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This thesis consists of two experimental applications of the Autler-Townes (AT) spectroscopy. In the first experiment, we have determined the electronic transition dipole moment for the 7Li2 A1Σu+ - X1Σg+ system experimentally by using a 4-level continuous wave extended Λ excitation scheme and compared our results with theoretical predictions. 7Li2 is a good test case for the accuracy of the AT splitting based technique to determine the transition dipole moment and its internuclear distance R dependence. The molecule has only 3 electrons per atom. The A1Σu+ - X1Σg+ potential energy curves were well known and thus, one could calculate accurate rovibrational wavefunctions for the simulations. In addition two different quantum mechanical models were available for the comparison: an all-electron valence bond self-consistent-field method and a pseudo-potential molecular orbital method. Our experimental results for the absolute magnitude of the transition dipole matrix elements for rovibronic transitions for different R-centroid values are in excellent agreement with ab initio theoretical calculations of the transition dipole moment. We believe that this technique will become an important method for accurate measurement of the absolute value and R-dependence of electronic transition dipole moments in molecules. The comparison with theory reinforces this view on the accuracy and universality of the AT method. The focus of the second part of this thesis is on experimentally controlling the singlet-triplet character of the 7Li2 molecule by using an external coupling laser field. We have demonstrated experimentally for the first time that the frequency domain quantum control scheme developed by T.Kirova and F. C. Spano (Physical Review A, 71, 063816, 2005) can be used to control the mixing coefficients of a weakly perturbed pair of singlet and triplet rovibrational levels. The coupling field, when tuned to resonance with the rovibronic transition involving the singlet component, causes it to AT split, leading to enhanced mixing of the pair of levels, as predicted by theory. / Physics

In this research, we have implemented an original technique to study the electronic properties of a single electron placed in YBa2 at 300K. Using a discretized extension of Feynman's Quantum Path Integral, we have been able to characterize effective electron-phonon interactions, and electron location site probability. We find that the electron stabilizes at oxygen vacant sites in the copper-oxygen chains. In the copper-oxygen planes, the electron is unstable and moves into the chain. Upon complementing the quantum electron to a positive charge thereby simulating a hole, we then find that the hole moves into favorable sites in the copper-oxygen planes. These sites are surrounded by four oxygens and two copper ions. Next, by decoupling the electron and hole from the lattice, we obtain effective electron-phonon and hole-phonon coupling constants on the order of 30. These results indicate that the next area of research is to move toward a multi-electron system and allow for further study of the electrons near the Fermi level. Some of the difficulties associated with multi-electron systems such as "exchange", are briefly discussed.

In this dissertation, reversed micelles of the surfactant AOT (sodium bis(2-ethylhexyl) sulfosuccinate) have been used for the synthesis of various materials. Peroxidase catalyzed polymerization of 4-hydroxythiophenol was conducted along the lines of poly(4-ethylphenol) synthesis. Polymerization in monophasic dioxane/water system without the surfactant seems to cause oxidation of the sulfhydryl groups producing an extensively crosslinked polymer. Polymerization in reversed micelles produces a soluble polymer that is mostly oxidatively coupled monomer units with minimal thiol oxidation A role for the surfactant AOT is demonstrated in the formation of spherical poly(4-ethylphenol) particles when synthesized in AOT reversed micellar systems. Mature polymer can be refolded from solution with the aid of the surfactant and precipitated as spherical particles. The technique seems to be directly applicable to the synthesis of poly(4-ethylphenol): iron oxide nanocomposites In nonpolar solvents, dry reversed micelles of AOT transform into a class of organogels upon the addition of suitable phenols. The gels are novel in that they form at very low concentrations of these low molecular weight solutes. Hydrogen-bonding interactions between phenols and the head group of AOT form the basis for such gels. The gel-liquid transition is sharply defined, and occurs over a very narrow temperature range when the gel is warmed or when trace amounts of moisture are absorbed. The underlying molecular architecture of these gels seems to contain strands of stacked and motionally restricted phenol molecules, with the surfactant adsorbed externally. These gels also admit doping with other species leading to the formation of mixed gels. NMR evidence indicates that some of these dopants stack into the gel matrix by 'intercalation' into the motionally restricted region of the aromatic strand. Factors such as the molecular shape and proton donor strength (acidity) that determine whether or not a dopant is intercalated are examined Cadmium sulfide semiconductor nanoclusters are prepared in AOT/isooctane reversed micelles. The interaction of various ligands with the nanoparticle surface is examined by monitoring changes in the cluster luminescence. Among the quenchers examined, 4-hydroxythiophenol quenches the CdS luminescence most efficiently. The kinetics are modified by the levels of the surfactant by diluting the quencher concentration at the crystallite surface at high micelle concentration. Quenching in the phenolic organogels is slower because both the quencher and the cluster undergo motional and diffusional restrictions / acase@tulane.edu

