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Making spintronic devices is a hot topic for future technical development. In this work the non-equilibrium dynamics of a single spin in a tunnel junction is analyzed and numerically simulated. This is done in order to understand the dynamics of e.g. a magnetic molecule between two metal contacts for future spintronic devices. The work starts with looking at the system in a many-body theory picture in order to derive the interesting properties of the system. An initial solution for the system is analytically calculated as well as for the dynamic case. The dynamic has then been numerically simulated in order to get the time evolution of the system. The results showed that the dynamics of the molecular spin induced a spin dependent charge and spin currents in the system and that the currents could be used to control the molecular spin. It showed qualitatively how different parameters, for example coupling strength, effect the system and what to consider when designing a system similar to this.

Classical and quantum spin systems are widely used models in both experimental and theoretical condensed matter physics. In many materials, the electronic interactions can be difficult to model exactly. However, in some insulators (Mott insulators), the magnetic (spin) interactions can be captured well with spin-only models. Several models are studied in this thesis. First, I report the solution of a long-standing issue in a classical frustrated spin model (i.e., where the quantum effects are neglected and the complexity is due to competing interactions): the nature of the thermal phase transition to a stripe state in the two dimensional (2D) J1-J2 model. Here J1 and J2 are nearest- and next-nearest-neighbor couplings. Monte Carlo simulations with single-spin updates are used for the calculations, and an extended-ensemble method, a generalization of the Wang-Landau algorithm, is also developed and tested. I focus on the study of "weak universality" behavior (continuously varying critical exponents, with one of the exponents staying fixed), for which I show a correspondence with a known class of conformal field theories with charge c = 1. Next, moving to quantum spins, to shed light on magnetic systems studied experimentally and to investigate new types of quantum states of interest in developing theories of quantum magnetism, I study the S = 1/2 Heisenberg model on the 2D square lattice with added six-spin interactions (the so-called J-Q3 model) as well as a set of 3D quantum antiferromagnets on dimerized lattices. Here I use the stochastic series expansion quantum Monte Carlo method. In the study of the J-Q3 model, I report on a similar weak-universality behavior as in the classical J1-J2 model, but with a mapping to a different known class of c = 1 conformal field theories. The critical behavior of the system again shows continuously changing exponents, in a way which corresponds to a gradual weakening of Z4 symmetry-breaking to an emergent U(1) symmetry. In the study of dimerized antiferromagnets, I report on a universal behavior of the Néel temperature TN, which can be related to ground state parameters independently of the microscopic interaction details in several different models.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19479号 / 理博第4139号 / 新制||理||1595(附属図書館) / 32515 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 戸塚 圭介, 教授 川上 則雄, 教授 石田 憲二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Many problems in applied mathematics and physics are formulated most naturally in terms of matrices, and can be solved by computing functions of these matrices. For example, in quantum mechanics, the coherent dynamics of physical systems is described by the matrix exponential of their Hamiltonian. In state of the art experiments, one can now observe such unitary evolution of many-body systems, which is of fundamental interest in the study of many-body quantum phenomena. On the other hand the theoretical simulation of such non-equilibrium many-body dynamics is very challenging. In this thesis, we develop a symbolic approach to matrix functions and quantum dynamics based on a novel algebraic structure we identify for sets of walks on graphs. We begin by establishing the graph theoretic equivalent to the fundamental theorem of arithmetic: all the walks on any finite digraph uniquely factorise into products of prime elements. These are the simple paths and simple cycles, walks forbidden from visiting any vertex more than once. We give an algorithm that efficiently factorises individual walks and obtain a recursive formula to factorise sets of walks. This yields a universal continued fraction representation for the formal series of all walks on digraphs. It only involves simple paths and simple cycles and is thus called a path-sum. In the second part, we recast matrix functions into path-sums. We present explicit results for a matrix raised to a complex power, the matrix exponential, matrix inverse, and matrix logarithm. We introduce generalised matrix powers which extend desirable properties of the Drazin inverse to all powers of a matrix. In the third part, we derive an intermediary form of path-sum, called walk-sum, relying solely on physical considerations. Walk-sum describes the dynamics of a quantum system as resulting from the coherent superposition of its histories, a discrete analogue to the Feynman path-integrals. Using walk-sum we simulate the dynamics of quantum random walks and of Rydberg-excited Mott insulators. Using path-sum, we demonstrate many-body Anderson localisation in an interacting disordered spin system. We give two observable signatures of this phenomenon: localisation of the system magnetisation and of the linear magnetic response function. Lastly we return to the study of sets of walks. We show that one can construct as many representations of series of walks as there are ways to define a walk product such that the factorisation of a walk always exist and is unique. Illustrating this result we briefly present three further methods to evaluate functions of matrices. Regardless of the method used, we show that graphs are uniquely characterised, up to an isomorphism, by the prime walks they sustain.

