This thesis presents the experimental study on the two-spin component, strongly interacting 6 Li Fermi gases in 3D and 1D traps. The interaction strength is tuned from the molecular BEC regime to the BCS regime using a Feshbach resonance. The trap dimension can be tuned from 3D to 1D with the implementation of optical lattice. The evaporation of imbalanced Fermi gases in 3D trap is studied. The anisotropic and fast evaporation is the cause of the deformation observed in the 2006 Rice experiment. In a balanced Fermi system, the fraction of correlated states is measured as a function of interaction and temperature. At unitarity, the fraction of correlated states is ∼85% and exists above T c . The one-body-like photoexcitation rate can be related to the contact quantity. Lastly, the spin-imbalance in a one-dimensional Fermi gas is studied. The 1D phase diagram is mapped out. The result agrees well with the 1D theory, in which the partially polarized regime is predicted to be a FFLO phase, an exotic superfluid with pairs carrying finite center-of-mass momentum proposed almost 50 years ago.

Four problems in non-equilibrium statistical physics are investigated: 1. The thermodynamics of single-photon gas; 2. Energy of the ground state in Multi-electron atoms; 3. Energy state of the H2 molecule; and 4. The Condensation behavior in N weakly interacting Boson gas. In the single-photon heat engine, we have derived the equation of state similar to that in classical ideal gas and applied it to construct the Carnot cycle with a single photon, and showed the Carnot efficiency in this single-photon heat engine. The energies of the ground state of multi-electron atoms are calculated using the modi ed Bohr model with a shell structure of the bound electrons. The di erential Schrodinger equation is simpli ed into the minimization problem of a simple energy functional, similar to the problem in dimensional scaling in the H-atom. For the C-atom, we got the ground state energy -37:82 eV with a relative error less than 6 %. The simplest molecular ion, H+ 2 , has been investigated by the quasi-classical method and two-center molecular orbit. Using the two-center molecular orbit derived from the exact treatment of the H+ 2 molecular ion problem, we can reduce the number of terms in wavefunction to get the binding energy of the H2 molecule, without using the conventional wavefunction with over-thousand terms. We get the binding energy for the H2 with Hylleraas correlation factor 1 + kr12 as 4:7eV, which is comparable to the experimental value of 4:74 eV. Condensation in the ground state of a weakly interacting Bose gas in equilibrium is investigated using a partial partition function in canonical ensemble. The recursive relation for the partition function developed for an ideal gas has been modi ed to be applicable in the interacting case, and the statistics of the occupation number in condensate states was examined. The well-known behavior of the Bose-Einstein Condensate for a weakly interacting Bose Gas are shown: Depletion of the condensate state, even at zero temperature, and a maximum uctuation near transition temperature. Furthermore, the use of the partition function in canonical ensemble leads to the smooth cross-over between low temperatures and higher temperatures, which has enlarged the applicable range of the Bogoliubov transformation. During the calculation, we also developed the formula to calculate the correlations among the excited states.

