Iterative quantum computations of HO2 bound states and resonances for J=4 and 5

Bound and resonance states of HO2 have been calculated by both the complex Lanczos homogeneous filter diagonalisation (LHFD) method(1,2) and the real Chebyshev filter diagonalisation method(3,4) for non-zero total angular momentum J = 4 and 5. For bound states, the agreement between the two methods is quite satisfactory; for resonances while the energies are in good agreement, the widths are only in general agreement. The relative performances of the two iterative FD methods have also been discussed in terms of efficiency as well as convergence behaviour for such a computationally challenging problem. A helicity quantum number Ohm assignment (within the helicity conserving approximation) is performed and the results indicate that Coriolis coupling becomes more important as J increases and the helicity conserving approximation is not a good one for the HO2 resonance states.

Recent developments in the quantum dynamical characterization of unimolecular resonances

We give a selective review of quantum mechanical methods for calculating and characterizing resonances in small molecular systems, with an emphasis on recent progress in Chebyshev and Lanczos iterative methods. Two archetypal molecular systems are discussed: isolated resonances in HCO, which exhibit regular mode and state specificity, and overlapping resonances in strongly bound HO2, which exhibit irregular and chaotic behavior. Recent progresses for non-zero total angular momentum J calculations of resonances including parallel computing models are also included and future directions in this field are discussed.

Tunable molecular resonances of a double quantum dot Aharonov-Bohm interferometer

We investigate resonant tunnelling through molecular states of an Aharonov-Bohm (AB) interferometer composed of two coupled quantum dots. The conductance of the system shows two resonances associated with the bonding and the antibonding quantum states. We predict that the two resonances are composed of a Breit-Wigner resonance and a Fano resonance, of which the widths and Fano factor depend on the AB phase very sensitively. Further, we point out that the bonding properties, such as the covalent and ionic bonding, can be identified by the AB oscillations.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition.

Characterization of infrared surface plasmon resonances generated from a fiber-optical sensor utilizing tilted Bragg gratings

We demonstrate the use of tilted fiber gratings to assist with the generation of infrared surface plasmons on a metal film coating the flat of a D-shaped fiber. The wavelength of the strong (>25 dB) resonance is tunable over similar to 1000 nm by adjusting the polarization state of the light and is highly sensitive to the refractive index of any aqueous medium surrounding the fiber (sensitivity= 3365 nm).

Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings

We demonstrate the use of tilted fiber gratings to assist the generation of localized infrared surface plasmons with short propagation lengths and a sensitivity of d lambda/dn = 3365 nm in the aqueous index regime. It was also found that the resonances could be spectrally tuned over 1000 nm at the same spatial region with high coupling efficiency (in excess of 25 dB) by altering the polarization of the light illuminating the device.

Multiple period resonances in long period gratings in photonic crystal fibres

In order to characterise long period gratings fabricated in endlessly single mode photonic crystal fibres with bulk cladding we perform eigenanalysis of guided modes supported by these fibres. Resonant coupling occurs only when the beating length equals the multiple grating periods. Experimentally obtained grating spectra and sensitivity are fully explained using modified phase matching condition. © Springer 2006.

Generation of infrared surface plasmon resonances with high refractive index sensitivity utilizing tilted fiber Bragg gratings

We demonstrate the use of tilted fiber gratings to assist the generation of localized infrared surface Plasmons with short propagation lengths and a sensitivity of dλ/dn = 3365 nm in the aqueous index regime. It was also found that the resonances could be spectrally tuned over 1000 nm at the same spatial region with high coupling efficiency (in excess of 25 dB) by altering the polarization of the light illuminating the device. © 2007 Optical Society of America.

Multiple period resonances of long period gratings in photonic crystal fibre

A comprehensive eigenmode analysis is performed of the guided modes supported by typical photonic crystal fiber. These modes exhibit unusual phase matching conditions requiring multiple grating periods for resonant coupling. All the signature features of the experimentally observed transmission spectra are explained by multiple-period resonances.

Sharp Bounds on the Number of Resonances for Symmertic Systems II. Non-Compactly Supported Perturbations

We extend the results in [5] to non-compactly supported perturbations for a class of symmetric first order systems.

Dynamical Resonances and SSF Singularities for a Magnetic Schrödinger Operator

We consider the Hamiltonian H of a 3D spinless non-relativistic quantum particle subject to parallel constant magnetic and non-constant electric field. The operator H has infinitely many eigenvalues of infinite multiplicity embedded in its continuous spectrum. We perturb H by appropriate scalar potentials V and investigate the transformation of these embedded eigenvalues into resonances. First, we assume that the electric potentials are dilation-analytic with respect to the variable along the magnetic field, and obtain an asymptotic expansion of the resonances as the coupling constant ϰ of the perturbation tends to zero. Further, under the assumption that the Fermi Golden Rule holds true, we deduce estimates for the time evolution of the resonance states with and without analyticity assumptions; in the second case we obtain these results as a corollary of suitable Mourre estimates and a recent article of Cattaneo, Graf and Hunziker [11]. Next, we describe sets of perturbations V for which the Fermi Golden Rule is valid at each embedded eigenvalue of H; these sets turn out to be dense in various suitable topologies. Finally, we assume that V decays fast enough at infinity and is of definite sign, introduce the Krein spectral shift function for the operator pair (H+V, H), and study its singularities at the energies which coincide with eigenvalues of infinite multiplicity of the unperturbed operator H.

Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

Optical control of interactions in ultracold gases opens new fields of research by creating ``designer" interactions with high spatial and temporal resolution. However, previous optical methods using single optical fields generally suffer from atom loss due to spontaneous scattering. This thesis reports new optical methods, employing two optical fields to control interactions in ultracold gases, while suppressing spontaneous scattering by quantum interference. In this dissertation, I will discuss the experimental demonstration of two optical field methods to control narrow and broad magnetic Feshbach resonances in an ultracold gas of $^6$Li atoms. The narrow Feshbach resonance is shifted by $30$ times its width and atom loss suppressed by destructive quantum interference. Near the broad Feshbach resonance, the spontaneous lifetime of the atoms is increased from $0.5$ ms for single field methods to $400$ ms using our two optical field method. Furthermore, I report on a new theoretical model, the continuum-dressed state model, that calculates the optically induced scattering phase shift for both the broad and narrow Feshbach resonances by treating them in a unified manner. The continuum-dressed state model fits the experimental data both in shape and magnitude using only one free parameter. Using the continuum-dressed state model, I illustrate the advantages of our two optical field method over single-field optical methods.

Resonances: Noise and Contemporary Music

Noise seems to stand for a lack of aesthetic grace, to alienate or distract rather than enrapture. And yet the drones of psychedelia, the racket of garage rock and punk, the thudding of rave, the feedback of shoegaze and post-rock, the bombast of thrash and metal, the clatter of jungle and the stuttering of electronica, together with notable examples of avant-garde noise art, have all found a place in the history of contemporary musics, and are recognised as representing key evolutionary moments. Noise therefore is the untold story of contemporary popular music, and in a critical exploration of noise lies the possibility of a new narrative – one that is wide-ranging, connects the popular to the underground and avant-garde, fully posits the studio as a musical instrument, and demands new critical and theoretical paradigms of those seeking to write about music. Resonances is a compelling collection of new essays by scholars, writers and musicians – all seeking to explore and enlighten this field of study.