Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics I. Theory

The quasi mode theory of macroscopic quantization in quantum optics and cavity QED developed by Dalton, Barnett and Knight is generalized. This generalization allows for cases in which two or more quasi permittivities, along with their associated mode functions, are needed to describe the classical optics device. It brings problems such as reflection and refraction at a dielectric boundary, the linear coupler, and the coupling of two optical cavities within the scope of the theory. For the most part, the results that are obtained here are simple generalizations of those obtained in previous work. However the coupling constants, which are of great importance in applications of the theory, are shown to contain significant additional terms which cannot be 'guessed' from the simpler forms. The expressions for the coupling constants suggest that the critical factor in determining the strength of coupling between a pair of quasi modes is their degree of spatial overlap. In an accompanying paper a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary is given as an illustration of the generalized theory. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes.

Generalized quasi mode theory of macroscopic canonical quantization in cavity quantum electrodynamics and quantum optics II. Application to reflection and refraction at a dielectric interface

The generalization of the quasi mode theory of macroscopic quantization in quantum optics and cavity QED presented in the previous paper, is applied to provide a fully quantum theoretic derivation of the laws of reflection and refraction at a boundary. The quasi mode picture of this process involves the annihilation of a photon travelling in the incident region quasi mode, and the subsequent creation of a photon in either the incident region or transmitted region quasi modes. The derivation of the laws of reflection and refraction is achieved through the dual application of the quasi mode theory and a quantum scattering theory based on the Heisenberg picture. Formal expressions from scattering theory are given for the reflection and transmission coefficients. The behaviour of the intensity for a localized one photon wave packet coming in at time minus infinity from the incident direction is examined and it is shown that at time plus infinity, the light intensity is only significant where the classical laws of reflection and refraction predict. The occurrence of both refraction and reflection is dependent upon the quasi mode theory coupling constants between incident and transmitted region quasi modes being nonzero, and it is seen that the contributions to such coupling constants come from the overlap of the mode functions in the boundary layer region, as might be expected from a microscopic theory.

Cavity QED analog of the harmonic-oscillator probability distribution function and quantum collapses

We establish a connection between the simple harmonic oscillator and a two-level atom interacting with resonant, quantized cavity and strong driving fields, which suggests an experiment to measure the harmonic-oscillator's probability distribution function. To achieve this, we calculate the Autler-Townes spectrum by coupling the system to a third level. We find that there are two different regions of the atomic dynamics depending on the ratio of the: Rabi frequency Omega (c) of the cavity field to that of the Rabi frequency Omega of the driving field. For Omega (c)

Quantum slow motion

We investigate the center-of-mass motion of cold atoms in a standing amplitude modulated laser field. We use a simple model to explain the momentum distribution of the atoms after any distinct number of modulation cycles. The atoms starting near a classical phase-space resonance move slower than we would expect classically. We explain this by showing that for a wave packet on the classical resonances we can replace the complicated dynamics in the quantum Liouville equation in phase space by its classical dynamics with a modified potential.

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.

