I. Spectroscopic evidence for slow vibrational relaxation in excited electronic states of diatomics in rare gas solids. II. Static crystal field effects in the electronic spectra of isotopically mixed benzene crystals

Part I

Studies of vibrational relaxation in excited electronic states of simple diatomic molecules trapped in solid rare-gas matrices at low temperatures are reported. The relaxation is investigated by monitoring the emission intensity from vibrational levels of the excited electronic state to vibrational levels of the ground electronic state. The emission was in all cases excited by bombardment of the doped rare-gas solid with X-rays.

The diatomics studied and the band systems seen are: N₂, Vegard-Kaplan and Second Positive systems; O₂, Herzberg system; OH and OD, A ²Σ⁺ - X²II_i system. The latter has been investigated only in solid Ne, where both emission and absorption spectra were recorded; observed fine structure has been partly interpreted in terms of slightly perturbed rotational motion in the solid. For N₂, OH, and OD emission occurred from v' > 0, establishing a vibrational relaxation time in the excited electronic state of the order, of longer than, the electronic radiative lifetime. The relative emission intensity and decay times for different v' progressions in the Vegard-Kaplan system are found to depend on the rare-gas host and the N₂ concentration, but are independent of temperature in the range 1.7°K to 30°K.

Part II

Static crystal field effects on the absorption, fluorescence, and phosphorescence spectra of isotopically mixed benzene crystals were investigated. Evidence is presented which demonstrate that in the crystal the ground, lowest excited singlet, and lowest triplet states of the guest deviate from hexagonal symmetry. The deviation appears largest in the lowest triplet state and may be due to an intrinsic instability of the ³B_1u state. High resolution absorption and phospho- rescence spectra are reported and analyzed in terms of site-splitting of degenerate vibrations and orientational effects. The guest phosphorescence lifetime for various benzene isotopes in C₆D₆ and sym-C₆H₃D₃ hosts is presented and discussed.

Studies of phonon anharmonicity in solids

Today our understanding of the vibrational thermodynamics of materials at low temperatures is emerging nicely, based on the harmonic model in which phonons are independent. At high temperatures, however, this understanding must accommodate how phonons interact with other phonons or with other excitations. We shall see that the phonon-phonon interactions give rise to interesting coupling problems, and essentially modify the equilibrium and non-equilibrium properties of materials, e.g., thermodynamic stability, heat capacity, optical properties and thermal transport of materials. Despite its great importance, to date the anharmonic lattice dynamics is poorly understood and most studies on lattice dynamics still rely on the harmonic or quasiharmonic models. There have been very few studies on the pure phonon anharmonicity and phonon-phonon interactions. The work presented in this thesis is devoted to the development of experimental and computational methods on this subject.

Modern inelastic scattering techniques with neutrons or photons are ideal for sorting out the anharmonic contribution. Analysis of the experimental data can generate vibrational spectra of the materials, i.e., their phonon densities of states or phonon dispersion relations. We obtained high quality data from laser Raman spectrometer, Fourier transform infrared spectrometer and inelastic neutron spectrometer. With accurate phonon spectra data, we obtained the energy shifts and lifetime broadenings of the interacting phonons, and the vibrational entropies of different materials. The understanding of them then relies on the development of the fundamental theories and the computational methods.

We developed an efficient post-processor for analyzing the anharmonic vibrations from the molecular dynamics (MD) calculations. Currently, most first principles methods are not capable of dealing with strong anharmonicity, because the interactions of phonons are ignored at finite temperatures. Our method adopts the Fourier transformed velocity autocorrelation method to handle the big data of time-dependent atomic velocities from MD calculations, and efficiently reconstructs the phonon DOS and phonon dispersion relations. Our calculations can reproduce the phonon frequency shifts and lifetime broadenings very well at various temperatures.

To understand non-harmonic interactions in a microscopic way, we have developed a numerical fitting method to analyze the decay channels of phonon-phonon interactions. Based on the quantum perturbation theory of many-body interactions, this method is used to calculate the three-phonon and four-phonon kinematics subject to the conservation of energy and momentum, taking into account the weight of phonon couplings. We can assess the strengths of phonon-phonon interactions of different channels and anharmonic orders with the calculated two-phonon DOS. This method, with high computational efficiency, is a promising direction to advance our understandings of non-harmonic lattice dynamics and thermal transport properties.

These experimental techniques and theoretical methods have been successfully performed in the study of anharmonic behaviors of metal oxides, including rutile and cuprite stuctures, and will be discussed in detail in Chapters 4 to 6. For example, for rutile titanium dioxide (TiO₂), we found that the anomalous anharmonic behavior of the B_1g mode can be explained by the volume effects on quasiharmonic force constants, and by the explicit cubic and quartic anharmonicity. For rutile tin dioxide (SnO₂), the broadening of the B_2g mode with temperature showed an unusual concave downwards curvature. This curvature was caused by a change with temperature in the number of down-conversion decay channels, originating with the wide band gap in the phonon dispersions. For silver oxide (Ag₂O), strong anharmonic effects were found for both phonons and for the negative thermal expansion.

