Theory of solid state quantum information processing

Recent theoretical work on solid-state proposals for the implementation of quantum computation and quantum information processing is reviewed. The differences and similarities between microscopic and macroscopic qubits are highlighted and exemplified by the spin qubit proposal on one side and the superconducting qubits on the other. Before explaining the spin and supercondcuting qubits in detail, some general concepts that are relevant for both types of solid-state qubits are reviewed. The controlled production of entanglement in solid-state devices, the transport of carriers of entanglement, and entanglement detection will be discussed in the final part of this review.Comment: 57 pages, 33 figures, review article, prepared for Handbook of Theoretical and Computational Nanotechnology. v.2: minor revision; references adde

Fast Super-Resolution Imaging with Ultra-High Labeling Density Achieved by Joint Tagging Super-Resolution Optical Fluctuation Imaging (JT-SOFI)

Previous stochastic localization-based super-resolution techniques are largely limited by the labeling density and the fidelity to the morphology of specimen. We report on an optical super-resolution imaging scheme implementing joint tagging using multiple fluorescent blinking dyes associated with super-resolution optical fluctuation imaging (JT-SOFI), achieving ultra-high labeling density super-resolution imaging. To demonstrate the feasibility of JT-SOFI, quantum dots with different emission spectra were jointly labeled to the tubulin in COS7 cells, creating ultra-high density labeling. After analyzing and combining the fluorescence intermittency images emanating from spectrally resolved quantum dots, the microtubule networks are capable of being investigated with high fidelity and remarkably enhanced contrast at sub-diffraction resolution. The spectral separation also significantly decreased the frame number required for SOFI, enabling fast super-resolution microscopy through simultaneous data acquisition. As the joint-tagging scheme can decrease the labeling density in each spectral channel, we can faithfully reflect the continuous microtubule structure with high resolution through collection of only 100 frames per channel. The improved continuity of the microtubule structure is quantitatively validated with image skeletonization, thus demonstrating the advantage of JT-SOFI over other localization-based super-resolution methods.Comment: 19 pages, 4 figures, with S

Unraveling the intricacies of spatial organization of the ErbB receptors and downstream signaling pathways

Faced with the complexity of diseases such as cancer which has 1012 mutations, altering gene expression, and disrupting regulatory networks, there has been a paradigm shift in the biological sciences and what has emerged is a much more quantitative field of biology. Mathematical modeling can aid in biological discovery with the development of predictive models that provide future direction for experimentalist. In this work, I have contributed to the development of novel computational approaches which explore mechanisms of receptor aggregation and predict the effects of downstream signaling. The coupled spatial non-spatial simulation algorithm, CSNSA is a tool that I took part in developing, which implements a spatial kinetic Monte Carlo for capturing receptor interactions on the cell membrane with Gillespies stochastic simulation algorithm, SSA, for temporal cytosolic interactions. Using this framework we determine that receptor clustering significantly enhances downstream signaling. In the next study the goal was to understand mechanisms of clustering. Cytoskeletal interactions with mobile proteins are known to hinder diffusion. Using a Monte Carlo approach we simulate these interactions, determining at what cytoskeletal distribution and receptor concentration optimal clustering occurs and when it is inhibited. We investigate oligomerization induced trapping to determine mechanisms of clustering, and our results show that the cytoskeletal interactions lead to receptor clustering. After exploring the mechanisms of clustering we determine how receptor aggregation effects downstream signaling. We further proceed by implementing the adaptively coarse grained Monte Carlo, ACGMC to determine if \u27receptor-sharing\u27 occurs when receptors are clustered. In our proposed \u27receptor-sharing\u27 mechanism a cytosolic species binds with a receptor then disassociates and rebinds a neighboring receptor. We tested our hypothesis using a novel computational approach, the ACGMC, an algorithm which enables the spatial temporal evolution of the system in three dimensions by using a coarse graining approach. In this framework we are modeling EGFR reaction-diffusion events on the plasma membrane while capturing the spatial-temporal dynamics of proteins in the cytosol. From this framework we observe \u27receptor-sharing\u27 which may be an important mechanism in the regulation and overall efficiency of signal transduction. In summary, I have helped to develop predictive computational tools that take systems biology in a new direction.\u2

Homodyne spin noise spectroscopy and noise spectroscopy of a single quantum dot

The steady-state fluctuations of a spin system are closely interlinked with its dynamics in linear response to external perturbations. Spin noise spectroscopy exploits this link to extract parameters characterizing the dynamics without needing an intricate spin polarization scheme. In samples with an accessible optical resonance, the spin fluctuations are imprinted onto a transmitted linearly polarized quasi-resonant probe laser beam according to the optical selection rules, making an all-optical observation of spin dynamics possible. The beam’s detuning and intensity determine whether the system is probed at thermal equilibrium or under optical driving. The technique is uniquely applicable for studying single quantum dots, where a charge carrier’s spin and occupancy dynamics can be observed simultaneously. This thesis presents a step-by-step derivation of the shape and statistical properties of experimental spectra and highlights the experimental limitations faced by the technique at very low probe intensities through uncorrelated broadband technical noise contributions. Optical homodyne amplification is evaluated in a proof-of-principle experiment to determine whether this limitation can be overcome at low frequencies < 5 MHz. Unlike previous attempts, the presented proof-of-principle experiment demonstrates that shot-noise limited spin noise measurements are possible in low-frequency ranges down to ≳ 100 kHz. For even lower frequencies, the suppression of laser intensity noise by the limited common-mode rejection of conventional balanced detectors is found to be the limiting contribution. In the second part of the thesis, optical spin noise spectroscopy is used to conduct a long-term study of spin and occupancy dynamics of an individual hole spin confined in an (In,Ga)As quantum dot with high radial symmetry in the high magnetic fields regime. For magnetic fields ≳ 250 mT, the splitting of the Zeeman branches with an effective g-factor of 2.159(2) exceeds the quantum dot’s trion resonance’s homogeneous line width of 6.3(2) μeV, revealing a rich spectral structure of spin and occupancy dynamics. This structure reveals a so far neglected contribution of an internal photoeffect to the charge dynamics between the quantum dot and its environment. Previously developed theoretical modeling is extended to incorporate the photoeffect and successfully achieves excellent qualitative correspondence with experimental spectra for almost all detuning ranges. The photoeffect shuffles the charge from and into the quantum dot with two distinct rates. Within the model, the previously required Auger process is unnecessary to describe the experimental data. The rates of discharging and recharging the quantum dot are determined to be on the order of 12(7) kHz·μm²·nW⁻¹ and 6(2) kHz·μm²·nW⁻¹, respectively. For magnetic fields < 500 mT, very long T1 hole spin relaxation times ≫ 1 ms are observed, while above 500 mT, T1 falls to 5(2) μs at 2.5 T, qualitatively confirming the theoretical prediction of a single-phonon mediated relaxation process. Furthermore, the electron spin relaxation time T1 in the trion state shows no pronounced dependence on magnetic fields above 500 mT and stays at a constant value of 101(2) ns. The saturation intensity of the transition also does not depend on the magnetic field and stays at a constant value of 4.8(7) nW·μm⁻²

A topological approximation of the nonlinear Anderson model

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance-overlap in phase space, ranging from a fully developed chaos involving Levy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on a Cayley tree. It is found in vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha, with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of stripes propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for publication in Physical Review