Reversal of cardiovascular remodelling with candesart

Cardiovascular remodelling, defined as ventricular and vascular hypertrophy together with fibrosis, characterises hypertension following inhibition of the production of the endogenous vasodilator, nitric oxide (NO). This study has determined whether the cardiovascular remodelling following chronic NO synthase inhibition can e reversed by administration of the selective angiotensin II AT(1)-receptor antagonist, candesartan. Male Wistar rats were treated with L-nitroarginine methyl ester (L-NAME, 400 mg/l in drinking water) for eight weeks and with candesartan cilexetil (2 mg/kg/day by oral gavage) for the last four weeks. L-NAME-treated rats became hypertensive with systolic blood pressure increasing from 110 +/- 4 mmHg (control) to 170 +/- 10 mmHg. Rats developed left ventricular hypertrophy (control 1.70 +/- 0.06; L-NAME 2.10 +/- 0.04 mg/kg body wt) with markedly increased deposition of perivascular and interstitial collagen. Candesartan returned blood pressure, left ventricular weights and collagen deposition to control values. Echo cardiographic assessment showed concentric hypertrophy with an increased fractional shortening; this was reversed by candesartan treatment. Heart failure was not evident. In the isolated Langendorff heart, diastolic stiffness increased in L-NAME-treated rats while the rate of increase in pressure (+dP/dt) increased after eight weeks only; candesartan reduced collagen deposition and normalised +dP/dt. In isolated left ventricular papillary muscles, the potency (negative log EC50) of noradrenaline as a positive inotropic compound was unchanged, (control 6.56 +/- 0.14); maximal increase in force before ectopic beats was reduced from 5.0 +/- 0.4 mN to 2.0 +/- 0.2 mN. Noradrenaline potency as a vasoconstrictor in thoracic aortic rings was unchanged, but maximal contraction was markedly reduced from 25.2 +/- 2.0 mN to 3.0 +/- 0.3 mN; this was partially reversed by candesartan treatment. Thus, chronic inhibition of NO production with L-NAME induces hypertension, hypertrophy and fibrosis with increased toxicity and significant decreases in vascular responses to noradrenaline. These changes were at least partially reversible by treatment with candesartan, implying a significant role of AT(1)-receptors in L-NAME-induced cardiovascular changes.

Quasimode theory of quantum optical processes in photonic band gap materials

This paper deals with atomic systems coupled to a structured reservoir of quantum EM field modes, with particular relevance to atoms interacting with the field in photonic band gap materials. The case of high Q cavities has been treated elsewhere using Fano diagonalization based on a quasimode approach, showing that the cavity quasimodes are responsible for pseudomodes introduced to treat non-Markovian behaviour. The paper considers a simple model of a photonic band gap case, where the spatially dependent permittivity consists of a constant term plus a small spatially periodic term that leads to a narrow band gap in the spectrum of mode frequencies. Most treatments of photonic band gap materials are based on the true modes, obtained numerically by solving the Helmholtz equation for the actual spatially periodic permittivity. Here the field modes are first treated in terms of a simpler quasimode approach, in which the quasimodes are plane waves associated with the constant permittivity term. Couplings between the quasimodes occur owing to the small periodic term in the permittivity, with selection rules for the coupled modes being related to the reciprocal lattice vectors. This produces a field Hamiltonian in quasimode form. A matrix diagonalization method may be applied to relate true mode annihilation operators to those for quasimodes. The atomic transitions are coupled to all the quasimodes, and the true mode atom-EM field coupling constants (one-photon Rabi frequencies) are related to those for the quasimodes and also expressions are obtained for the true mode density. The results for the one-photon Rabi frequencies differ from those assumed in other work. Expressions for atomic decay rates are obtained using the Fermi Golden rule, although these are valid only well away from the band gaps.

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.

Quantum dynamics of spin polarized optoelectronic processes

We study the quantum dynamics of the emission of multimodal polarized light in light emitting devices (LED) due to spin polarized carriers injection. We present the equations for photon number and carrier numbers, and calculate the polarisation degree of the light generated by LED. (C) 2002 Elsevier Science B.V. All rights reserved.

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.

PFG-NMR measurements of the self-diffusion coefficients of water in equilibrium poly(HEMA-co-THFMA) hydrogels

