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 Title
 MODELING AND DESIGN OF A PHOTONIC CRYSTAL CHIP HOSTING A QUANTUM NETWORK MADE OF SINGLE SPINS IN QUANTUM DOTS THAT INTERACT VIA SINGLE PHOTONS.
 Creator

Seigneur, Hubert, Schoenfeld, Winston, University of Central Florida
 Abstract / Description

In this dissertation, the prospect of a quantum technology based on a photonic crystal chip hosting a quantum network made of quantum dot spins interacting via single photons is investigated. The mathematical procedure to deal with the LiouvilleVon Neumann equation, which describes the timeevolution of the density matrix, was derived for an arbitrary system, giving general equations. Using this theoretical groundwork, a numerical model was then developed to study the spatiotemporal dynamics...
Show moreIn this dissertation, the prospect of a quantum technology based on a photonic crystal chip hosting a quantum network made of quantum dot spins interacting via single photons is investigated. The mathematical procedure to deal with the LiouvilleVon Neumann equation, which describes the timeevolution of the density matrix, was derived for an arbitrary system, giving general equations. Using this theoretical groundwork, a numerical model was then developed to study the spatiotemporal dynamics of entanglement between various qubits produced in a controlled way over the entire quantum network. As a result, an efficient quantum interface was engineered allowing for storage qubits and traveling qubits to exchange information coherently while demonstrating little error and loss in the process; such interface is indispensable for the realization of a functional quantum network. Furthermore, a carefully orchestrated dynamic control over the propagation of the flying qubit showed highefficiency capability for onchip singlephoton transfer. Using the optimized dispersion properties obtained quantum mechanically as design parameters, a possible physical structure for the photonic crystal chip was constructed using the Plane Wave Expansion and FiniteDifference TimeDomain numerical techniques, exhibiting almost identical transfer efficiencies in terms of normalized energy densities of the classical electromagnetic field. These promising results bring us one step closer to the physical realization of an integrated quantum technology combining both semiconductor quantum dots and subwavelength photonic structures.
Show less  Date Issued
 2010
 Identifier
 CFE0003433, ucf:48391
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003433
 Title
 Solving Constraint Satisfaction Problems with Matrix Product States.
 Creator

Pelton, Sabine, Mucciolo, Eduardo, Ishigami, Masa, Leuenberger, Michael, University of Central Florida
 Abstract / Description

In the past decade, Matrix Product State (MPS) algorithms have emerged as an efficient method of modeling some manybody quantum spin systems. Since spin system Hamiltonians can be considered constraint satisfaction problems (CSPs), it follows that MPS should provide a versatile framework for studying a variety of general CSPs. In this thesis, we apply MPS to two types of CSP. First, use MPS to simulate adiabatic quantum computation (AQC), where the target Hamiltonians are instances of a...
Show moreIn the past decade, Matrix Product State (MPS) algorithms have emerged as an efficient method of modeling some manybody quantum spin systems. Since spin system Hamiltonians can be considered constraint satisfaction problems (CSPs), it follows that MPS should provide a versatile framework for studying a variety of general CSPs. In this thesis, we apply MPS to two types of CSP. First, use MPS to simulate adiabatic quantum computation (AQC), where the target Hamiltonians are instances of a fully connected, random Ising spin glass. Results of the simulations help shed light on why AQC fails for some optimization problems. We then present the novel application of a modified MPS algorithm to classical Boolean satisfiability problems, specifically kSAT and max kSAT. By construction, the algorithm also counts solutions to a given Boolean formula (\#SAT). For easy satisfiable instances, the method is more expensive than other existing algorithms; however, for hard and unsatisfiable instances, the method succeeds in finding satisfying assignments where other algorithms fail to converge.
Show less  Date Issued
 2017
 Identifier
 CFE0006902, ucf:51713
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006902
 Title
 COMPUTATIONAL STUDY OF THE NEAR FIELD SPONTANEOUS CREATION OF PHOTONIC STATES COUPLED TO FEW LEVEL SYSTEMS.
 Creator

Tafur, Sergio, Leuenberger, Michael, University of Central Florida
 Abstract / Description

