Dark periods and revivals of entanglement in a two-qubit system

In a recent paper Yu and Eberly [Phys. Rev. Lett. 93, 140404 (2004)] have shown that two initially entangled and afterward not interacting qubits can become completely disentangled in a finite time. We study transient entanglement between two qubits coupled collectively to a multimode vacuum field, assuming that the two-qubit system is initially prepared in an entangled state produced by the two-photon coherences, and find the unusual feature that the irreversible spontaneous decay can lead to a revival of the entanglement that has already been destroyed. The results show that this feature is independent of the coherent dipole-dipole interaction between the atoms but it depends critically on whether or not collective damping is present.

Co-registration of magnetoencephalography with magnetic resonance imaging using bite-bar-based fiducials and surface-matching

Objective: To introduce a new technique for co-registration of Magnetoencephalography (MEG) with magnetic resonance imaging (MRI). We compare the accuracy of a new bite-bar with fixed fiducials to a previous technique whereby fiducial coils were attached proximal to landmarks on the skull. Methods: A bite-bar with fixed fiducial coils is used to determine the position of the head in the MEG co-ordinate system. Co-registration is performed by a surface-matching technique. The advantage of fixing the coils is that the co-ordinate system is not based upon arbitrary and operator dependent fiducial points that are attached to landmarks (e.g. nasion and the preauricular points), but rather on those that are permanently fixed in relation to the skull. Results: As a consequence of minimizing coil movement during digitization, errors in localization of the coils are significantly reduced, as shown by a randomization test. Displacement of the bite-bar caused by removal and repositioning between MEG recordings is minimal (∼0.5 mm), and dipole localization accuracy of a somatosensory mapping paradigm shows a repeatability of ∼5 mm. The overall accuracy of the new procedure is greatly improved compared to the previous technique. Conclusions: The test-retest reliability and accuracy of target localization with the new design is superior to techniques that incorporate anatomical-based fiducial points or coils placed on the circumference of the head. © 2003 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

The topographic distribution of the magnetic P100M to full- and half-field stimulation

Visual evoked magnetic responses were recorded to full-field and left and right half-field stimulation with three check sizes (70′, 34′ and 22′) in five normal subjects. Recordings were made sequentially on a 20-position grid (4 × 5) based on the inion, by means of a single-channel direct current-Superconducting Quantum Interference Device second-order gradiometer. The topographic maps were consistent on the same subjects recorded 2 months apart. The half-field responses produced the strongest signals in the contralateral hemisphere and were consistent with the cruciform model of the calcarine fissure. Right half fields produced upper-left-quadrant outgoing fields and lower-left-quadrant ingoing fields, while the left half field produced the opposite response. The topographic maps also varied with check size, with the larger checks producing positive or negative maximum position more anteriorly than small checks. In addition, with large checks the full-field responses could be explained as the summation of the two half fields, whereas full-field responses to smaller checks were more unpredictable and may be due to sources located at the occipital pole or lateral surface. In addition, dipole sources were located as appropriate with the use of inverse problem solutions. Topographic data will be vital to the clinical use of the visual evoked field but, in addition, provides complementary information to visual evoked potentials, allowing detailed studies of the visual cortex. © 1992 Kluwer Academic Publishers.

Attentional modulation of oscillatory activity in human visual cortex

The effects of attentional modulation on activity within the human visual cortex were investigated using magnetoencephalography. Chromatic sinusoidal stimuli were used to evoke activity from the occipital cortex, with attention directed either toward or away from the stimulus using a bar-orientation judgment task. For five observers, global magnetic field power was plotted as a function of time from stimulus onset. The major peak of each function occurred at about 120 ms latency and was well modeled by a current dipole near the calcarine sulcus. Independent component analysis (ICA) on the non-averaged data for each observer also revealed one component of calcarine origin, the location of which matched that of the dipolar source determined from the averaged data. For two observers, ICA revealed a second component near the parieto-occipital sulcus. Although no effects of attention were evident using standard averaging procedures, time-varying spectral analyses of single trials revealed that the main effect of attention was to alter the level of oscillatory activity. Most notably, a sustained increase in alpha-band (7-12 Hz) activity of both calcarine and parieto-occipital origin was evident. In addition, calcarine activity in the range of 13-21 Hz was enhanced, while calcarine activity in the range of 5-6 Hz was reduced. Our results are consistent with the hypothesis that attentional modulation affects neural processing within the calcarine and parieto-occipital cortex by altering the amplitude of alpha-band activity and other natural brain rhythms. © 2003 Elsevier Inc. All rights reserved.