The self-diffusion coefficients for water in a series of copolymers of 2-hydroxyethyl methacrylate, HEMA, and tetrahydrofurfuryl methacrylate, THFMA, swollen with water to their equilibrium states have been studied at 310 K using PFG-NMR. The self-diffusion coefficients calculated from the Stejskal-Tanner equation, D-obs, for all of the hydrated polymers were found to be dependent on the NMR storage time, as a result of spin exchange between the proton reservoirs of the water and the polymers, reaching an equilibrium plateau value at long storage times. The true values of the diffusion coefficients were calculated from the values of D-obs, in the plateau regions by applying a correction for the fraction of water protons present, obtained from the equilibrium water contents of the gels. The true self-diffusion coefficient for water in polyHEMA obtained at 310 K by this method was 5.5 x 10(-10) m(2) s(-1). For the copolymers containing 20% HEMA or more a single value of the self-diffusion coefficient was found, which was somewhat larger than the corresponding values obtained for the macroscopic diffusion coefficient from sorption measurements. For polyTHFMA and copolymers containing less than 20% HEMA, the PFG-NMR stimulated echo attenuation decay curves and the log-attenuation plots were characteristic of the presence of two diffusing water species. The self-diffusion coefficients of water in the equilibrium-hydrated copolymers were found to be dependent on the copolymer composition, decreasing with increasing THFMA content.

Use of stress echocardiography to predict mortality in patients with diabetes and known or suspected coronary artery disease

OBJECTIVE - This study sought to determine whether stress echocardiography using exercise (when feasible) or dobutamine echo could be used to predict mortality in patients with diabetes. RESEARCH DESIGN AND METHODS - Stress echo was performed in 937 patients with diabetes (aged 59 +/- 13 years, 529 men) for symptom evaluation (42%) and follow-up of known coronary artery disease (CAD) (58%). Stress echocardiography using exercise was performed in 333 patients able to exercise maximally, and dobutamine echo using a standard dobutamine stress was used in 604 patients. Patients were followed for less than or equal to9 years (mean 3.9 +/- 2.3) for all-cause mortality. RESULTS - Normal studies were obtained in 567 (60%) patients; 29% had resting left ventricular (LV) dysfunction, and 25% had ischemia. Abnormalities were confined to one territory in 183 (20%) patients and to multiple territories in 187 (20%) patients. Death (in 275 [29%] patients) was predicted by referral for pharmacologic stress (hazard ratio [HR] 3.94, P < 0.0001), ischemia (1.77, P <0.0001), age (1.02, P = 0.002), and heart failure (1.54, P = 0.01). The risk of death in patients With a normal scan was 4% per year, and this was associated with age and selection for pharmacologic stress testing. In stepwise models replicating the sequence of clinical evaluation, the predictive power of independent clinical predictors (age, selection for pharmacologic stress, previous infarction, and heart failure; model chi(2) = 104.8) was significantly enhanced by addition of stress echo data (model chi(2) = 122.9). CONCLUSIONS - The results of stress echo are independent predictors of death in diabetic patients with known or suspected CAD.. Ischemia adds risk that is incremental to clinical risks and LV dysfunction.

Prediction of outcomes in hypertensive patients with suspected coronary disease

Stress echocardiography has been shown to improve the diagnosis of coronary artery disease in the presence of hypertension, but its value in prognostic evaluation is unclear. We sought to determine whether stress echocardiography could be used to predict mortality in 2363 patients with hypertension, who were followed for up to 10 years (mean 4.0+/-1.8) for death and revascularization. Stress echocardiograms were normal in 1483 patients (63%), 16% had resting left ventricular (LV) dysfunction alone, and 21% had ischemia. Abnormalities were confined to one territory in 489 patients (21%) and to multiple territories in 365 patients (15%). Cardiac death was less frequent among the patients able to exercise than among those undergoing dobutamine echocardiography (4% versus 7%, P<0.001). The risk of death in patients with a negative stress echocardiogram was <1% per year. Ischemia identified by stress echocardiography was an independent predictor of mortality in those able to exercise (hazard ratio 2.21, 95% confidence intervals 1.10 to 4.43, P=0.0001) as well as those undergoing dobutamine echo (hazard ratio 2.39, 95% confidence intervals 1.53 to 3.75, P=0.0001); other predictors were age, heart failure, resting LV dysfunction, and the Duke treadmill score. In stepwise models replicating the sequence of clinical evaluation, the results of stress echocardiography added prognostic power to models based on clinical and stress-testing variables. Thus, the results of stress echocardiography are an independent predictor of cardiac death in hypertensive patients with known or suspected coronary artery disease, incremental to clinical risks and exercise results.

