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.

Monoatomic chain formation for Ag, Au, Pd and Pt has been investigated using a model for the tip structure. First-principles calculations, mostly spin polarized, were performed within the framework of the Density Functional theory. Results are presented and discussed on the basis of the electronic structure. Tendencies for chain formation were noted for Ag, Au and Pt.

The mechanisms of the sublimation of graphene at zero pressure and the condensation of carbon vapor is investigated by molecular dynamics (MD) simulations. The interatomic interactions are described by the Reactive Empirical Bond Order potential (REBO). It is found that graphene sublimates at a temperature of 5,200 K. At the onset of sublimation, defects that contain several pentagons and heptagons are formed, that are shown to evolve from double vacancies and stone wales defects. These defects consisting of pentagons and heptagons act as nucleation sites for the gaseous phase. The influence of the interatomic interactions on the sublimation process are also investigated by comparing the results using the REBO potential with the Screened Environment Dependent (SED)-REBO potential. Two-dimensional MD simulations are also performed, and it is found that graphene melts at a much higher temperature and forms many more point defects than in three dimensions. It is also observed that carbon chains make up the two-dimensional molten state. The isothermal equation of state of gaseous and liquid carbon, as well as the coexistence of the two phases is calculated at 6,000 K and up to a few GPa. The analysis shows that the material that forms immediately following the phase transformation in graphene is actually a coexistence of liquid and gaseous phases, but it is primarily two-fold coordinated, so it is mostly a gas, hence the identification of the phase transformation as sublimation. The coexistence pressure for liquid and gaseous carbon is found using the Maxwell Construction to be 0.0365 GPa at 6,000 K. It was previously believed that carbon vapor consists exclusively of carbon chains. We find that under compression, at a pressure lower than the coexistence pressure, carbon vapor develops a small amount (6 %) of sp2 bonds indicating a slight non-chain bonding character. The diffusion coefficient of this dense gas is calculated to be in between that of the liquid and gaseous phases.

This dissertation reports on the synthesis, structural and thermal characterization and electrical and thermal transport properties of a variety of strongly correlated spinels. General structure property relationships for electrical and thermal transport are discussed. However, the relationship between thermopower and features of the crystal structure such as spin, crystal field, anti-site disorder, and structural distortions are explored in depth. The experimental findings are reported in the context of improving existing oxide thermoelectric materials, screening for new materials or using thermopower as a unique characterization tool to determine the cation distribution in spinels. The need for improved n-type oxide thermoelectric materials has led researchers to consider mixed valence \((+3/+4)\) manganese oxides. Contrary to previous findings we report herein that the \(LiMn_2O_4\) compound reaches the relatively large n-type thermopower of \(-73 \mu V/K\) which is three times larger than the value observed in other manganese oxides, \(-25 \mu V/K\). The cause of this increase in thermopower is shown to be the absence of a Jahn-Teller distortion on the \(Mn^{3+}\) ions in \(LiMn_2O_4\). By avoiding this structural distortion the orbital degeneracy is doubled and the Koshibae et al.’s modified Heikes formula predicts a thermopower of \(-79 \mu V/K\) in good agreement with the experiment. Altering the \(Mn^{3+/4+}\) ratio via aliovalent doping did not affect the thermopower and is a second evidence of universal charge transport first reported by Kobayashi et al. The role of anti-site disorder was further examined in \(Fe_xMn_{1-x}NiCrO_4\) x=0, ½, ¾, 1 spinels but the effect on thermopower was inconclusive due to the presence of impurity phases. Next, the thermopower as a function of temperature in \(Co_3O_4\) was investigated as a means whereby the Wu and Mason’s 30 year old model for using thermopower to calculate cation distribution in spinels could be revisited. We report evidence that Wu and Mason’s original model using the standard Heikes formula and considering octahedral sites alone leads to a stoichiometrically inconsistent result at high temperatures. Alternate models are evaluated considering Koshibae et al.’s modified Heikes formula and accounting for tetrahedral site contributions. Furthermore, the effect of a possible spin state transition is considered. / Engineering and Applied Sciences