Topographic mapping and source localization of the pattern reversal visual evoked magnetic response

The topography of the visual evoked magnetic response (VEMR) to pattern reversal stimulation was studied in four normal subjects using a single channel BTI magnetometer. VEMRs were recorded from 20 locations over the occipital scalp and the topographic distribution of the most consistent component (P100M) studied. A single dipole in a sphere model was fitted to the data. Topographic maps were similar when recorded two months apart on the same subject to the same stimulus. Half field (HF) stimulation elicited responses from sources on the medial surface of the calcarine fissure mainly in the contralateral hemisphere as predicted by the cruciform model. The full field (FF) responses to large checks were approximately the sum of the HF responses. However, with small checks, FF stimulation appeared to activate a different combination of sources than the two HFs. In addition, HF topography was more consistent between subjects than FF for small check sizes. Topographic studies of the VEMR may help to explain the analogous visual evoked electrical response and will be essential to define optimal recording positions for clinical applications.

Topography of the visual evoked magnetic response and hemispherical specialization

The visual evoked magnetic response CIIm component to a pattern onset stimulus presented half field produced a consistent scalp topography in 15 normal subjects. The major response was seen over the contralateral hemisphere, suggesting a dipole with current flowing away from the medial surface of the brain. Full field responses were more unpredictable. The reponses of five subjects were studied to the onset of a full, left half and right half checkerboard stimuli of 38 x 27 min arc checks appearing for 200 ms. In two subjects the full field CIIm topography was consistent with that of the mathematical summation of their relevant half field distribution. The remaining subjects had unpredictable full field topographies, showing little or no relationship to their half or summated half fields. In each of these subjects, a distribution matching that of the summated half field CIIm distribution appears at an earlier latency than that of the predominant full field waveform peak. By examining the topography of the full and half field responses at 5 ms intervals along the waveform for one such subject, the CIIm topography of the right hemisphere develops 10 ms before that of the left hemisphere, and is replaced by the following CIIIm component 20 ms earlier. Hence, the large peak seen in full field results from a combination of the CIIm component of the left hemisphere plus that of the CIIIm from the right. The earlier peak results from the CIIm generated in both hemispheres, at a latency where both show similar amplitudes. As the relative amplitudes of these two peaks alter with check and field size, topographic studies would be required for accurate CIIm identification. In addition. the CIIm-CIIIm complex lasts for 80 ms in the right hemisphere and 135 ms in the left, suggesting hemispherical apecialization in the visual processing of the pattern onset response.

Conformational analysis and dielectric relaxation of polycarbosilanes and related materials

The conformational characteristics of poly(dimethylsilmethylene), poly(dimethylsilethene), poly(dimethylsilethane) and a related material, poly(2,2,5,5-tetramethyl-1-oxa-2,5-disilapentane), have been investigated using the method of molecular mechanics. In this method, a quantitative analysis of the factors affecting the nature and magnitude of the bond rotation potentials governing their conformational behaviour has been undertaken. Along with their structural data, the results obtained were employed to calculate a variety of conformationally-dependent properties for these polymers, including the characteristic ratio, the dipole moment ratio and the mean-square radius of gyration. In addition, the dielectric relaxation behaviour of two samples of poly(2,2,5,5-tetramethyl-1-oxa-2,5-disilapentane) with molar masses Mw = 28000 and Mw = 46000 respectively, have been studied as a function of temperature (179K-205K) and frequency (100-105Hz). Activation energies for the α-relaxation process and Davidson-Cole empirical distribution factors have been calculated.