Diese Dissertation besteht aus zwei Teilen von Studien. Der erste Teil demonstriert die Steuerung der Elektron-Kern-Spin-Systems in II-VI Halbleiter Quantum Dots (QDs) durch elektrische Ströme über Mikrospulen. Mikrometer-große Leiterschleifen sind auf der Oberseite von Heterostrukturen mit geladenen CdSe/ZnS QDs hergestellt worden. Eine Strominjektion erzeugt magnetische Felder im Bereich von einige 10 mT, welche stark genug sind, um die Hyperfeinwechselwirkung in CdSe QDs modulieren zu können. Der Durchmesser des Spulen im Mikrometer-Bereich ermöglicht die Generation von schnellen Feld transienten im Bereich von wenigen ns. Mit diesen Vorteilen der Mikrospulen werden die Steuerungs des Spins der residenten Elektronen sowie das Auslesen des Kernspinzustandes durch elektrische Impulse nachgewiesen. Der zweite Teil befasst sich mit der Ladungsträger-Spindynamik in ZnO Quantum Well (QW) Strukturen und Epitaxieschichten, die mittels des optischen Übergang von negativ geladenen Exzitonen X− beziehungsweise des am neutralen Donator gebunden Exziton D0X untersucht werden. Der Loch-Spin kann direkt über die zirkular polarisierten Photolumineszenz der beiden Komplexe zurückverfolgt werde. Die Spin-Relaxationszeit von QW und Epiplyer verfolgt werden. Der Spin des Donatorelektronens wird über die Ausbleichung des Spin-selektive Anregungprozesses nachgewiesen. Es werden longitudinale Loch-Spinrelaxationszeiten von 80 bis 140 ps für D0X und X− gefunden. Deutlich längere longitudinalen Elektronen-Spin-Relaxationszeiten in Bereich von mehreren 100 ns werden gefunden, wenn die Hyperfeinwechselwirkung durch ein geeignetes externes Magnetfeld unterdrückt wird. Eine Feldstärke von 2 mT ist groß genug. Dies zeigt den extrem kleinen Wert des Overhauser-Feldes in ZnO auf, der durch die sehr begrenzte Anzahl von magnetischen Kernen in Wechselwirkung mit dem Elektronen innerhalb des Volumens des Donators verursacht wird. / This work is composed of two parts of studies. The first part represents an electron-nuclear spin control in II-VI semiconductor quantum dots (QDs) by electrical currents via micro coils. Micrometer single turn coils are fabricated on top of heterostructures with charged CdSe/ZnSe QDs. Current injection creates magnetic fields in the range of some 10 mT which is strong enough to modulate the hyperfine interaction in CdSe. The micrometer-range diameter of coil allows for generation of fast field transient in the range of few ns. Using these advantages of micro coils, local control of the resident electron spin as well as read out of the nuclear spin state are demonstrated by electrical pulses. The second part presents charged carrier spin dynamics in ZnO quantum wells and epilayers using the optical transition of the negatively charged exciton X− and the neutral donor bound exciton D0X, respectively. The hole spin can be directly traced by the circular polarized photoluminescence of both complexes. The spin relaxation of the resident electrons and donor electrons is accessed via the bleaching of the spin selective excitation process. Longitudinal hole spin relaxation times of 80 and 140 ps are found for D0X and X−, respectively. Much longer longitudinal electron spin relaxation times in the several 100 ns range are uncovered if the hyperfine interaction is suppressed by a proper external magnetic field. A field strength of 2 mT is large enough proving that the extremely small value of the Overhauser field in ZnO caused by the very restricted number of magnetic nuclei interacting with the electron inside the donor volume.