Kohn-Sham (KS) density-functional theory (DFT), where only the exchange-correlation energy needs to be approximated, is one of the most frequently applied methods in many-body theory. On the Jacob's ladder for the exchange-correlation energy of density functional approximations, higher rungs are usually built on and thus improve accuracy over lower ones. However, climbing from the lowest three semilocal rungs (local spin density approximation (LSDA), generalized gradient approximation (GGA), and meta-GGA (MGGA)) to the higher fully-nonlocal rungs increases the computational cost dramatically. Due to the efficiency of the semilocal approximations, there are still efforts to refine the widely used semilocal approximations To make a firmer base for the higher rungs, a new model called density parameter interpolation is designed for the correlation energy per electron, ec(rs, &zgr;), of the uniform electron gas for LSDA. It shows that known or knowable information about the high- (rs &rarr; 0) and low-density ( rs &rarr; infinity) asymptotes can be used to predict the correlation energy per electron, ec(r s, &zgr;), of the three-dimensional (3D) uniform electron gas over the whole range of the density parameter (0 &le; rs < 1) and relative spin polarization (0 &le;&mid;&zgr;&mid;&le; 1), without Quantum Monte Carlo or other input At the MGGA level, The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-GGA and its revised version, the newly proposed revTPSS, are implemented self-consistently within the framework of project augmented wavefunction (PAW) in the Vienna Abinitio Simulation Package (VASP). The application of revTPSS on a set of 61 solids shows that revTPSS performs on average as well as Perdew-Burke-Ernzerhof (PBE)sol and Armiento-Mattsson (AM)05, the two GGA's designed for solids, in terms of lattice constants and bulk moduli. But revTPSS is also known to be accurate for the atomization energies of molecules, as PBEsol and AM05 are not. As for the magnetic properties, revTPSS predicts for Fe the right ground-state solid phase, the ferromagnetic (FM) body-centered-cubic (bcc) structure, with an accurate magnetic moment. However, there still remains the challenge of finding a semilocal functional which can predict the right adsorption site with an accurate adsorption energy for the problem of CO adsorption on Pt (111) surface and, meanwhile, yield an accurate lattice constant for Pt, since revTPSS still fails to predict the right adsorption site Two new nonlocal exchange and correlation functionals, the interaction strength interpolation extended to negative coupling constant (ISIN) functional and its enhanced version ISIN2, of the fifth rung in the Jacob's ladder are presented. They are based on the explicit approximation of Wlambda , the integrand in the adiabatic connection (AC) with lambda representing the coupling constant. The results of ISIN2 show that the correlation energies and the information about the limit lambda &rarr; -- infinity of the ideal system of two electrons on the surface of a sphere (2ESS) can be useful for the construction of new functionals / acase@tulane.edu

Traditionally, density-functional theory (DFT) has been a theory of the ground state of a multi-electronic system. Although excited states were of concern since the beginning of DFT history, realistic calculational schemes have evolved only recently. The reason is that the techniques of ground-state DFT are not suitable enough for an adequate description of excited states. However, there are recent approaches to excited-state DFT that have turned out to be very promising in this notoriously difficult area The object is to find accurate approximations to excited-state energies and densities. In this dissertation several main approaches of modern excited-state DFT are reviewed, certain interrelation between them are revealed, and several new results announced Two universal functionals F1r and F1r are defined. By the use of constraint-search, the following property is proven: E0v<min F1r +&smallint;d 3vrr r r =E1v &le;E1v&le; E1v=min F1r +&smallint;d3rv rrr , 1 r where E0(v) and E1(v) are the round-state energy and the first excited-state energy, respectively, for a given external potential v(r). The minima in the above are achieved at the densities r1r and r1r , respectively Two universal tack-on functionals F'r and F'r are found. Once the minimizations are done in Eq. (1), they correct the minimizing values E1( v) and E1( v) to the exact first excited-state energy E 1(v), i.e. E1v=E 1v+F 'r1 2 and E1v=E 1v+F 'r1 , 3 respectively New properties of the Levy-Nagy's bifunctional F1r,rv 0 are announced. For example, a new derivation of dF1rv 1,rd r&vbm0;r=ru 0=0 4 is given. Moreover, d3rd 3r'd2F1 ru1,r dr rdrr '&vbm0; r=ru0f rfr' &le;0 5 for any function f(r). These properties could be used to model F1r,r0 A new scaling relation of the correlation part of F1r,r0 is presented: Ec,ara ,r0,a=a 2Ec,1r,r0 , 6 It could be used as a key formula for a Goerling-Levy type perturbation theory in which the first excited-state density r1r (instead of r0r as in the original Goerling-Levy perturbation theory) is kept fixed along the adiabatic-connection path. This perturbation theory could very well be adapted for excited-state DFT Two theorems are proven concerning a new universal unifunctional! Theorem 1 states that there is a universal functional U1r , such that E1v=mi nU1 r+ d3rv rrr =U1r 1&d5;+ d3 rvrr&d5; 1r 7 r for any external potential v(r). However, the minimizing density r&d5;1 r is not necessarily the true first excited-state density r1r . Theorem 2 states that there is a universal map M:r&d5;1 r &rarr;r1r . (Similarly: M':r1 r &rarr;r1r and M'':r 1r &rarr;r1r .) A sketch of the local-scaling method (LSM) approximation to the Levy-Nagy bifunctional is presented and a technical (for LSM purposes but with general validity) 'sewing theorem' is proven. It is used for variations with certain types of constraints The exact equivalence between first-order Goerling-Levy perturbation theory and the time-dependent optimized potential model (OPM) for excitation energies of two-electron systems is proven at the end / acase@tulane.edu

