Multiple Silicon Dangling-Bond Charge qubits for quantum computing: A Hilbert-Space Analysis of the Hamiltonian

Silicon-based dangling-bond charge qubit is one of the auspicious models for universal fault-tolerant solid-state quantum computing. In universal quantum computing, it is crucial to evaluate and characterize the computational Hilbert space and reduce the complexity and size of the computational space. Here, we recognize this problem to understand the complexity and characteristics of the Hilbert space in our dangling-bond qubit model. The size of the desired Hilbert space can prominently be reduced by considering assumptions regarding the qubit loss. Moreover, the dimension of the desired subsets in the space shrinks by a factor of two due to the spin preservation property. Finally, the required classical memory for storage of the qubit information, Hamiltonian and Hilbert space is analysed when the number of qubits grows.Comment: 8 pages, 5 figures, 2 table

Quantum Sensing with Scanning Near-Field Optical Photons Scattered by an Atomic-Force Microscope Tip

Scattering scanning near-field optical microscopy (s-SNOM) is known as a promising technique for overcoming Abbe diffraction limit and substantially enhancing the spatial resolution in spectroscopic imaging. The s-SNOM works by exposing an atomic force microscope (AFM) tip to an optical electromagnetic (EM) field, while the tip is so close to a sample that the incident beam lies within the near-field regime and displays nonlinear behaviour. We suggest replacing the incident field by quantized EM fields, i.e. photons, and propose a quantum model for the suggested system, by employing electric-dipole approximation, image theory, and perturbation theory. Quantum state of scattered photons from the AFM tip is extracted from the proposed model, which contain information about electrical permittivity of the dielectric material beneath the tip. The permittivity of the sample can be extracted through spectroscopic setups. Our proposed scheme can be used for quantum imaging or quantum spectroscopy with high resolution.Comment: 4 pages and 3 figure

Characterizing the rate and coherence of single-electron tunneling between two dangling bonds on the surface of silicon

We devise a scheme to characterize tunneling of an excess electron shared by a pair of tunnel-coupled dangling bonds on a silicon surface -- effectively a two-level system. Theoretical estimates show that the tunneling should be highly coherent but too fast to be measured by any conventional techniques. Our approach is instead to measure the time-averaged charge distribution of our dangling-bond pair by a capacitively coupled atomic-force-microscope tip in the presence of both a surface-parallel electrostatic potential bias between the two dangling bonds and a tunable midinfrared laser capable of inducing Rabi oscillations in the system. With a nonresonant laser, the time-averaged charge distribution in the dangling-bond pair is asymmetric as imposed by the bias. However, as the laser becomes resonant with the coherent electron tunneling in the biased pair the theory predicts that the time-averaged charge distribution becomes symmetric. This resonant symmetry effect should not only reveal the tunneling rate, but also the nature and rate of decoherence of single-electron dynamics in our system

Dangling-bond charge qubit on a silicon surface

Two closely spaced dangling bonds positioned on a silicon surface and sharing an excess electron are revealed to be a strong candidate for a charge qubit. Based on our study of the coherent dynamics of this qubit, its extremely high tunneling rate ~ 10^14 1/s greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming a critical obstacle of charge qubit quantum computing. We investigate possible configurations of dangling bond qubits for quantum computing devices. A first-order analysis of coherent dynamics of dangling bonds shows promise in this respect.Comment: 17 pages, 3 EPS figures, 1 tabl

Coherence of Coupled Dangling-Bond Pairs on the Silicon Surface

We characterize coherent dynamics of closely-spaced dangling bond (DB) pairs positioned on a silicon surface and sharing an excess electron. We investigate whether a coupled-DB pair is a potential candidate for a charge qubit. A dangling bond is an atomic-scale entity that acts like a quantum dot. By shrinking the scale of the quantum dots and the spacing between them, we expect that the excess-electron tunneling rate increases dramatically with decreasing inter-dot separation, while decoherence scales weakly. Our analysis of the coherent dynamics of coupled-DB pairs shows promise in this respect. The extremely high tunneling rate of the DB excess charge greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming the critical obstacle of charge qubits for quantum computing purposes. However, this scaling advantage comes at the price of requiring rapid control and readout. We devise a scheme for measuring the DB-pair dynamics, but investigating the fast control is beyond the scope of this thesis. Furthermore, we investigate the effect of the silicon-surface structure on the coherence of a coupled-DB pair. The silicon surface of interest is well patterned, but it has an anisotropic structure. Therefore, the coupling strength of a DB pair depends on the arrangement of the DBs on the silicon surface. We employ ab initio techniques and calculate the energy splitting for a wide variety of coupled DB-pair configurations on this surface. The results show that the energy splitting (and consequently the tunneling rate of the DB-pair excess charge) is a function of the DBs’ location on the surface and also it strongly depends on the structural orientation of the DBs’ orbital. Based on the results, DB-pair configurations are categorized into four groups, such that the changing rate of energy splitting versus DB-pair separation is different among the groups. Knowing about the effect of the surface structure on the DB-pair energy splitting is especially useful when dealing with more complex systems such as DB subnanowires, quantum cellular automata cells, and quantum computing schemes. Also, the results help to have a better understanding of the coherence and bonding on this Si surface. As mentioned earlier, the highly coherent dynamics of coupled-DB pairs comes at the price of being too fast to be directly measured by any conventional technique. We therefore devise a scheme to characterize tunneling of the DB excess charge by measuring the time-averaged charge distribution of the DB pair with an atomic force microscope. In our approach, a DB pair is capacitively coupled to an atomic force microscope tip in the presence of an electrostatic potential bias applied along the DB pair, and a tunable mid-infrared laser to drive the pair. With a non-resonant laser field, the time-averaged charge distribution in the dangling-bond pair is asymmetric as imposed by the bias. However, as the laser becomes resonant with the coherent electron tunneling in the biased pair the theory predicts that the time-averaged charge distribution becomes symmetric. This resonant symmetry effect should not only reveal the tunneling rate, but also the nature and rate of decoherence of single-electron dynamics in our system

Characterization of multipartite squeezed states by su(1,1) symmetry

Bibliography: p. 75-8

Comparison of Efficacy of Nortriptyline Versus Transcutaneous Electrical Nerve Stimulation on Painful Peripheral Neuropathy in Patients with Diabetes

Background and aims: Diabetic peripheral neuropathic pain (DPNP) is one of the most common complications of diabetes and is difficult to treat. Existing treatments are often inadequate at controlling pain and limited by side-effects and drug tolerance. This study assessed the efficacy of nortriptyline versus Transcutaneous Electrical Nerve Stimulation (TENS) in patients with DPNP