Models of the spontaneous emission and absorption of photons coupled to the electronic states of quantum dots, molecules, NV (single nitrogen vacancy) centers in diamond, that can be modeled as artificial few level atoms, are important to the development of quantum computers and quantum networks. A quantum source modeled after an effective few level system is strongly dependent on the type and coupling strength the allowed transitions. These selection rules are subject to the WignerEckert...
Show moreModels of the spontaneous emission and absorption of photons coupled to the electronic states of quantum dots, molecules, NV (single nitrogen vacancy) centers in diamond, that can be modeled as artificial few level atoms, are important to the development of quantum computers and quantum networks. A quantum source modeled after an effective few level system is strongly dependent on the type and coupling strength the allowed transitions. These selection rules are subject to the WignerEckert theorem which specifies the possible transitions during the spontaneous creation of a photonic state and its subsequent emission. The model presented in this dissertation describes the spatiotemporal evolution of photonic states by means of a Diraclike equation for the photonic wave function within the region of interaction of a quantum source. As part of this aim, we describe the possibility to shift from traditional electrodynamics and quantum electrodynamics, in terms of electric and magnetic fields, to one in terms of a photonic wave function and its operators. The mapping between these will also be presented herein. It is further shown that the results of this model can be experimentally verified. The suggested method of verification relies on the direct comparison of the calculated density matrix or Wigner function, associated with the quantum state of a photon, to ones that are experimentally reconstructed through optical homodyne tomography techniques. In this nonperturbative model we describe the spontaneous creation of photonic state in a nonMarkovian limit which does not implement the WeisskopfWigner approximation. We further show that this limit is important for the description of how a single photonic mode is created from the possibly infinite set of photonic frequencies $\nu_k$ that can be excited in a dielectriccavity from the vacuum state. We use discretized centraldifference approximations to the space and time partial derivatives, similar to finitedifference time domain models, to compute these results. The results presented herein show that near field effects need considered when describing adjacent quantum sources that are separated by distances that are small with respect to the wavelength of their spontaneously created photonic states. Additionally, within the future scope of this model,we seek results in the Purcell and Rabi regimes to describe enhanced spontaneous emission events from these fewlevel systems, as embedded in dielectric cavities. A final goal of this dissertation is to create novel computational and theoretical models that describe single and multiple photon states via single photon creation and annihilation operators.
Show less  Date Issued
 2011
 Identifier
 CFE0003881, ucf:48739
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003881
 Title
 Field Theoretic Lagrangian Stencils from OffShell Supermultiplet Gauge Quotients.
 Creator

Katona, Gregory, Klemm, Richard, Hubsch, Tristan, Peale, Robert, Shivamoggi, Bhimsen, University of Central Florida
 Abstract / Description

Recent efforts to classify offshell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a nodepair transformtion between fermionic / bosonic componentfields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge quotients by supersymmetric images of other Adinkras,...
Show moreRecent efforts to classify offshell representations of supersymmetry without a central charge have focused upon directed, supermultiplet graphs of hypercubic topology known as Adinkras. These encodings of Super Poincare algebras, depict every generator of a chosen supersymmetry as a nodepair transformtion between fermionic / bosonic componentfields. This research thesis is a culmination of investigating novel diagrammatic sums of gauge quotients by supersymmetric images of other Adinkras, and the correlated building of field theoretic worldline Lagrangians to accommodate both classical and quantum venues. We find Ref [40], that such gauge quotients do not yield other stand alone or (")proper(") Adinkras as afore sighted, nor can they be decomposed into supermultiplet sums, but are rather a connected (")Adinkraic network("). Their iteration, analogous to Weyl's construction for producing all finitedimensional unitary representations in Lie algebras, sets off chains of algebraic paradigms in discretegraph and continuousfield variables, the links of which feature distinct, supersymmetric Lagrangian templates. Collectively, these Adiankraic series air new symbolic genera for equation to phase moments in Feynman path integrals. Guided in this light, we proceed by constructing Lagrangians actions for the N = 3 supermultiplet YI /(iDI X) for I = 1, 2, 3, where YI and X are standard, SalamStrathdee superfields: YI fermionic and X bosonic. The system, bilinear in the component fields exhibits a total of thirteen free parameters, seven of which specify Zeemanlike coupling to external background (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory responses, some of which are found to be surprisingly controlled by the golden ratio, ? ? 1.61803, Ref [52]. It is further determined that these Lagrangians allow an N = 3 ? 4 supersymmetric extension to the ChiralChiral and ChiraltwistedChiral multiplet, while a subset admits two inequivalent such extensions. In a natural progression, a continuum of observably and usefully inequivalent, finitedimensional offshellrepresentations of worldline N = 4 extended supersymmetry are explored, that are variatefrom one another but in the value of a tuning parameter, Ref [53]. Their dynamics turnsout to be nontrivial already when restricting to just bilinear Lagrangians. In particular, wefind a 34parameter family of bilinear Lagrangians that couple two differently tuned supermultiplets to each other and to external magnetic fluxes, where the explicit parameter dependence is unremovable by any field redefinition and is therefore observable. This offers the evaluation of Xphase sensitive, offshell path integrals with promising correlationsto group product decompositions and to deriving source emergences of higherorder background fluxforms on 2dimensional manifolds, the stacks of which comprise spacetime volumes. Application to nonlinear sigma models would naturally follow, having potential use in M and F string theories.
Show less  Date Issued
 2013
 Identifier
 CFE0005011, ucf:50004
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005011