Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 179-187). Available also in a digital version from Dissertation Abstracts.

In recent years there has been a significant development of the dynamical map formalism for initially correlated states of a system and its environment. Based on some of these results, we study quantum process tomography for initially correlated states of the system and the environment. This is beyond the usual assumption that the state of the system and the environment are initially uncorrelated. Since quantum process tomography is an experimental procedure, we wind up having to study the role of preparation of input states for open quantum experiments. We work out a theory for the general preparation procedure, and study two preparation procedures in detail. In specific, we study the stochastic preparation procedure and the projective preparation procedure and apply them to quantum process tomography. The two preparation procedures describe the ways to uncorrelate the state of the system and the environment. However the specifics of how this is implemented plays a role on the outcomes of the experiment. When the stochastic preparation procedure is applied properly, quantum process tomography yields a linear process maps. We point out what it means to apply the stochastic preparation procedure properly by constructing several simple examples where inconsistencies in preparations leads to errors. When the projective preparation procedure is applied, quantum process tomography leads to a non-linear process map. We show that these processes can only be consistently described by a general dynamical map, which we call M-map. The M-map contains all of the dynamical information for the state of the system without the affects of a preparation procedure. By carefully extracting some of this dynamical information, we construct a quantitative measure for the memory effect due to the initial correlations with the environment. / text

published_or_final_version / Physics / Master / Master of Philosophy

Spin degrees of freedom have been extensively explored in the context of quantum information processing. Many proposals of quantum computation architectures use spins as carriers of quantum of information. A central problem is to efficiently generate quantum entanglement between spin qubits which proves to be a crucial resource for quantum information tasks. On the other hand, uncontrollable spin degrees of freedom in the environment of spin qubits are the major causes of errors at low temperature, for example, the lattice nuclear spins hyperfine coupled to single electron spin qubit localized in semiconductor nano-structures. An outstanding problem for scalable quantum computation is to suppress the collective fluctuations from such spin baths so that the coherence time of the spin qubit can be improved. With these two motivations, the problems of suppressing collective spin fluctuations and generating entanglement in various spin ensembles are addressed in this thesis. In the first half of the thesis, two approaches are introduced for suppressing the collective fluctuations in the nuclear spin bath so that the quantum coherence time of electron spin qubit in semiconductor quantum dots can be improved. The first approach works for a coupled double dot system. A theory for the interaction with the nuclear spins is developed when the two-electron singlet state is in resonance with one of the triplet state in moderate external magnetic field. At this resonance condition, the nuclear-electron flip-flop process caused by the hyperfine interaction can lead to a feedback mechanism, which can be used to suppress the nuclear hyperfine field. The second approach works for a single dot system. It is shown that strong pumping of the nuclear spins in dynamic nuclear polarization processes can saturate the nuclear spin bath towards the collective “dark states”. In such dark states, the transverse nuclear field fluctuation can be substantially suppressed compared to the value at thermal equilibrium. Two physical schemes are proposed to realize the nuclear dark states for suppression of the nuclear field fluctuations. In the second half of the thesis, schemes are presented for generating large scale quantum entanglement in two types of spin qubit systems. For atomic spin qubits in optical lattices, schemes are proposed on how to prepare pure spin coherent state (SCS) with low collective spin by incoherent pumping with collective spin raising and lowering operations. Such SCS realize networks of mutually entangled spins which can be idea resources for the quantum telecloning algorithm. For donor nuclear spin qubits in silicon architecture, proposals are shown on how to deterministic prepare Dicke states which constitute an important class of multipartite entangled states. Our scheme is capable of preparing both symmetric and asymmetric Dicke states which form a complete basis set of the spin Hilbert space. The required controls are in situ to the prototype Kane’s quantum computer. The preparation is robust because each desired Dicke state is the steady state under designed pumping process. The schemes presented here also make possible the construction of decoherence free subspaces where quantum information is protected from collective noises. / published_or_final_version / Physics / Doctoral / Doctor of Philosophy

The time-dependent quantum transport theory has attracted a great deal of interest in the past decade. However, some concepts in the frequency-dependent transport theory remain confused. Based on the Keldysh non-equilibrium green’s function formalism for time-dependent quantum transport, new expressions for dynamic current and admittance are derived in this thesis, which satisfy gauge invariance and current continuity. The key concepts in this field are clarified. The derivation is under wideband limit (WBL) and first order approximations. This new formalism is validated by first-principle time-dependent calculations of three carbon-based nano-devices. Later a study on asymmetric systems is carried out by this new theory, and discussion on current conversation problem is presented. This new ac quantum transport theory can cooperate with electromagnetic method to solve a mesoscopic problem. The active core part which is usually under atomistic scale is simulated by frequency-domain quantum transport theory, while the broad environment is tackled with electromagnetic solver. By a careful treatment at the interface between two solvers, this quantum mechanic / electromagnetic (QM/EM) method is implemented self-consistently. This QM/EM method is also validated by calculations of the transient current through a carbon-nanotube based device surrounded by silicon environment under a small ac bias voltage. The small signal and WBL approximations are also adopted in the development of this method. As a supplementary to the family of QM/EM methods (static and time-dependent QM/EM method are already established), this method shows very good efficient and high accuracy. Beyond linear response in frequency domain, we have also studied some nonlinear effects. As one application of nonlinear effect, memristor has attracted great attention in the past few years. Through Fourier analysis method, we have now understood the physical and mathematical mechanisms of ideal memristor, memcapacitor and meminductor. We have proposed methods to verify ideal memristor, memcapacitor and memdicutor, and to find out their intrinsic parameters which can be employed to predict their behavior under various input signals. This study may also provide an instruction on experimental research. / published_or_final_version / Chemistry / Doctoral / Doctor of Philosophy

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I examine some logical and epistemological problems arising in quantum theory. Two historical episodes are considered in detail: Planck's adoption of the quantum hypothesis and Heisenberg's discovery of matrix mechanics. The former episode is, I argue, more compa tLbLe with logical empiricist views of scientific progress than it is with more recent and currently influential philosophies. My examination of the latter concerns the influences - epistemological as well as.sci~ntific- which may have affected the manner in which Heisenberg chose to present. his discoveries; these considerations a~low me to rebut ... the suggestion that Heisenberg's practice was incompatible with his professed views and to counter the claim that this episode provided unwarranted support to formalistic ideas concerning scientific explanation. The connexions between Bohr's principle of complementarity and logical empiricist views concerning language change in science are explored, and I argue that the transition from classical to quantum mechanics· can be seen as involving a shift in the meanings of "position" and "momentum" so that these terms obtain unambiguous empirical meanings from the viewpoint of quantum· theory. Discussing the relevance of quantum mechanics to logic I contend that, although classical logic may be retained, empirical considerations may make it advisable to adopt a non-classical logic for quantum theory. An analysis of Bell' s inequality.:is a prelude to some speculations concerning the interpretation of quantum theory. I examine the possibility of interpreting the formalism as descriptive not of an external world but of the expectati.ons of subjects. The final chapter explores the relevance of physics to questions concerning human freedom. Classical physics, I argue, did not have the devastating implications for personal autonomy that it was often assumed to have; quantum physics does not explain . human freedom but, under certain assumptions, it does show how it is possible.

published_or_final_version / Physics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy