Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Atom lasers, coherent states, and coherence. I. Physically realizable ensembles of pure states

A laser, be it an optical laser or an atom laser, is an open quantum system that produces a coherent beam of bosons (photons or atoms, respectively). Far above threshold, the stationary state rho(ss) of the laser mode is a mixture of coherent-field states with random phase, or, equivalently, a Poissonian mixture of number states. This paper answers the question: can descriptions such as these, of rho(ss) as a stationary ensemble of pure states, be physically realized? Here physical realization is as defined previously by us [H. M. Wiseman and J. A. Vaccaro, Phys. Lett. A 250, 241 (1998)]: an ensemble of pure states for a particular system can be physically realized if, without changing the dynamics of the system, an experimenter can (in principle) know at any time that the system is in one of the pure-state members of the ensemble. Such knowledge can be obtained by monitoring the baths to which the system is coupled, provided that coupling is describable by a Markovian master equation. Using a family of master equations for the (atom) laser, we solve for the physically realizable (PR) ensembles. We find that for any finite self-energy chi of the bosons in the laser mode, the coherent-state ensemble is not PR; the closest one can come to it is an ensemble of squeezed states. This is particularly relevant for atom lasers, where the self-energy arising from elastic collisions is expected to be large. By contrast, the number-state ensemble is always PR. As the self-energy chi increases, the states in the PR ensemble closest to the coherent-state ensemble become increasingly squeezed. Nevertheless, there are values of chi for which states with well-defined coherent amplitudes are PR, even though the atom laser is not coherent (in the sense of having a Bose-degenerate output). We discuss the physical significance of this anomaly in terms of conditional coherence (and hence conditional Bose degeneracy).

Dynamics of a strongly driven two-component Bose-Einstein condensate

We consider a two-component Bose-Einstein condensate in two spatially localized modes of a double-well potential, with periodic modulation of the tunnel coupling between the two modes. We treat the driven quantum field using a two-mode expansion and define the quantum dynamics in terms of the Floquet Operator for the time periodic Hamiltonian of the system. It has been shown that the corresponding semiclassical mean-field dynamics can exhibit regions of regular and chaotic motion. We show here that the quantum dynamics can exhibit dynamical tunneling between regions of regular motion, centered on fixed points (resonances) of the semiclassical dynamics.

Electric-field-induced Mott insulating states in organic field-effect transistors

We consider the possibility that the electrons injected into organic field-effect transistors are strongly correlated. A single layer of acenes can be modeled by a Hubbard Hamiltonian similar to that used for the κ-(BEDT-TTF)2X family of organic superconductors. The injected electrons do not necessarily undergo a transition to a Mott insulator state as they would in bulk crystals when the system is half-filled. We calculate the fillings needed for obtaining insulating states in the framework of the slave-boson theory and in the limit of large Hubbard repulsion U. We also suggest that these Mott states are unstable above some critical interlayer coupling or long-range Coulomb interaction.

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.

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.

Total synthesis and absolute stereochemistry of plakortone D

The first total synthesis of plakortone D is described and thereby establishes the structure and absolute stereochemistry of the most biologically active member of the marine-derived plakortone family. The sterically congested bicyclic lactone core results from a Pd(II)-induced hydroxycyclization−carbonylation−lactonization sequence on an enediol whose chirality was installed by AD-technology. Attachment of the side chain, also constructed using AD-methodology, was achieved by using a modified Julia coupling. The described approach enables acquisition of other plakortones and analogues, in the correct (natural) stereochemical series.

An XPS study of an isomorphous trivalent lanthanoid series

X-ray photoelectron spectroscopy has been used to investigate the core electron binding energies within an isomorphous series of lanthanoid complexes; [LnL(1)] where Ln=La-Lu (except Pm) and H3L is the heptadentate ligand 2,2',2-tris(salicylideneimino)triethylamine. This study also examines spin-orbit coupling of the trivalent lanthanoids bound to this organic ligand and addresses the issue of satellite peaks in the spectra. (C) 2002 Elsevier Science B.V. All rights reserved.

