Quantum optomechanics with silicon nanostructures

Mechanical resonators are the most basic and ubiquitous physical systems known. In on-chip form, they are used to process high frequency signals in every cell phone, television, and laptop. They have also been in the last few decades in different shapes and forms, a critical part of progress in quantum information sciences with kilogram-scale mirrors for gravitational wave detection measuring motion at its quantum limits, and the motion of single ions being used to link qubits for quantum computation.

Optomechanics is a field primarily concerned with coupling light to the motion of mechanical structures. This thesis contains descriptions of recent work with mechanical systems in the megahertz to gigahertz frequency range, formed by nanofabricating novel photonic/phononic structures on a silicon chip. These structures are designed to have both optical and mechanical resonances, and laser light is used to address and manipulate their motional degrees of freedom through radiation pressure forces. We laser cool these mechanical resonators to their ground states, and observe for the first time the quantum zero-point motion of a nanomechanical resonator. Conversely, we show that engineered mechanical resonances drastically modify the optical response of our structures, creating large effective optical nonlinearities not present in bulk silicon. We experimentally demonstrate aspects of these nonlinearities by proposing and observing ``electromagnetically induced transparency'' and light slowed down to 6 m/s, as well as wavelength conversion, and generation of nonclassical optical radiation. Finally, the application of optomechanics to longstanding problems in quantum and classical communications are proposed and investigated.

Diagonal forms, linear algebraic methods and Ramsey-type problems

This thesis focuses mainly on linear algebraic aspects of combinatorics. Let N_t(H) be an incidence matrix with edges versus all subhypergraphs of a complete hypergraph that are isomorphic to H. Richard M. Wilson and the author find the general formula for the Smith normal form or diagonal form of N_t(H) for all simple graphs H and for a very general class of t-uniform hypergraphs H.

As a continuation, the author determines the formula for diagonal forms of integer matrices obtained from other combinatorial structures, including incidence matrices for subgraphs of a complete bipartite graph and inclusion matrices for multisets.

One major application of diagonal forms is in zero-sum Ramsey theory. For instance, Caro's results in zero-sum Ramsey numbers for graphs and Caro and Yuster's results in zero-sum bipartite Ramsey numbers can be reproduced. These results are further generalized to t-uniform hypergraphs. Other applications include signed bipartite graph designs.

Research results on some other problems are also included in this thesis, such as a Ramsey-type problem on equipartitions, Hartman's conjecture on large sets of designs and a matroid theory problem proposed by Welsh.

Repeat-until-success distributed quantum computation by using single-photon interference at a beam splitter

A repeat-until-success (RUS) measurement-based scheme for the implementation of the distributed quantum computation by using single-photon interference at a 50:50 beam splitter is proposed. It is shown that the 50:50 beam splitter can naturally project a suitably encoded matter-photon state to either a desired entangling gate-operated state of the matter qubits or to their initial state when the photon is detected. The recurrence of the initial state permits us to implement the desired entangling gate in a RUS way. To implement a distributed quantum computation we suggest an encoding method by means of the effect of dipole-induced transparency proposed recently [E. Waks and J. Vuckovic, Phys. Rev. Lett. 96, 153601 (2006)]. The effects of the unfavorable factors on our scheme are also discussed.

Quantum computation based on a quantum switch in cavity QED

A feasible scheme for constructing quantum logic gates is proposed on the basis of quantum switches in cavity QED. It is shown that the light field which is fed into the cavity due to the passage of an atom in a certain state can be used to manipulate the conditioned quantum logical gate. In our scheme, the quantum information is encoded in the states of Rydberg atoms and the cavity mode is not used as logical qubits or as a communicating "bus"; thus, the effect of atomic spontaneous emission can be neglected and the strict requirements for the cavity can be relaxed.

Mixed entanglement distillation by means of parity measurements

We present a mixed entanglement distillation protocol by means of the parity measurement of qubits. Without the use of controlled-NOT (CNOT) operations, the efficiency of our protocol can approach that of the CNOT protocol. In comparison, the total successful probability of our protocol can reach a quantity twice as large as that of the linear optics-based protocol.

Redes bipartitas: aplicación a un caso económico real

[ES]El TFG consta de dos partes: en la primera se expondrá la teoría sobre las redes que se utilizarán en la segunda parte, que consistirá en el análisis de un caso real donde se aplicarán las redes estudiadas en la primera parte.