Dielectric and electro-optical properties of some cyanobiphenyl liquid-crystals

A variety of methods have been reviewed for obtaining parallel or perpendicular alignment in liquid-crystal cells. Some of these methods have been selected and developed and were used in polarised spectroscopy, dielectric and electro-optic studies. Also, novel dielectric and electro-optic cells were constructed for use over a range of temperature. Dielectric response of thin layers of E7 and E8 (eutectic mixture liquid-crystals) have been measured in the frequency range (12 Hz-100 kHz) and over a range of temperature (183-337K). Dielectric spectra were also obtained for supercooled E7 and E8 in the Hz and kHz range. When the measuring electric field was parallel to the nematic director, one loss peak (low-frequency relaxation process) was observed for E7 and for E8, that exhibits a Debye-type behaviour in the supercooled systems. When the measuring electric field was perpendicular to the nematic director, two resolved dielectric processes have been observed. The phase transitions, effective molecular polarisabilities, anisotropy of polarisabilities and order parameters of three liquid crystal homologs (5CB, 6CB, and 7CB), 60CB and three eutectic nematic mixtures E7, E8, and E607 were calculated using optical and density data measured at several temperatures. The order parameters calculated using the different methods of Vuks, Neugebauer, Saupe-Maier, and Palffy-Muhoray are nearly the same for the liquid crystals considered in the present study. Also, the interrelationship between density and refractive index and the molecular structure of these liquid crystals were established. Accurate dielectric and dipole results of a range of liquid-crystal forming molecules at several temperatures have reported. The role of the cyano-end group, biphenyl core, and flexible tail in molecular association, were investigated using the dielectric method for some molecules which have a structural relationship to the nematogens. Analysis of the dielectric data for solution of the liquid-crystals indicated a high molecular association, comparable to that observed in the nematic or isotropic phases. Electro-optic Kerr effect were investigated for some alkyl cyanobiphenyls, their nematic mixtures and the eutectic mixture liquid-crystals E7 and E8 in the isotropic phase and solution. The Kerr constant of these liquid crystals found to be very high at the nematic-isotropic transition temperatures as the molecules are expected to be highly ordered close to phase transition temperatures. Dynamic Kerr effect behaviour and transient molecular reorientation were also observed in thin layers of some alkyl cyanobiphenyls. Dichroic ratio R and order parameters of solutions containing some azo and anthraquinone dyes in the nematic solvent (E7 and E8), were investigated by the measurement of the intensity of the absorption bands in the visible region of parallel aligned samples. The effective factors on the dichroic ratio of the dyes dissolved in the nematic solvents were determined and discussed.

Solvent induced NMR chemical shifts that arise from molecular encounters

Recently Homer and Percival have postulated that intermolecular van der Waals dispersion forces can be characterized by three mechanisms. The first arises via the mean square reaction field < R1; 2> due to the transient dipole of a particular solute molecule that is considered situated in a cavity surrounded by solvent molecules; this was characterized by an extended Onsager approach. The second stems from the extra cavity mean square reaction field < R2; 2> of the near neighbour solvent molecules. The third originates from square field electric fields E2BI due to a newly characterized effect in which solute atoms are `buffeted' by the peripheral atoms of adjacent solvent molecules. The present work concerns more detailed studies of the buffeting screening, which is governed by sterically controlled parameter (2T - T)2, where and are geometric structural parameters. The original approach is used to characterise the buffeting shifts induced by large solvent molecules and the approach is found to be inadequate. Consequently, improved methods of calculating and are reported. Using the improved approach it is shown that buffeting is dependent on the nature of the solvent as well as the nature of the solute molecule. Detailed investigation of the buffeting component of the van der Waals chemical shifts of selected solutes in a range of solvents containing either H or Cl as peripheral atoms have enabled the determination of a theoretical acceptable value for the classical screening coefficient B for protons. 1H and 13C resonance studies of tetraethylmethane and 1H, 13C and 29Si resonance studies of TMS have been used to support the original contention that three (< R1; 2> , < R2; 2> and E2BI) components of intermolecular van der Waals dispersion fields are required to characterise vdW chemical shifts.