Fatigue-related changes in torque output and electromyographic parameters of trunk muscles during isometric axial rotation exertion - An investigation in patients with back pain and in healthy subjects

Study Design. A cross-sectional case-control study. Objectives. To examine the effect of fatigue on torque output as well as electromyographic frequency and amplitude values of trunk muscles during isometric axial rotation exertion in back pain patients and to compare the results with a matched control group. Summary of Background Data. Back pain patients exhibited different activation strategies in trunk muscles during the axial rotation exertions. Fatigue changes of abdominal and back muscles during axial rotation exertion have not been examined in patients with back pain. Methods. Twelve back pain patients and 12 matched controls performed isometric fatiguing axial rotation to both sides at 80% maximum voluntary contraction in a standing position. During the fatiguing exertion, electromyographic changes of rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum, and multifidus were recorded bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were also measured. Results. No difference in the endurance capacity was found between back pain and control groups. At the initial period of the exertion, back pain patients demonstrated a statistical trend (P = 0.058) of greater sagittal coupling torque as well as lower activity of rectus abdominis and multifidus and higher activity in external oblique. During the fatigue process similar changes of coupling torque were demonstrated in both sagittal and coronal planes, but a smaller fatigue rate for right external oblique, increase in median frequency for latissimus dorsi, and lesser increase in activity for back muscles were found in the back pain group compared with the control group. Conclusions. Alterations in electromyographic activation and fatigue rates of abdominal and back muscles demonstrated during the fatigue process provide insights into the muscle dysfunctions in back pain and may help clinicians to devise more rational treatment strategies.

Preparing encoded states in an oscillator

Recently a scheme has been proposed for constructing quantum error-correcting codes that embed a finite-dimensional code space in the infinite-dimensional Hilbert space of a system described by continuous quantum variables. One of the difficult steps in this scheme is the preparation of the encoded states. We show how these states can be generated by coupling a continuous quantum variable to a single qubit. An ion trap quantum computer provides a natural setting for a continuous system coupled to a qubit. We discuss how encoded states may be generated in an ion trap.

Modelling of microstructure formation and evolution during solidification

A comprehensive probabilistic model for simulating microstructure formation and evolution during solidification has been developed, based on coupling a Finite Differential Method (FDM) for macroscopic modelling of heat diffusion to a modified Cellular Automaton (mCA) for microscopic modelling of nucleation, growth of microstructures and solute diffusion. The mCA model is similar to Nastac's model for handling solute redistribution in the liquid and solid phases, curvature and growth anisotropy, but differs in the treatment of nucleation and growth. The aim is to improve understanding of the relationship between the solidification conditions and microstructure formation and evolution. A numerical algorithm used for FDM and mCA was developed. At each coarse scale, temperatures at FDM nodes were calculated while nucleation-growth simulation was done at a finer scale, with the temperature at the cell locations being interpolated from those at the coarser volumes. This model takes account of thermal, curvature and solute diffusion effects. Therefore, it can not only simulate microstructures of alloys both on the scale of grain size (macroscopic level) and the dendrite tip length (mesoscopic level), but also investigate nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies. The calculated results are compared with values of grain sizes and solidification morphologies of microstructures obtained from a set of casting experiments of Al-Si alloys in graphite crucibles.

EMG activity of trunk muscles and torque output during isometric axial rotation exertion: a comparison between back pain patients and matched controls

Abnormal patterns of trunk muscle activity could affect the biomechanics of spinal movements and result in back pain. The present study aimed to examine electromyographic (EMG) activity of abdominal and back muscles as well as triaxial torque output during isometric axial rotation at different exertion levels in back pain patients and matched controls. Twelve back pain patients and 12 matched controls performed isometric right and left axial rotation at 100%, 70%, 50%, and 30% maximum voluntary contractions in a standing position. Surface EMG activity of rectus abdominis, external oblique, internal oblique, latissimus dorsi, iliocostalis lumborum and multifidus were recorded bilaterally. The primary torque in the transverse plane and the coupling torques in sagittal and coronal planes were measured. Results showed that there was a trend (P = 0.08) of higher flexion coupling torque during left axial rotation exertion in back pain patients. Higher activity for external oblique and lower activity for multifidus was shown during left axial rotation exertion in back pain group when compared to the control group. In right axial rotation, back pain patients exhibited lesser activity of rectus abdominis at higher levels of exertion when compared with matched controls. These findings demonstrated that decreased activation of one muscle may be compensated by overactivity in other muscles. The reduced levels of activity of the multifidus muscle during axial rotation exertion in back pain patients may indicate that spinal stability could be compromised. Future studies should consider these alternations in recruitment patterns in terms of spinal stability and internal loading. The findings also indicate the importance of training for coordination besides the strengthening of trunk muscles during rehabilitation process. (C) 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.