Avaliação da influência do material de confecção das matrizes no teste de conversão monomérica por espectrometria no infravermelho de um compósito

Este estudo teve por objetivo avaliar, in vitro, a influência do material de confecção das matrizes, traçando um perfil da conversão monomérica de um compósito micro-híbrido, além de avaliar qual dos materiais testados mais se assemelha a uma matriz de dentina. A avaliação foi feita através da análise do grau de conversão (GC). Foram confeccionadas 3 matrizes bipartidas, sendo estas de teflon negro, tefon branco e aço inoxidável, ambas com 10mm de diâmetro e 2 mm de profundidade. Para o grupo controle foi utilizado um incisivo central bovino, o qual teve sua face vestibular aplainada em uma lixadeira sob refrigeração constante, com o auxílio de uma lixa de carbeto de silício, número 800. Após, este dente foi preparado com uma broca diamantada número 2294 (KG Sorensen) em alta rotação, própria para a preparação de cavidades padronizadas para ensaios de laboratório, apresentando um limitador de penetração. Em seguida, com um motor de baixa rotação foi realizado o acabamento das paredes, obtendo-se uma cavidade de 2,0 mm de profundidade por 9,0 mm de diâmetro. Pela palatina desse dente, com uma broca carbide cilíndrica de numeração 2056 (KG Sorensen), fez-se uma penetração até se obter uma parede de dentina extremamente fina, porém sem que esta fosse rompida. Assim, com uma agulha, fez-se uma pequena perfuração no centro dessa dentina para que este instrumental servisse como um pino para remoção do corpo de prova de dentro da matriz de dente. Os corpos de prova (CP) foram obtidos a partir da inserção do compósito no interior da perfuração das matrizes em um único incremento e cobertos na superfície externa com uma matriz de poliéster mais uma lamínula de vidro. Os CP foram fotopolimerizados por 40 s pela fonte de luz halógena Optilux 501 (Demetron), com 500 mW/cm. Imediatamente após a polimerização, os corpos de prova eram submetidos no topo e na base para a análise de espectrometria no infravermelho para a determinação da profundidade de polimerização, pela técnica do filme vazado para o compósito não polimerizado e pela técnica da pastilha de brometo de potássio (KBr) para o compósito polimerizado. Foram confeccionados 5 CP de cada grupo. Em cada grupo, o compósito da base e do topo das amostras foi moído até se obter de 1,5 a 2,0 mg de pó e misturado com 70 mg de KBr, para obtenção da pastilha de KBr. Foi feita a análise de espectrofotometria no infravermelho por Transformada de Fourier (FTIR). As absorções selecionadas para o cálculo foram 1610 cm-1 e 1637 cm-1, os picos dos espectros das ligações dos carbonos aromáticos e alifáticos, respectivamente. Os dados obtidos foram tratados estatisticamente. Os grupos Gr1B, Gr2B, Gr3B e Gr4B representam, respectivamente, as bases dos CP confeccionados pelas matrizes de DB, TN, TB e AI. Já os Gr1T, Gr2T, Gr3T e Gr4T representam os topos. Médias (%) e DP: Gr1T (46,461,99), Gr2T (39,864,51), Gr3T (44,053,44) e Gr4T (38,045,08). Gr1B (40,441,49), Gr2B (36,153,81), Gr3B (40,093,18) e Gr4B (35,593,35). Em posse dos resultados, pôde-se concluir que os grupos do teflon negro, teflon branco e aço inoxidável não apresentaram diferenças entre o grau de conversão do topo e da base, enquanto que o grupo da dentina apresentou maior conversão do topo. Comparando as matrizes entre elas, pôde-se perceber que no topo, o GC do dente bovino é maior que o GC do aço inoxidável e do que o de teflon negro, o GC do teflon branco é maior que o GC do aço inoxidável e do que o de teflon negro. Já o topo dos grupos de dente bovino e teflon banco foram semelhantes. Nas bases dos CPs, não houve diferença significativa entre os grupos testados. De acordo com os resultados obtidos no experimento, pôde-se concluir que nos grupos do teflon negro, teflon branco e aço inoxidável não houve diferença entre 0 e 2 mm, ou seja, topo e base, o que mostra que o material de confecção da matriz não influênciou o grau de conversão do compósito. Já para o grupo da matriz de dentina, o topo apresentou valor de conversão monomérica maior, mostrando que, neste caso, o material da matriz interferiu no grau de conversão. Pode-se perceber também que existe uma tendência da matriz de teflon branco se assemelhar mais a matriz de dentina, pois foi o único grupo que apresentou semelhança nos valores de conversão monomérica no topo das amostras. Porém analisando a base das amostras, percebe-se que todos os grupos se comportaram de forma semelhante, obtendo valores do grau de conversão sem diferença significante.

Complex systems in quantum technologies

124 p.

Spin-related phenomena in magnetic and spin-orbit couppled bose-einstein condensates

129 p.

Symmetry restoration and quantumness reestablishment

A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.