This thesis describes experiments on quantum dots made by locally gating one-dimensional quantum wires. The first experiment studies a double quantum dot device formed in a Ge/Si core/shell nanowire. In addition to measuring transport through the double dot, we detect changes in the charge occupancy of the double dot by capacitively coupling it to a third quantum dot on a separate nanowire using a floating gate. We demonstrate tunable tunnel coupling of the double dot and quantify the strength of the tunneling using the charge sensor. The second set of experiments concerns carbon nanotube double quantum dots. In the first nanotube experiment, spin-dependent transport through the double dot is compared in two sets of devices. The first set is made with carbon containing the natural abundance of \(^{12}C\) (99%) and \(^{13}C\) (1%), the second set with the 99% \(^{13}C\) and 1% \(^{12}C\). In the devices with predominantly \(^{13}C\), we find evidence in spin-dependent transport of the interaction between the electron spins and the \(^{13}C\) nuclear spins that was much stronger than expected and not present in the \(^{12}C\) devices. In the second nanotube experiment, pulsed gate experiments are used to measure the timescales of spin relaxation and dephasing in a two-electron double quantum dot. The relaxation time is longest at zero magnetic field and goes through a minimum at higher field, consistent with the spin-orbit-modified electronic spectrum of carbon nanotubes. We measure a short dephasing time consistent with the anomalously strong electron-nuclear interaction inferred from the first nanotube experiment. / Physics

One of the most important results emerging from string theory is the gauge gravity duality (AdS/CFT correspondence) which tells us that certain problems in particular gravitational backgrounds can be exactly mapped to a particular dual gauge theory a quantum theory very similar to the one explaining the interactions between fundamental subatomic particles. The chief merit of the duality is that a difficult problem in one theory can be mapped to a simpler and solvable problem in the other theory. The duality can be used both ways. Most of the current theoretical framework is suited to study equilibrium systems, or systems where time dependence is at most adiabatic. However in the real world, systems are almost always out of equilibrium. Generically these scenarios are described by quenches, where a parameter of the theory is made time dependent. In this dissertation I describe some of the work done in the context of studying quantum quench using the AdS/CFT correspondence. We recover certain universal scaling type of behavior as the quenching is done through a quantum critical point. Another question that has been explored in the dissertation is time dependence of the gravity theory. Present cosmological observations indicate that our universe is accelerating and is described by a spacetime called de-Sitter(dS). In 2011 there had been a speculation over a possible duality between de-Sitter gravity and a particular field theory (Euclidean SP(N) CFT). However a concrete realization of this proposition was still lacking. Here we explicitly derive the dS/CFT duality using well known methods in field theory. We discovered that the time dimension emerges naturally in the derivation. We also describe further applications and extensions of dS/CFT.

There is no apparent, dominant interaction in heavy transition metal oxides (TMO), especially in 5d-TMO, where all relevant interactions are of comparable energy scales, and therefore strongly compete. In particular, the spin-orbit interaction (SOI) strongly competes with the electron-lattice and on-site Coulomb interaction (U). Therefore, any tool that allows one to tune the relative strengths of SOI and U is expected to offer an opportunity for the discovery and study of novel materials. BaIrO3 is a magnetic insulator driven by SOI whereas the isostructural BaRuO3 is a paramagnetic metal. The contrasting ground states have been shown to result from the critical role of the strong SOI in the iridate. This dissertation thoroughly examines a wide array of newly observed novel phenomena induced by adjusting the relative strengths of SOI and U via a systematic chemical substitution of the Ru4+(4d4) ions for Ir4+(5d5) ions in BaIrO3, i.e., in high quality single crystals of BaIr1-xRuxO3(0.0 < x < 1.0) . Our investigation of structural, magnetic, transport and thermal properties reveals that Ru substitution directly rebalances the competing energies so profoundly that it generates a rich phase diagram for BaIr1-xRuxO3 featuring two major effects: (1) Light Ru doping (0 < x < 0.15) prompts a simultaneous and precipitous drop in both the magnetic ordering temperature TC and the electrical resistivity, which exhibits metal-insulator transition at around TC. (2) Heavier Ru doping (0.41 < x < 0.82) induces a robust metallic and spin frustration state. For comparison and contrast, we also substituted Rh4+(4d5) ions for Ir4+(5d5) ions in BaIrO3, i.e. BaIr1-xRhxO3(0.0 < x < 0.10), where Rh only reduces the SOI, but without altering the band filling. Hence, this system remains tuned at the Mott instability and is very susceptible to disorder scattering which gives rise to Anderson localization.

