A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of quantum computers with spin-based qubits coupled by the exchange interaction. Current theory predicts an exchange interaction with a -1 power-law dependence on the detuning ϵ, the energy offset between the two dots. However, experiment has shown a -3/2 power-law dependence on ϵ. Using WKB analysis, this thesis explores one possible source of the modified dependence, namely an ϵ-dependent tunnel coupling between the two wells. WKB quantization is used to find expressions for the tunnel coupling of a one-dimensional double-well, and these results are compared to the exact, numerical solutions, as determined by the finite difference method and the transfer matrix method. Small ϵ-dependent corrections to the tunnel coupling are observed. In typical cases, WKB correctly predicts a constant tunnel coupling at leading-order. WKB also predicts small ϵ-dependent corrections for typical cases and strongly ϵ-dependent tunnel couplings for certain exceptional cases. However, numerical simulations suggest that WKB is not accurate enough to analyze the small corrections, and is not valid in the exceptional cases. Deviations from the conventional form of the low-energy Hamiltonian for a double-well are also observed and discussed.

A simplified model of a double quantum dot is presented and analyzed, with applications to spin-qubit quantum computation. The ability to trap single electrons in semiconductor nanostructures has led to the proposal of quantum computers with spin-based qubits coupled by the exchange interaction. Current theory predicts an exchange interaction with a -1 power-law dependence on the detuning ϵ, the energy offset between the two dots. However, experiment has shown a -3/2 power-law dependence on ϵ. Using WKB analysis, this thesis explores one possible source of the modified dependence, namely an ϵ-dependent tunnel coupling between the two wells. WKB quantization is used to find expressions for the tunnel coupling of a one-dimensional double-well, and these results are compared to the exact, numerical solutions, as determined by the finite difference method and the transfer matrix method. Small ϵ-dependent corrections to the tunnel coupling are observed. In typical cases, WKB correctly predicts a constant tunnel coupling at leading-order. WKB also predicts small ϵ-dependent corrections for typical cases and strongly ϵ-dependent tunnel couplings for certain exceptional cases. However, numerical simulations suggest that WKB is not accurate enough to analyze the small corrections, and is not valid in the exceptional cases. Deviations from the conventional form of the low-energy Hamiltonian for a double-well are also observed and discussed.

We report on conductance measurements in carbon nanotube based double quantum dots connected to two normal electrodes and a central superconducting finger. By operating our devices as Cooper pair beam splitters, we provide evidence for Crossed Andreev Reflection (CAR). We inject Cooper pairs in the superconducting electrode and measure the differential conductance at both left and right arm. The contacts split the device into two coupled quantum dots. Each of the quantum dots can be tuned by a lateral sidegate. If the two sidegates are tuned such that both quantum dots are at a transmission resonance, a considerable part of the injected Cooper pairs splits into different normal contacts. On the contrary, if only one of the two dots is at resonance, nearly all pairs tunnel to the same normal contact. By comparing different triple points in the double dot stability diagram, we demonstrate the contribution of split Cooper pairs to the total current. In this manner, we are able to extract a splitting efficiency of up to 50% in the resonant case. Carbon Nanotubes ensure ballistic transport and long spin-flip scattering lengths. Due to these properties they are promising candidates to investigate EPR-type correlations in solid state systems.

Spin selective MQ-SQ correlation has been demonstrated by either selective pulses in homo-nuclear spin systems in isotropic and weakly orienting chiral media or by nonselective pulses in hetero-nuclear spin systems in strongly aligned media. As a consequence of the spin selective correlation, the coherence transfer pathway from MQ to SQ is spin state selective. This two dimensional approach enables the utilization of the passive couplings (remote couplings) to break a complex one dimensional spectrum into many sub spectra. Each sub spectrum contains fewer transitions and hence fewer couplings (active couplings). The role of the passive couplings is to displace the sub spectra and measurement of the displacements taking into account their relative tilt provides the magnitude of the passive couplings along with relative signs. Further possibility of a spin state selective MQ-SQ resolved experiment to determine very small remote couplings otherwise buried within linewidth in one dimensional spectrum has been demonstrated. The resolution of the multiple quantum spectrum in indirect dimension has also been exploited to separate the sub spectra. The technique renders the analysis of complex spectrum in isotropic system much simpler. The potentialities of the technique have also been demonstrated for discrimination of optical enantiomers and derivation of the residual dipolar couplings from very complicated spectrum. The second order spectrum in strongly aligned media restrict selective excitation, however in hetero-nuclear spin system the nonselective pulses on protons do not interact with the hetero-nuclear spins. Thus the weakly coupled part of a strongly coupled spectrum has been exploited for simplifying the second order spectrum and thereby its analysis. Thus several methodologies derived from spin selective correlation has been demonstrated. Enantiopure spectrum has been recorded from a mixture of R and S enantiomers by a novel pulse scheme called Double Quantum Selective Refocusing Experiment. The dipolar coupled methyl protons in weakly orienting media are utilized. The selective excitation of double quantum coherence reduces the three spin system into a two spin system and remote couplings are refocused which otherwise leads to broadening. The sum of passive couplings being different for the enantiomers resolution in the DQ dimension is enhanced and thereby their discrimination. Finally several decoupling schemes has been compared in the indirect dimension of HSQC experiment to resolve 13C satellite spectra otherwise buried within line width for increased confidence in determining hetero-nuclear framework information.