The temperature dependence of the electro-optic kerr effect in solutions

A novel Kerr cell of greater optical path length and temperature stability has been designed and built. The Kerr effect experimental has been substantially automated using an Apple IIe computer. Software has been written allowing the computer to partially control the Kerr effect equipment and to acquire and analyse the relevant data.The temperature dependent electro-optic Kerr effect of 2-methyl-4-nitroaniline, p-nitroaniline, nitrobenzene, aniline, and toluene as solutions in 1, 4-dioxane has been studied. The Kerr effect measurements combined with dipole moment, depolarisation ratio, dielectric, and electronic polarisation measurements have been used to calculate the first hyperpolarisability of the solute.Although first hyperpolarisabilities for the compounds studied have been measured in various physical states using a variety of experimental techniques, it is gratifying to find that the values presented in this thesis have a linear relationship with values reported by other workers.

The beta effect in alkylsilanes

It was suggested to us that compounds of the type XCH2SiR2CH2CH2Y might show interesting chemical and biological activity due to them possessing both an alpha group and a beta group. The aim of this research was to discover whether or not the alpha and beta effects interact with each other, and if so whether interaction is via steric or electronic effects. A series of compounds were made with a constant chloromethyl alpha function and varying beta functions (hydroxy, methoxy and chloro groups); plus a second series of trimethylsilyl substituted silanes with the same variety of beta functions were synthesised. The stereochemistry of the products was investigated by analysis of NMR spectra and of dipole moment data. It was found that the β-chloro-substituted compounds possessed restricted rotation. The methoxy- and hydroxy-substituted compounds which displayed more or less simple triplets, appear to possess free rotation; the smaller sized hydroxy and methoxy groups seemingly no great barrier to rotation. Similarly, compounds possessing larger alpha alkyl groups appeared also to possess restricted rotation, it was concluded that for the compounds possessing large alpha or a large beta function steric effects dominate. The kinetics of the solvolysis reaction were studied. β-functional alkylsilanes commonly undergo solvolysis by unimolecular elimination at remarkably enhanced rates. The β-hydroxy- and β-methoxy-substituted chloroethyl derivatives reacted substantially slower that their trimethylsilyl analogues, due to the electronegative chlorine pulling electrons into the Si-C bond. For compounds possessing an electronegative substituent alpha to silicon it seems it is the electronic effects that act to inhibit the beta effect. 2-Chloroethylchloromethyldimethylsilane initially appeared not to react solvolytically, however NMR analysis of the solvolysis products indicated that a reaction did occur but by an as yet unknown mechanism. For compounds with an a α-electronegative substituent in conjunction with a large β-function it was concluded both steric and electronic effects are important.

Interaction of metal salts with polyethers

The dielectric properties of pure low to medium molecular weight poly(ethylene glycol) and poly(propylene glycol) and a variety of their salt complexes have been studied through the measurement of the dielectric permittivity and dielectric loss over a range of frequency and temperature. The major proportion of this study has been concerned with the examination of the nature of the interaction between mercuric chloride and poly(propylene glycol) (PPG). Other salt-poly-ether combinations have also been considered such as cobalt chloride-PPG cadmium chloride-PPG zinc chloride-PPG and ferric chloride-PEG (polyethylene glycol). Some of this work was also supported by chemical shift and spin-lattice Nuclear Magnetic Resonance (N.M.R.) spectroscopy. The dielectric permittivity data were analysed using the Onsager relation to calculate the mean dipole moment per dipolar unit. This approach was employed in the discussion of various models proposed for the structure of salt-polyether complexes. The effect of mercuric chloride on the statistical conformations of poly(propylene-glycol) was studied in a quantitative manner using the relationships of marchal-Benoit. The dielectric relaxation activation energy and mean energy difference between gauche and trans conformations of poly(propylene glycol) in the presence of mercuric chloride, both showed a distinct minimum when the concentration of mercuric chloride was close to 5 mole %. Opposite behaviour was observed for the Cole-Cole parameter. It was concluded that the majority of the dielectric data could be rationalised in terms of a 5-membered cyclic complex formed between mercuric chloride and PPG in which the complexed segment of the polyether-(OMeCH2CH2O)- adopted either gauche or cis conformations.