Among nature's creation, terpenoids are more versatile and exciting natural products. In a remarkable display of synthetic ingenuity and creativity, nature has endowed terpenes, more so sesquiterpenes, with a bewildering array of carbocyclic frameworks with unusual assemblage of rings and functionality. This phenomenal structural diversity of this class of natural products makes them ideal targets for developing and testing new synthetic strategies for efficient articulation of carbocyclic frameworks. The present thesis entitled "Synthesis of sesquiterpenes containing two vicinal quaternary carbon atoms" describes the synthesis of a number of herbertane sesquiterpenoids, antimicrobial sesquiterpenes enokipodins A and Bf and spirocyclic sesquiterpenes acorone and isoacorones based on ring-closing metathesis reaction. In the thesis, the compounds are sequentially numbered (bold), and references are marked sequentially as superscript and listed at the end of thesis. All the figures included in-the thesis were obtained by DIRECT XEROX OF THE ORIGINAL NMR SPECTRA, and in some of them uninformative areas have been cut to save the space. The herbertane sesquiterpenes are relatively a new class of aromatic sesquiterpenes, containing sterically crowded l-aryl-l,2,2-trimethylcyclopentane carbon framework incorporating two vicinal quaternary carbon atoms on a cyclopentane ring. The sterically crowded molecular framework coupled with the novel biological properties associated with the phenolic herbertanes made the herbertenoids challenging synthetic targets. In the present investigations, to begin with, a formal total synthesis of (±)-herbertenediol and (±)~ mastigophorenes A-D was developed starting from vanillin, based on a combination of Wacker oxidation and intramolecular aldol reactions. A general ring-closing metathesis (RCM) based methodology was developed for a-cuparenone and the herbertane sesquiterpenes herbertene, a-herbertenol, f)~herbertenol and herbertenediol starting from the appropriately substituted acetophenones. The acetophenones on Horner-Wadsworth-Emmons reaction followed by regioselective reduction generated 5-arylbut-2-enols, which on Claisen rearrangement furnished 3~aryl-3-methylpent-4-enals. Grignard reaction with vinylmagnesium bromide followed by RCM reaction and oxidation transformed 3-aryl-3-methylpent~4-enals into 4~aryl-4-methylcylopentenones, which were further transformed into 3-aryl-2,2,3-trimethylcyclopentanones, thus, completing the formal synthesis of the sesquiterpenes (±)-a-cuparenone, (±)-herbertene, (±)-a-herbertenol, (±)-pherbertenol and (±)'herbertenediol. In continuation of the synthesis of herbertane sesquiterpenes, a Claisen rearrangement and RCM reaction based strategy was developed for the synthesis of (±)~lt14-herbertenediol and (±)-71-epi-herbertenolide, and marine sesquiterpenes {£)-tochuinyl acetate and (±)-dihydrotochuinyl acetate. Ortho ester Claisen rearrangement of 3-arylbut-2~ enols generated 3-aryl~3-methylpent-4-enoates, which on allylation and RCM reactions generated 2~methyl-2-arylcyclopent-3-encarboxylates. Stereoselective alkylation followed by functional group manipulations transformed 2-methyl'2-arylcyclopent'3-encarboxylates into the marine sesquiterpenes (±)-tochuinyl acetate and (±)-dihydrotochuinyl acetate, (±)-ll-epiherbertenolide and (±)~l,,14-herbertenediol. Total synthesis of (±)-lt13-herbertenediol has been accomplished employing an RCM reaction as the key step. The requisite starting material 2-methoxy-5-methylphenyl acetate was obtained from p-cresol. Two sequential allylation reactions followed by RCM reaction transformed 2-methoxy-5-methylphenyl acetate into 1 -arylcyclopent-3-en-l-carboxylate. Allylic oxidation and alkylation followed by functional group manipulation transformed I-arylcyclopent-3-en-l-carboxylate into (±)-U3-herbertenediol. For the enantiospecific synthesis of (+)-a-herbertenol, an aromatic Claisen rearrangement based strategy was developed starting from the readily available monoterpene (R)-limonene. To begin with, limonene was converted into 5-isopropenyl-2-methylcyclopent-l-enemethanol which on Mitsunobu reaction with p-cresol followed by Claisen rearrangement of the resultant aryl ether generated a mixture of3-isopropenyl-3a,7,8b-trimethyl-2,3,3a,8b-tetrahydro-1H-cyclopenta[b]benzofurans. Degradation of the isopropenyl group and cleavage of the central ether ring transformed the major cyclopentabenzofuran into 3-aryl-2,3-dimethylcyclopentanone, which was further elaborated into (+)-a-herbertenol. The general RCM reaction methodology developed for the herbertenoids has been further extended to the first total synthesis of the antimicrobial sesquiterpenes (±)~ enokipodins A andB, and a formal total syntheses of (±)-cuparene-l,4-diol, (±)-cuparene-lt4-quinone and (±)~HM-1 methyl ether star*w« from 2,5~dimethoxy~4-methylacetophenone. It has been further extended to the formal synthesis of spirocydic sesquiterpenes (±)-acorone and (±)-isoacorones starting from cyclohexane-1,4-dione.

This dissertation presents the implementation of a technique to generate atomic Fock states of Lithium 6 with ultra-high fidelity, called laser culling. Fock states, atomic states with a definite number of particles, are a mandatory step for studying few-body quantum phenomena such as quantum tunneling, quantum entanglement, and serve as building blocks for quantum simulators. The creation of ultra-high fidelity Fock states begins with a degenerate Fermi gas in an optical dipole trap. Being fermions, lithium-6 atoms fill the energy levels of the dipole trap with 2 atoms per energy level. Introducing a magnetic field gradient creates a linear potential that tilts the potential produced by the optical dipole trap. The initially bound energy levels become quasi-bound states, each with a different lifetime. By exploiting the difference between these lifetimes, one can generate a single pair of atoms in the ground state of the trap with fidelities that can exceed 99.9%. This dissertation first presents the details of the design and construction of an apparatus for laser culling, and then reports on the progress made towards the creation of atomic Fock states with ultra-high fidelity. / text