Absolute phase control of spectra effects in a two-level medium driven by two-color ultrashort laser pulses

Using a omega-3 omega combination scenario, we investigate the absolute phase control of the spectra effects for ultrashort laser pulses propagating in a two-level medium. It is found that the higher spectral components can be controlled by the absolute phases. In particular, different absolute phase combinations can lead to the buildup or split of the even harmonics. (c) 2006 Elsevier B.V. All rights reserved.

The power of quantum Fourier sampling

How powerful are Quantum Computers? Despite the prevailing belief that Quantum Computers are more powerful than their classical counterparts, this remains a conjecture backed by little formal evidence. Shor's famous factoring algorithm [Shor97] gives an example of a problem that can be solved efficiently on a quantum computer with no known efficient classical algorithm. Factoring, however, is unlikely to be NP-Hard, meaning that few unexpected formal consequences would arise, should such a classical algorithm be discovered. Could it then be the case that any quantum algorithm can be simulated efficiently classically? Likewise, could it be the case that Quantum Computers can quickly solve problems much harder than factoring? If so, where does this power come from, and what classical computational resources do we need to solve the hardest problems for which there exist efficient quantum algorithms?

We make progress toward understanding these questions through studying the relationship between classical nondeterminism and quantum computing. In particular, is there a problem that can be solved efficiently on a Quantum Computer that cannot be efficiently solved using nondeterminism? In this thesis we address this problem from the perspective of sampling problems. Namely, we give evidence that approximately sampling the Quantum Fourier Transform of an efficiently computable function, while easy quantumly, is hard for any classical machine in the Polynomial Time Hierarchy. In particular, we prove the existence of a class of distributions that can be sampled efficiently by a Quantum Computer, that likely cannot be approximately sampled in randomized polynomial time with an oracle for the Polynomial Time Hierarchy.

Our work complements and generalizes the evidence given in Aaronson and Arkhipov's work [AA2013] where a different distribution with the same computational properties was given. Our result is more general than theirs, but requires a more powerful quantum sampler.

Low-noise THz Niobium SIS Mixers

This thesis describes the development of low-noise heterodyne receivers at THz frequencies for submillimeter astronomy using Nb-based superconductor-insulator-superconductor (SIS) tunneling junctions. The mixers utilize a quasi-optical configuration which consists of a planar twin-slot antenna and antisymmetrically-fed two-junctions on an antireflection-coated silicon hyperhemispherical lens. On-chip integrated tuning circuits, in the form of microstrip lines, are used to obtain maximum coupling efficiency in the designed frequency band. To reduce the rf losses in the integrated tuning circuits above the superconducting Nb gap frequency (~ 700 GHz), normal-metal Al is used to replace Nb as the tuning circuits.

To account the rf losses in the micros trip lines, we calculated the surface impedance of the AI films using the nonlocal anomalous skin effect for finite thickness films. Nb films were calculated using the Mattis-Bardeen theory in the extreme anomalous limit. Our calculations show that the losses of the Al and Nb microstrip lines are about equal at 830 GHz. For Al-wiring and Nb-wiring mixers both optimized at 1050 GHz, the RF coupling efficiency of Al-wiring mixer is higher than that of Nb-wiring one by almost 50%. We have designed both Nb-wiring and Al-wiring mixers below and above the gap frequency.

A Fourier transform spectrometer (FTS) has been constructed especially for the study of the frequency response of SIS receivers. This FTS features large aperture size (10 inch) and high frequency resolution (114 MHz). The FTS spectra, obtained using the SIS receivers as direct detectors on the FTS, agree quite well with our theoretical simulations. We have also, for the first time, measured the FTS heterodyne response of an SIS mixer at sufficiently high resolution to resolve the LO and the sidebands. Heterodyne measurements of our SIS receivers with Nb-wiring or Al-wiring have yielded results which arc among the best reported to date for broadband heterodyne receivers. The Nb-wiring mixers, covering 400 - 850 GHz band with four separate fixed-tuned mixers, have uncorrected DSB receiver noise temperature around 5hv/k_b to 700 GHz, and better than 540 K at 808 GHz. An Al-wiring mixer designed for 1050 GHz band has an uncorrected DSB receiver noise temperature 840 K at 1042 GHz and 2.5 K bath temperature. Mixer performance analysis shows that Nb junctions can work well up to twice the gap frequency and the major cause of loss above the gap frequency is the rf losses in the microstrip tuning structures. Further advances in THz SIS mixers may be possible using circuits fabricated with higher-gap superconductors such as NbN. However, this will require high-quality films with low RF surface resistance at THz frequencies.