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Quantum simulations, where controllable quantum systems are used to simulate other quantum systems, originally proposed by Richard Feynman, are one of the most remarkable applications of quantum information science. Compared to computation, quantum simulations require much less number of qubits for the m to be practical. In the work described in this thesis, we have performed a few quantum simulations of small quantum systems using Nuclear Magnetic Resonance(NMR) techniques. These simulations have been used to experimentally demonstrate the underlying interesting quantum protocols. All the experiments presented have been carried out using liquid-state or liquid crystal NMR. Numerical pulse optimization techniques have been utilized in some of the experiments, to achieve better control over the spin systems. The first chapter contains “Introduction” to quantum information processing, NMR, and numerical pulse optimization techniques. In chapter 2, we describe quantum simulation of a 3-spin Heisenberg-XY spin chain having only nearest neighbour interactions. Recently, spin chains having pre-engineered short-range interactions have been proposed to efficiently transfer quantum information between different parts of a quantum information processor. Other important proposals involving these spin chains include generating entangled states and universal quantum computation. However, such engineered interactions do not occur naturally in any system. In such a scenario, the experimental viability of these proposals can be tested by simulating the spin chains in other controllable quantum systems. In this work, we first theoretically study the time evolution of bipartite and tripartite entanglement measures for a 3-spin open ended XY spin chain. Then, by simulating the XY interactions in a 3-spin nuclear spin system, we experimentally generate, (i)a bipartite maximally(pseudo-)entangled state(Bell state) between end qubits, and(ii) multipartite(pseudo-)entangled states(Wand GHZ states),starting from separable pseudo-pure states. Bell state has been generated by using only the natural unitary evolution of the XY spin chain. W-state and GHZ-state have been generated by applying a single-qubit rotation to the second qubit, and a global rotation of all the three qubits respectively after the unitary evolution of the spin chain. In chapter 3, we simulate a 3-spin quantum transverse Ising spin system in a triangular configuration, and show that multipartite quantum correlations can be used to distinguish between the frustrated and non-frustrated regimes in the ground state of this spin system. The ground state of the spin system has been prepared by using adiabatic state preparation method. Gradient ascent pulse engineering technique has been utilized to efficiently realize the adiabatic evolution of the spin system. To analyse the experimental ground state of the system, we employ two different multipartite quantum correlation measures, generated from monogamy studies of bipartite quantum correlations. Chapter 4 contains a digital quantum simulation of the mirror inversion propagator corresponding to the time evolution of an XY spin chain. This simulation has been used to experimentally demonstrate the mirror inversion of quantum states, proposed by Albanese et al.[Phys.Rev.Lett.93,230502(2004)], by which entangled states can be transferred from one end of the chain to the other end. The experiments have been performed in a 5-qubit dipolar coupled nuclear spin system. For simulation, we make use of the recently proposed unitary operator decomposition algorithm along with the numerical pulse optimization techniques, which assisted in achieving high experimental fidelities. Chapter 5 contains a digital quantum simulation of the unitary propagator of a transverse Ising spin chain, which has been used to experimentally demonstrate the perfect state transfer protocol of Di Franco et al. [Phys.Rev.Lett.101,230502(2008)]. The importance of this protocol arises due to the fact that it achieves perfect state transfer from one end of the chain to the other end without the necessity of initializing the intermediate spins of the chain, whereas most of the previously proposed protocols require initialization. The experiments have been performed in a 3-spin nuclear spin system. The simulation has also been used to demonstrate the generation of a GHZ state.