The charge-density-wave (CDW) material orthorhombic tantalum trisulfide (TaS3) is a quasi-one dimensional material that forms long ribbon shaped crystals, and exhibits unique physical behavior. We have measured the dependence of the hysteretic voltage-induced torsional strain (VITS) in TaS3, which was first discovered by Pokrovskii et. al. in 2007, on temperature and applied torque. Our experimental results shows that the application of torque to the crystal could also change the VITS time constant, magnitude, and sign. This suggests that the VITS is a consequence of residual torsional strain originally present in the sample which twists the polarizations of the CDW when voltage is applied. This polarization twist then results in torque on the crystal. Another group of materials that may attract interest is that of small-molecule soluble organic semiconductors. Due to their assumed small phonon thermal conductivities and higher charge carrier mobilities, which will increase their seebeck coefficients with doping as compared to polymers, the small-molecule organic materials are promising for thermoelectric applications. In our experiments, we have measured the interlayer thermal conductivity of rubrene (C42H28), using ac-calorimetry. For rubrene, we find that the interlayer thermal conductivity, ≈ 0.7 mW/cm·K, is several times smaller than the (previously measured) in-plane value. Also, we have measured the interlayer and in-plane thermal conductivities of 6,13-bis((triisopropylsilyl)ethynyl) pentacene (TIPS-Pn). The in-plane value is comparable to that of organic metals with excellent π-orbital overlap. The interlayer (c-axis) thermal diffusivity is at least an order of magnitude larger than the in-plane, and this unusual anisotropy implies very strong dispersion of optical modes in the interlayer direction, presumably due to interactions between the silyl-containing side groups. Similar values for both in-plane and interlayer conductivities have been observed for several other functionalized pentacene semiconductors with related structures.

<p>The role of the surroundings, or <italic> environment </italic>, is essential in understanding funda- mental quantum-mechanical concepts, such as quantum measurement and quantum entanglement. It is thought that a dissipative environment may be responsible for certain types of quantum (i.e. zero-temperature) phase transitions. We observe such a quantum phase transition in a very basic system: a resonant level coupled to a dissipative environment. Specifically, the resonant level is formed by a quantized state in a carbon nanotube, and the dissipative environment is realized in resistive leads; and we study the shape of the resonant peak by measuring the nanotube electronic conductance.</p><p>In sequential tunneling regime, we find the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weakly than the conventional T<super>-1</super>. Moreover, the observed scaling signals a close connec- tion between fluctuations that influence tunneling phenomenon and macroscopic models of the electromagnetic environment.</p><p>In the resonant tunneling regime (temperature smaller than the intrinsic level width), we characterize the resonant conductance peak, with the expectation that the width and height of the resonant peak, both dependent on the tunneling rate, will be suppressed. The observed behavior crucially depends on the ratio of the coupling between the resonant level and the two contacts. In asymmetric barriers the peak width approaches saturation, while the peak height starts to decrease.</p><p>Overall, the peak height shows a non-monotonic temperature dependence. In sym- metric barriers case, the peak width shrinks and we find a regime where the unitary conductance limit is reached in the incoherent resonant tunneling. We interpret this behavior as a manifestation of a quantum phase transition.</p><p>Finally, our setup emulates tunneling in a Luttinger liquid (LL), an interacting one-dimensional electron system, that is distinct from the conventional Fermi liquids formed by electrons in two and three dimensions. Some of the most spectacular properties of LL are revealed in the process of electron tunneling: as a function of the applied bias or temperature the tunneling current demonstrates a non-trivial power-law suppression. Our setup allows us to address many prediction of resonant tunneling in a LL, which have not been experimentally tested yet.</p> / Dissertation

Electron spin resonance (ESR) experiments are used to assess the possibilities for processing quantum information in the electronic and nuclear spins of endohedral fullerenes. It is shown that ¹⁵N@C₆₀ can be used for universal two-qubit quantum computing. The first step in this scheme is to initialize the nuclear and electron spins that each store one qubit. This was achieved with a magnetic field of 8.6 T at 3 K, by applying resonant RF and microwave radiation. This dynamic nuclear polarization technique made it possible to show that the nuclear T₁ time of ¹⁵N@C₆₀ is on the order of twelve hours at 4.2 K. The electronic T₂ is the limiting decoherence time for the system. At 3.7 K, this can be extended to 215 μs by using amorphous sulphur as the solvent. Pulse sequences are described that could perform all single-qubit gates to the two qubits independently, as well as CNOT gates. After these manipulations, the value of the qubits should be measured. Two techniques are demonstrated for this, by measuring the nuclear spin. Sc@C₈₂ could also be useful for quantum computation. By comparing ESR measurements with density functional theory calculations, it is shown how the orientation of a Sc@C₈₂ molecule in an applied magnetic field affects the molecule's Zeeman and hyperfine coupling. Hence the g- and A-tensors are written in the coordinate frame of the molecule. Pulsed ESR measurements show that the decoherence time at 20 K is 13 μs, which is 20 times longer than had been previously reported. Carbon nanotubes have been filled with endohedral fullerenes, forming 1D arrays that could lead to a scalable quantum computer. N@C₀₆ and Sc@C₈₂ have been used for this filling in various concentrations. ESR measurements of these samples are consistent with simulations of the dipolar coupling.