: alcohol (four patients), primary biliary cirrhosis (three patients), non-A, non-B, non-C hepatitis (one patient), and cryptogenic (one patient). Treatment with rhGH increased serum IGF-I (median increase over placebo, +93 mug.liter(-1); P = 0.004), IGF-binding protein-3 (+0.9 mg.liter(-1): P = 0.004), and acid labile subunit (+10.7 nM; P = 0.004). Total body potassium (+8.0 g; P = 0.023), body weight (+1.6 kg; P = 0.008), and total body water (by bioelectrical impedance; +4.9 kg; P = 0.004) increased. Resting metabolic rate (+313 ml.kg(-1).min(-1); P = 0.004) and lipid oxidation (+1072.0 kcal.d(-1); P = 0.032) increased. Metabolic changes included increased fasting plasma glucose (+1.2 mm; P = 0.008), insulin (+33.8 mU.liter(-1); P = 0.004), C-peptide (+0.7 nM; P = 0.004), and free-fatty acids (+0.1 mEq.liter(-1); P = 0.04). Clinical side effects included worsening edema and ascites. Hepatocellular function did not change. Therefore, rbGH treatment in CLD: 1) overcame hepatic GH resistance; 2) may have improved whole-body protein catabolism; 3) increased lipolysis and lipid oxidation; 4) increased insulin resistance; and 5) had potent antinatriuretic effects. Long-term safety and efficacy require further assessment.

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.

Implementing the quantum random walk

Recently, several groups have investigated quantum analogues of random walk algorithms, both on a line and on a circle. It has been found that the quantum versions have markedly different features to the classical versions. Namely, the variance on the line, and the mixing time on the circle increase quadratically faster in the quantum versions as compared to the classical versions. Here, we propose a scheme to implement the quantum random walk on a line and on a circle in an ion trap quantum computer. With current ion trap technology, the number of steps that could be experimentally implemented will be relatively small. However, we show how the enhanced features of these walks could be observed experimentally. In the limit of strong decoherence, the quantum random walk tends to the classical random walk. By measuring the degree to which the walk remains quantum, '' this algorithm could serve as an important benchmarking protocol for ion trap quantum computers.

Quantum dynamics of two coupled qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as nonpositive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. It is this feature that enables the quantum system to evolve to an entangled state. We conclude that the dynamics are a quantum element of nuclear magnetic resonance quantum-information processing. There are two limits where our quantum evolution coincides with the classical one: the short-time limit before spin-spin interaction sets in and the long-time limit when phase diffusion is incorporated.

Coherent superposition states as quantum rulers

We explore the sensitivity of an interferometer based on a quantum circuit for coherent states. We show that its sensitivity is at the Heisenberg limit. Moreover, we show that this arrangement can measure very small length intervals.

Universal quantum computation and simulation using any entangling Hamiltonian and local unitaries

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? We provide an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling n-qubit Hamiltonian and local unitary operations. It follows that universal quantum computation can be performed using any entangling interaction and local unitary operations.

Universal simulation of Hamiltonian dynamics for quantum systems with finite-dimensional state spaces

What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd [Phys. Rev. A 65, 040301(R) (2002)] provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired two-body Hamiltonian evolution using any fixed two-body entangling N-qubit Hamiltonian, and local unitaries. We extend this result to the case where the component systems are qudits, that is, have D dimensions. As a consequence we explain how universal quantum computation can be performed with any fixed two-body entangling N-qudit Hamiltonian, and local unitaries.