<p>A trapped Fermi gas near a collisional resonance provides a unique laboratory for testing many-body theories in a variety of fields. The ultracold Fermi gas produced in our lab is comprised of the lowest two spin states of $^6$Li. At 834 G there is a collisional or Feshbach resonance between the two spin states. The scattering length between trapped atoms of opposing spins far exceeds the interparticle spacing of the gas. On resonance, a strongly interacting, unitary, Fermi gas is created which exhibits universal behavior. The unitary Fermi gas is a prototype for other exotic systems in nature from nuclear matter to neutron stars and high temperature superconductors.</p> <p>For magnetic fields less than 834 G the scattering length is positive, and pairs Fermi atoms can form molecular dimers. These dimers, comprised of two fermions, are bosons. At ultracold temperatures the molecular bosons populate the lowest energy level and form a Bose Einstein Condensate (BEC). For magnetic fields greater than 834G the scattering length between fermions in opposing spin states is negative, like Cooper pairs formed between electrons in a superconductor. The Bardeen, Cooper, and Shriefer (BCS) theory was developed to describe the pairing effect in the context of superconductors. In our experiment we produce an ultracold unitary gas. By tuning the magnetic field to either side of the Feshbach resonance we can transform the gas into a weakly interacting BEC or BCS superfluid. Therefore, the region near a Feshbach resonance is called the BEC-BCS crossover.</p> <p>This dissertation presents a precision measurement of the hydrodynamic sound velocity in an ultracold Fermi gas near a Feshbach resonance. The sound velocity is measured at various magnetic fields both above and below resonance. Moreover, we are able compare our measurements to theoretical descriptions of hydrodynamic sound propagation. Further, our measurement of sound velocity exactly reproduces the non-perturbative case, eliminating the need to consider nonlinear effects. At resonance the sound velocity exhibits universal scaling with the Fermi velocity to within 1.8\% over a factor of 30 in density. In a near zero temperature unitary gas the average sound velocity at the axial center was measured, $c(0)/v_F$ = 0.364(0.005), as well as the universal constant, $\beta$ = -0.565(0.015). The measurement of sound velocity in an ultracold gas throughout the BEC-BCS crossover provides further evidence of the continuous connection between the physics of the BEC, unitary, and BCS systems.</p> / Dissertation

We develop a new Quantum Molecular Dynamics simulation method. The method is based on the discretized path integral representaion of quantum mechanics. In this representation, a quantum particle is isomorphic to a closed polymer chain. The problem of the indistinguishability between quantum particles is tackled with a non-local exchange potential. When the exact density matrix of the quantum particles is used, the exchange potential is exact. However we use a high temperature approximation to the density matrix and the exchange potential is only approximate. This new quantum molecular dynamics method allows the simulation of collections of quantum particles at finite temperature. Our algorithm can be made to scale linearly with the number of quantum states on which the density matrix is projected. Therefore, it can be optimized to run efficiently on parallel computers. We apply this method to the simulation of the electron plasma in 3-dimensions with different densities (rs = 5.0, 7.5, and 10.0) at various temperatures. Under these conditions, the electron plasma are at the border of the degenerate and the semi-degenerate regimes. The kinetic and potential energies are calculated and compared with results for similar systems simulated with a variational Monte Carlo method. Both results show good agreements with each other at all the densities studied. The quantum path integral molecular dynamics is also employed to study the effect of temperature on the electronic and atomic structural properties of liquid and crystalline alkali metal, namely potassium. In these simulations, ions and valence electrons are treated as classical and quantum particles, respectively. The simple metal undergoes a phase transformation upon heating. Calculated dynamic properties indicate that the atomic motion changes from a vibrational to a diffusive character identifying the transformation as melting. Calculated structural properties further confirm the nature of the transformation. Ionic vibrations in the crystal state and the loss of long range order during melting modify the electronic structure and in particular localize the electrons inside and at the border of the ion core.

Cross sections for electron impact ionization of molecules and rare gases are necessary for the modeling of phenomena related to the earth's upper atmosphere and to plasmas. The construction of an apparatus to improve the accuracy of measurements of such cross sections is reported. The ions are produced in a static gas target crossed by an electron beam and are counted with a new ion detector technology, which insures a increased accuracy of the ion flux measurement and of the target length. The target gas density is measured using an ionization gauge calibrated against a high accuracy capacitive transducer. This apparatus also features a pulsed mode of operation, which allows a product analysis through time of flight measurement.