Studies of molecular interactions using physical techniques

The investigations described in this thesis concern the molecular interactions between polar solute molecules and various aromatic compounds in solution. Three different physical methods were employed. Nuclear magnetic resonance (n.m.r.) spectroscopy was used to determine the nature and strength of the interactions and the geometry of the transient complexes formed. Cryoscopic studies were used to provide information on the stoichiometry of the complexes. Dielectric constant studies were conducted in an attempt to confirm and supplement the spectroscopic investigations. The systems studied were those between nitromethane, chloroform, acetonitrile (solutes) and various methyl substituted benzenes. In the n.m.r. work the dependence of the solute chemical shift upon the compositions of the solutions was determined. From this the equilibrium quotients (K) for the formation of each complex and the shift induced in the solute proton by the aromatic in the complex were evaluated. The thermodynamic parameters for the interactions were obtained from the determination of K at several temperatures. The stoichiometries of the complexes obtained from cryoscopic studies were found to agree with those deduced from spectroscopic investigations. For most systems it is suggested that only one type of complex, of 1:1 stiochiometry, predominates except that for the acetonitrile-benzene system a 1:2 complex is formed. Two sets of dielectric studies were conducted, the first to show that the nature of the interaction is dipole-induced dipole and the second to calculate K. The equilibrium quotients obtained from spectroscopic and dielectric studies are compared. Time-averaged geometries of the complexes are proposed. The orientation of solute, with respect to the aromatic for the 1:1 complexes, appears to be the one in which the solute lies symmetrically about the aromatic six-fold axis whereas for the 1:2 complex, a sandwich structure is proposed. It is suggested that the complexes are formed through a dipole-induced dipole interaction and steric factors play some part in the complex formation.

The development of constrained source localisation algorithms for human brain imaging

This work sets out to evaluate the potential benefits and pit-falls in using a priori information to help solve the Magnetoencephalographic (MEG) inverse problem. In chapter one the forward problem in MEG is introduced, together with a scheme that demonstrates how a priori information can be incorporated into the inverse problem. Chapter two contains a literature review of techniques currently used to solve the inverse problem. Emphasis is put on the kind of a priori information that is used by each of these techniques and the ease with which additional constraints can be applied. The formalism of the FOCUSS algorithm is shown to allow for the incorporation of a priori information in an insightful and straightforward manner. In chapter three it is described how anatomical constraints, in the form of a realistically shaped source space, can be extracted from a subject’s Magnetic Resonance Image (MRI). The use of such constraints relies on accurate co-registration of the MEG and MRI co-ordinate systems. Variations of the two main co-registration approaches, based on fiducial markers or on surface matching, are described and the accuracy and robustness of a surface matching algorithm is evaluated. Figures of merit introduced in chapter four are shown to given insight into the limitations of a typical measurement set-up and potential value of a priori information. It is shown in chapter five that constrained dipole fitting and FOCUSS outperform unconstrained dipole fitting when data with low SNR is used. However, the effect of errors in the constraints can reduce this advantage. Finally, it is demonstrated in chapter six that the results of different localisation techniques give corroborative evidence about the location and activation sequence of the human visual cortical areas underlying the first 125ms of the visual magnetic evoked response recorded with a whole head neuromagnetometer.