Usefulness of clinical risk markers and ischemic threshold to stratify risk in patients undergoing major noncardiac surgery

The risk of cardiac events in patients undergoing major noncardiac surgery is dependent on their clinical characteristics and the results of stress testing. The purpose of this study was to develop a composite approach to defining levels of risk and to examine whether different approaches to prophylaxis influenced this prediction of outcome. One hundred forty-five consecutive patients (aged 68 +/- 9 years, 79 men) with >1 clinical risk variable were studied with standard dobutamine-atropine stress echo before major noncardiac surgery. Risk levels were stratified according to the presence of ischemia (new or worsening wall motion abnormality), ischemic threshold (heart rate at development of ischemia), and number of clinical risk variables. Patients were followed for perioperative events (during hospital admission) and death or infarction over the subsequent 16 10 months. Ten perioperative events occurred in 105 patients who proceeded to surgery (10%, 95% confidence interval [CI] 5% to 17%), 40 being cancelled because of cardiac or other risk. No ischemia was identified in 56 patients, 1 of whom (1.8%) had a perioperative infarction. Of the 49 patients with ischemia, 22 (45%) had 1 or 2 clinical risk factors; 2 (9%, 95% CI 1% to 29%) had events. Another 15 patients had a high ischemic threshold and 3 or 4 risk factors; 3 (20%, 95% Cl 4% to 48%) had events. Twelve patients had a low ischemic threshold and 3 or 4 risk factors; 4 (33%, 95% CI 10% to 65%) had events. Preoperative myocardial revascularization was performed in only 3 patients, none of whom had events. Perioperative and long-term events occurred despite the use of beta blockers; 7 of 41 eta blocker-treated patients had a perioperative event (17%, 95% CI 7% to 32%); these treated patients were at higher anticipated risk than untreated patients (20 +/- 24% vs 10 +/- 19%, p = 0.02). The total event rate over late follow-up was 13%, and was predicted by dobutamine-atropine stress echo results and heart rate response. (C) 2002 by Excerpta Medica, Inc.

Refinements in stress echocardiographic techniques improve inter-institutional agreement in interpretation of dobutamine stress echocardiograms

Aims To determine the degree of inter-institutional agreement in the assessment of dobutamine stress echocardiograms using modern stress echo cardiographic technology in combination with standardized data acquisition and assessment criteria. Method and Results Among six experienced institutions, 150 dobutamine stress echocardiograms (dobutamine up to 40 mug.kg(-1) min(-1) and atropine up to I mg) were performed on patients with suspected coronary artery disease using fundamental and harmonic imaging following a consistent digital acquisition protocol. Each dobutamine stress echocardiogram was assessed at every institution regarding endocardial visibility and left ventricular wall motion without knowledge of any other data using standardized reading criteria. No patients were excluded due to poor image quality or inadequate stress level. Coronary angiography was performed within 4 weeks. Coronary angiography demonstrated significant coronary artery disease (less than or equal to50% diameter stenosis) in 87 patients. Using harmonic imaging an average of 5.2+/-0.9 institutions agreed on dobutamine stress echocardiogram results as being normal or abnormal (mean kappa 0.55; 95% CI 0.50-0.60). Agreement was higher in patients with no (equal assessment of dobutamine stress echocardiogram results by 5.5 +/- 0.8 institutions) or three-vessel coronary artery disease (5.4 +/- 0.8 institutions) and lower in one- or two- vessel disease (5.0 +/- 0.9 and 5.2 +/- 1.0 institutions, respectively-, P=0.041). Disagreement on test results was greater in only minor wall motion abnormalities. Agreement on dobutamine stress echocardiogram results was lower using fundamental imaging (mean kappa 0.49; 95% CI 0.44-0.54; P