Conformationally constrained macrocycles that mimic tripeptide beta-strands in water and aprotic solvents

The beta-strand conformation is unknown for short peptides in aqueous solution, yet it is a fundamental building block in proteins and the crucial recognition motif for proteolytic enzymes that enable formation and turnover of all proteins. To create a generalized scaffold as a peptidomimetic that is preorganized in a beta-strand, we individually synthesized a series of 15-22-membered macrocyclic analogues of tripeptides and analyzed their structures. Each cycle is highly constrained by two trans amide bonds and a planar aromatic ring with a short nonpeptidic linker between them. A measure of this ring strain is the restricted rotation of the component tyrosinyl aromatic ring (DeltaG(rot) 76.7 kJ mol(-1) (16-membered ring), 46.1 kJ mol(-1) (17-membered ring)) evidenced by variable temperature proton NMR spectra (DMF-d(7), 200-400 K). Unusually large amide coupling constants ((3)J(NH-CHalpha) 9-10 Hz) corresponding to large dihedral angles were detected in both protic and aprotic solvents for these macrocycles, consistent with a high degree of structure in solution. The temperature dependence of all amide NH chemical shifts (Deltadelta/T7-12 ppb/deg) precluded the presence of transannular hydrogen bonds that define alternative turn structures. Whereas similar sized conventional cyclic peptides usually exist in solution as an equilibrium mixture of multiple conformers, these macrocycles adopt a well-defined beta-strand structure even in water as revealed by 2-D NMR spectral data and by a structure calculation for the smallest (15-membered) and most constrained macrocycle. Macrocycles that are sufficiently constrained to exclusively adopt a beta-strand-mimicking structure in water may be useful pre-organized and generic templates for the design of compounds that interfere with beta-strand recognition in biology.

Solution Structures of the cis- and trans-Pro30 Isomers of a Novel 38-Residue Toxin from the Venom of Hadronyche Infensa sp. that Contains a Cystine-Knot Motif within Its Four Disulfide Bonds

The primary sequence and three-dimensional structure of a novel peptide toxin isolated from the Australian funnel-web spider Hadronyche infensa sp. is reported. ACTX-HI:OB4219 contains 38 amino acids, including eight-cysteine residues that form four disulfide bonds. The connectivities of these disulfide bonds were previously unknown but have been unambiguously determined in this study. Three of these disulfide bonds are arranged in an inhibitor cystine-knot (ICK) motif, which is observed in a range of other disulfide-rich peptide toxins. The motif incorporates an embedded ring in the structure formed by two of the disulfides and their connecting backbone segments penetrated by a third disulfide bond. Using NMR spectroscopy, we determined that despite the isolation of a single native homologous product by RP-HPLC, ACTX-HI:OB4219 possesses two equally populated conformers in solution. These two conformers were determined to arise from cis/trans isomerization of the bond preceding Pro30. Full assignment of the NMR spectra for both conformers allowed for the calculation of their structures, revealing, the presence of a triple-stranded antiparallel sheet consistent with the inhibitor cystine-knot (ICK) motif.

The Three-dimensional Solution Structure of NaD1, a New Floral Defensin from Nicotiana alata and its Application to a Homology Model of the Crop Defense Protein alfAFP

NMR spectroscopy and simulated annealing calculations have been used to determine the three-dimensional structure of NaD1, a novel antifungal and insecticidal protein isolated from the flowers of Nicotiana alata. NaD1 is a basic, cysteine-rich protein of 47 residues and is the first example of a plant defensin from flowers to be characterized structurally. Its three-dimensional structure consists of an a-helix and a triple-stranded anti-parallel beta-sheet that are stabilized by four intramolecular disulfide bonds. NaD1 features all the characteristics of the cysteine-stabilized up motif that has been described for a variety of proteins of differing functions ranging from antibacterial insect defensins and ion channel-perturbing scorpion toxins to an elicitor of the sweet taste response. The protein is biologically active against insect pests, which makes it a potential candidate for use in crop protection. NaD1 shares 31% sequence identity with alfAFP, an antifungal protein from alfalfa that confers resistance to a fungal pathogen in transgenic potatoes. The structure of NaD1 was used to obtain a homology model of alfAFP, since NaD1 has the highest level of sequence identity with alfAFP of any structurally characterized antifungal defensin. The structures of NaD1 and alfAFP were used in conjunction with structure - activity data for the radish defensin Rs-AFP2 to provide an insight into structure-function relationships. In particular, a putative effector site was identified in the structure of NaD1 and in the corresponding homology model of alfAFP. (C) 2002 Elsevier Science Ltd. All rights reserved.