Biomimetic Cloning of Quantum Observables

We propose a bio-inspired sequential quantum protocol for the cloning and preservation of the statistics associated to quantum observables of a given system. It combines the cloning of a set of commuting observables, permitted by the no-cloning and no-broadcasting theorems, with a controllable propagation of the initial state coherences to the subsequent generations. The protocol mimics the scenario in which an individual in an unknown quantum state copies and propagates its quantum information into an environment of blank qubits Finally, we propose a realistic experimental implementation of this protocol in trapped ions.

Digital Quantum Simulation of Spin Models with Circuit Quantum Electrodynamics

Systems of interacting quantum spins show a rich spectrum of quantum phases and display interesting many-body dynamics. Computing characteristics of even small systems on conventional computers poses significant challenges. A quantum simulator has the potential to outperform standard computers in calculating the evolution of complex quantum systems. Here, we perform a digital quantum simulation of the paradigmatic Heisenberg and Ising interacting spin models using a two transmon-qubit circuit quantum electrodynamics setup. We make use of the exchange interaction naturally present in the simulator to construct a digital decomposition of the model-specific evolution and extract its full dynamics. This approach is universal and efficient, employing only resources that are polynomial in the number of spins, and indicates a path towards the controlled simulation of general spin dynamics in superconducting qubit platforms.

Dynamical behavior of damped driven coupled single electron simple harmonic oscillators

Coherent coupling between a large number of qubits is the goal for scalable approaches to solid state quantum information processing. Prototype systems can be characterized by spectroscopic techniques. Here, we use pulsed-continuous wave microwave spectroscopy to study the behavior of electrons trapped at defects within the gate dielectric of a sol-gel-based high-k silicon MOSFET. Disorder leads to a wide distribution in trap properties, allowing more than 1000 traps to be individually addressed in a single transistor within the accessible frequency domain. Their dynamical behavior is explored by pulsing the microwave excitation over a range of times comparable to the phase coherence time and the lifetime of the electron in the trap. Trap occupancy is limited to a single electron, which can be manipulated by resonant microwave excitation and the resulting change in trap occupancy is detected by the change in the channel current of the transistor. The trap behavior is described by a classical damped driven simple harmonic oscillator model, with the phase coherence, lifetime and coupling strength parameters derived from a continuous wave (CW) measurement only. For pulse times shorter than the phase coherence time, the energy exchange between traps, due to the coupling, strongly modulates the observed drain current change. This effect could be exploited for 2-qubit gate operation. The very large number of resonances observed in this system would allow a complex multi-qubit quantum mechanical circuit to be realized by this mechanism using only a single transistor.

Ballistic Single-Electron Quputer

We propose a new solid state implementation of a quantum computer (quputer) using ballistic single electrons as flying qubits in 1D nanowires. We use a single electron pump (SEP) to prepare the initial state and a single electron transistor (SET) to measure the final state. Single qubit gates are implemented using quantum dots as phase shifters and electron waveguide couplers as beam splitters. A Coulomb coupler acts as a 2-qubit gate, using a mutual phase modulation effect. Since the electron phase coherence length in GaAs/AlGaAs heterostructures is of the order of 30$\mu$m, several gates (tens) can be implemented before the system decoheres.

Plerchis heterorchis N. sp. (Digenea: Acanthocolpidae Luhe, 1909) from fishes Lutjanus johnii and Otolithus argenteus of Karachi coast, Pakistan

A new species of trematodes Pleorchis heterorchis is described from the fishes Lutjanus johnii and Otolithus argenteus of Karachi coast. The new species is characterized by having a lanceolate body with a notch at the middle of the posterior end of the body. Body surface is smooth, ventral sucker rounded, situated at the anterior middle region of the body, pre-pharynx is well developed, widened posteriorly, pharynx muscular, oesophagus short, intestine H-shaped with anterior arms much shorter than the posterior, intestinal bifurcation almost in the middle of fore body, anterior caeca wide and short extending as far as anterior limit of pharynx. Posteriorly caeca reach to posterior end of the body with no lateral out pocketing. Testes 44 in number, intercecal arranged in 2 parallel rows, sub-globular, entire to slightly irregular, almost of same sizes extending immediately from posterior of the ovary to anterior of excretory vesicle. Cirrus pouch overlaps the ventral sucker, extends into hind body, terminating above the ovary, containing bipartite seminal vesicle, pars prostatica and ejaculatory duct. Genital pore behind the intestinal bifurcation and pre-acetabular. Ovary pre-testicular, consists of 16 follicles of varying sizes. Vitellaria lateral, follicular, extending from post bifurcal to posterior extremity. Excretory vesicle reaches to the posterior level of last pair of testes.