This thesis discusses two ensembles, the study of which was dependent upon the controllable production of cold gas-phase samples using supersonic beams. The experiments on DNA bases and base clusters were carried out in Germany at the Max Born Institute. The experiments anticipating the construction of a molecular beam slower were carried out in the United States at the University of Texas at Austin. Femtosecond pump-probe techniques were employed to study the dynamics and electronic character of DNA bases, pairs and clusters in the gas phase. Experiments on DNA base monomers confirmed the dominance of a particular relaxation pathway, the nπ* state. Competition between this state and another proposed relaxation pathway was demonstrated through observations of the DNA base pairs and base-water clusters, settling a recent controversy. Further, it was determined that the excited state dynamics in base pairs is due to intramolecular processes rather than intermolecular processes. Finally, results from base-water clusters confirm that microsolvation permits comparison with biologically relevant liquid phase experiments and with ab initio calculations, bridging a long-standing gap. A purely mechanical technique that does not rely upon quantum or electronic properties to produce very cold, very slow atoms and molecules would be more generally applicable than current approaches. The approach described here uses supersonic beam methods to produce a very cold beam of particles and a rotating paddle-wheel, or rotor, to slow the cold beam. Initial experiments testing the possibility of elastic scattering from a single crystal surface were conducted and the implications of these experiments are discussed. / text

Laser-cooled atoms offer an excellent platform for testing new ideas of quantum control and measurement. I will discuss experiments where we use light and magnetic fields to drive and monitor non-trivial quantum dynamics of a large spin-angular momentum associated with an atomic hyperfine ground state. We can design Hamiltonians to generate arbitrary spin states and perform a full quantum state reconstruction of the results. We have implemented and verified time optimal controls to generate a broad variety of spin states, including spin-squeezed states useful for metrology. Yields achieved are of the range 0.8-0.9.We present a first experimental demonstration of the quantum kicked top, a popular paradigm for quantum and classical chaos. We make `movies' of the evolving quantum state which provides a direct observation of phase space dynamics of this system. The spin dynamics seen in the experiment includes dynamical tunneling between regular islands, rapid spreading of states throughout the chaotic sea, and surprisingly robust signatures of classical phase space structures. Our data show differences between regular and chaotic dynamics in the sensitivity to perturbations of the quantum kicked top Hamiltonian and in the average electron-nuclear spin entanglement during the first 40 kicks. The difference, while clear, is modest due to the small size of the spin.

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No description available.

Theoretical investigation of the dynamics of adiabatic quantum mechanics in two different, highly polar systems has been made. The systems were chosen for their fundamental scientific interest, as they represent atoms and molecules with exaggerated properties, as well as ease of experimental study as such highly polar systems are easier to manipulate using readily-available electric fields. A model two-level system is used to derive one approach for maximizing the probability of adiabatic passage through an avoided crossing and this is compared with the classic Landau-Zener result, and the commonly encountered spin-flip problem of a particle with spin located in a rotating magnetic field. This approach is applied to the avoided crossing between the n = 13, n1 − n2 = 11 (dipole moment of 532 D) and the n = 14, n1 − n2 = −12 (dipole moment of -657 D) highly polar Stark states of the lithium atom at 447 kV/m. Ion-pair formation from two neutral lithium atoms, one in the 2s ground state and the other in an excited state, is also investigated. The cross section σ(v) for free ion-pairs is calculated for the initial colliding pairs of atomic states located below the ion-pair threshold. Li(2s) + Li(3d) is seen to possess the largest cross section (σ(v0) = 569.2 a.u.) at its threshold velocity. The implications of this for bound ion-pair, i.e. heavy Rydberg system, production are briefly discussed. Furthermore, experimental progress towards the production of these atomic and molecular systems from a beam of lithium is presented. / Thesis (Master, Physics, Engineering Physics and Astronomy) -- Queen's University, 2009-12-09 16:49:41.184

In the last decade, ultracold plasmas have been created in the laboratory by photo-ionizing laser-cooled atoms. To understand the overall dynamics of ultracold plasmas, one needs to understand Rydberg collisional processes at ultracold temperatures. The two kinds of problems addressed in this thesis are: study of Rydberg atomic processes at ultracold temperatures, and a study of the overall dynamics of the ultracold plasmas. Theoretical methods based on quantal-classical correspondence is used to understand Rydberg atomic processes such as radiative cascade, and radiative recombination. A simulation method suitable for ultracold collisions is developed and tested. This method is then applied to study collisional-Stark mixing in Rydberg atoms. To study the dynamics of the ultracold plasmas, a King model for the electrons in plasmas is proposed. The King model is a stationary, finite sized electron distribution for the electrons in a cloud of fixed ions with a Gaussian distribution. A Monte-Carlo method is developed to simulate the overall dynamics of the King distribution.