Investigation of bulk indium antimonide as heterodyne detector for the submillimeter wavelength region

Bulk n-lnSb is investigated at a heterodyne detector for the submillimeter wavelength region. Two modes or operation are investigated: (1) the Rollin or hot electron bolometer mode (zero magnetic field), and (2) the Putley mode (quantizing magnetic field). The highlight of the thesis work is the pioneering demonstration or the Putley mode mixer at several frequencies. For example, a double-sideband system noise temperature of about 510K was obtained using a 812 GHz methanol laser for the local oscillator. This performance is at least a factor or 10 more sensitive than any other performance reported to date at the same frequency. In addition, the Putley mode mixer achieved system noise temperatures of 250K at 492 GHz and 350K at 625 GHz. The 492 GHz performance is about 50% better and the 625 GHz is about 100% better than previous best performances established by the Rollin-mode mixer. To achieve these results, it was necessary to design a totally new ultra-low noise, room-temperature preamp to handle the higher source impedance imposed by the Putley mode operation. This preamp has considerably less input capacitance than comparably noisy, ambient designs.

In addition to advancing receiver technology, this thesis also presents several novel results regarding the physics of n-lnSb at low temperatures. A Fourier transform spectrometer was constructed and used to measure the submillimeter wave absorption coefficient of relatively pure material at liquid helium temperatures and in zero magnetic field. Below 4.2K, the absorption coefficient was found to decrease with frequency much faster than predicted by Drudian theory. Much better agreement with experiment was obtained using a quantum theory based on inverse-Bremmstrahlung in a solid. Also the noise of the Rollin-mode detector at 4.2K was accurately measured and compared with theory. The power spectrum is found to be well fit by a recent theory of non- equilibrium noise due to Mather. Surprisingly, when biased for optimum detector performance, high purity lnSb cooled to liquid helium temperatures generates less noise than that predicted by simple non-equilibrium Johnson noise theory alone. This explains in part the excellent performance of the Rollin-mode detector in the millimeter wavelength region.

Again using the Fourier transform spectrometer, spectra are obtained of the responsivity and direct detection NEP as a function of magnetic field in the range 20-110 cm^-1. The results show a discernable peak in the detector response at the conduction electron cyclotron resonance frequency tor magnetic fields as low as 3 KG at bath temperatures of 2.0K. The spectra also display the well-known peak due to the cyclotron resonance of electrons bound to impurity states. The magnitude of responsivity at both peaks is roughly constant with magnet1c field and is comparable to the low frequency Rollin-mode response. The NEP at the peaks is found to be much better than previous values at the same frequency and comparable to the best long wavelength results previously reported. For example, a value NEP=4.5x10^-13/Hz^1/2 is measured at 4.2K, 6 KG and 40 cm^-1. Study of the responsivity under conditions of impact ionization showed a dramatic disappearance of the impurity electron resonance while the conduction electron resonance remained constant. This observation offers the first concrete evidence that the mobility of an electron in the N=0 and N=1 Landau levels is different. Finally, these direct detection experiments indicate that the excellent heterodyne performance achieved at 812 GHz should be attainable up to frequencies of at least 1200 GHz.

The energy spectra of uranium atoms sputtered from uranium metal and uranium dioxide targets

The energy spectra of ²³⁵U atoms sputtered from a 93% enriched ²³⁵U metal foil and a hot pressed ²³⁵U0₂ pellet by an 80 keV ⁴⁰Ar⁺ beam have been measured in the range 1 eV to 1 keV. The measurements were made using a mechanical time-of-flight spectrometer in conjunction with the fission track technique for detecting ²³⁵U. The design and construction of this spectrometer are discussed in detail, and its operation is mathematically analyzed.

The results of the experiment are discussed in the context of the random collision cascade model of sputtering. The spectrum obtained by the sputtering of the ²³⁵U metal target was found to be well described by the functional form E(E+E_b)^-2.77, where E_b = 5.4 eV. The ²³⁵U0₂ target produced a spectrum that peaked at a lower energy (~ 2 eV) and decreased somewhat more rapidly for E ≳ 100 eV.

Buffer-gas-induced narrowing of electromagnetically induced transparent spectra for an open system

We have investigated the spectra of the electromagnetically induced transparency (EIT) when a cell is filled with a buffer gas. Our theoretical results show that the buffer gas can induce a narrower spectra line and steeper dispersion than those of the usual EIT case in a homogeneous and Doppler broadened system. The linewidth decreases with the increase of the buffer gas pressure. This narrow spectra may be applied to quantum information processing, nonlinear optics and atomic frequency standard.

A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object's amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented. (C) 2008 Elsevier B.V. All rights reserved.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens. (C) 1997 Optical Society of America.

Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Optical multichannel-scale range-tunable Fourier-transforming system: experiment

The authors have demonstrated the principle of a novel optical multichannel-scale range-tunable Fourier-transforming system. The experimental results show good agreement with the theoretical analysis.