arXiv subjects

Walter Pötz

Publications and source records attributed to Walter Pötz.

13 recordsLinked to original sources

arXiv2015

Single-cone real-space finite difference schemes for the Dirac von Neumann equation

Two finite difference schemes for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian are presented. Both utilize a single-cone staggered space-time grid which ensures a single-cone energy dispersion to formulate a numerical treatment of the mixed-state dynamics within the von Neumann equation. The first scheme executes the time-derivative according to the product rule for "bra" and "ket" indices of the density operator. It therefore directly inherits all the favorable properties of the difference scheme for the pure-state Dirac equation and conserves positivity. The second scheme proposed here performs the time-derivative in one sweep. This direct scheme is investigated regarding stability and convergence. Both schemes are tested numerically for elementary simulations using parameters which pertain to topological insulator surface states. Application of the schemes to a Dirac Lindblad equation and real-space-time Green's function formulations are discussed.

physics.comp-ph↗

arXiv2014

Single-cone real-space finite difference scheme for the time-dependent Dirac equation

A finite difference scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to optimal linear scaling behavior for the computational effort per space-time grid-point. It allows for an easy and efficient parallelization. A functional for a norm on the grid is identified. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation is shown and exact stability conditions are derived. Finally, a single-cone scheme for the two-component (2+1)D Dirac equation, its properties, and a simulation of scattering at a Klein step are presented.

physics.comp-ph↗

arXiv2013

Dynamics of domain-wall Dirac fermions on a topological insulator: a chiral fermion beam splitter

The intersection of two ferromagnetic domain walls placed on the surface of topological insulators provides a one-way beam splitter for domain-wall Dirac fermions. Based on an analytic expression for a static two-soliton magnetic texture we perform a systematic numerical study of the propagation of Dirac wave packets along such intersections. A single-cone staggered-grid finite difference lattice scheme is employed in the numerical analysis. It is shown that the angle of intersection plays a decisive role in determining the splitting ratio of the fermion beam. For a non-rectangular intersection, the width and, to a lesser extent, the type of domain walls, e.g. Bloch or N{é}el, determine the properties of the splitter. As the ratio between domain-wall width and transverse localization length of the Dirac fermion is increased its propagation behavior changes from quantum-mechanical (wave-like) to classical ballistic (particle-like). An electric gate placed near the intersection offers a dynamic external control knob for adjusting the splitting ratio.

cond-mat.mes-hall↗

arXiv2013

Staggered grid leap-frog scheme for the (2+1)D Dirac equation

A numerical scheme utilizing a grid which is staggered in both space and time is proposed for the numerical solution of the (2+1)D Dirac equation in presence of an external electromagnetic potential. It preserves the linear dispersion relation of the free Weyl equation for wave vectors aligned with the grid and facilitates the implementation of open (absorbing) boundary conditions via an imaginary potential term. This explicit scheme has second order accuracy in space and time. A functional for the norm is derived and shown to be conserved. Stability conditions are derived. Several numerical examples, ranging from generic to specific to textured topological insulator surfaces, demonstrate the properties of the scheme which can handle general electromagnetic potential landscapes.

physics.comp-ph↗

arXiv2013

A dispersion and norm preserving finite difference scheme with transparent boundary conditions for the Dirac equation in (1+1)D

A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and time-staggered leap-frog scheme it avoids fermion doubling and preserves the dispersion relation of the continuum problem for mass zero (Weyl equation) exactly. Considering boundary regions, each with a constant mass and potential term, the associated DTBCs are derived by first applying this finite difference scheme and then using the Z-transform in the discrete time variable. The resulting constant coefficient difference equation in space can be solved exactly on each of the two semi-infinite exterior domains. Admitting only solutions in $l_2$ which vanish at infinity is equivalent to imposing outgoing boundary conditions. An inverse Z-transformation leads to exact DTBCs in form of a convolution in discrete time which suppress spurious reflections at the boundaries and enforce stability of the whole space-time scheme. An exactly preserved functional for the norm of the Dirac spinor on the staggered grid is presented. Simulations of Gaussian wave packets, leaving the computational domain without reflection, demonstrate the quality of the DTBCs numerically, as well as the importance of a faithful representation of the energy-momentum dispersion relation on a grid.

physics.comp-ph↗

arXiv2012

Dirac fermion wave guide networks on topological insulator surfaces

Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting of two parallel pathways, whereby a newly developed staggered-grid leap-frog discretization scheme in 2+1 dimensions with absorbing boundary conditions is employed. The net transmission can be tuned between constructive to destructive interference, either by variation of the magnetization (path length) or an applied bias (wave length). Based on this principle, a Dirac fermion transistor is proposed. Extensions to more general networks are discussed.

cond-mat.mes-hall↗

arXiv2011

Electrical control of ferromagnetism in Mn-doped semiconductor heterostructures

The interplay of tunneling transport and carrier-mediated ferromagnetism in narrow semiconductor multi-quantum well structures containing layers of GaMnAs is investigated within a self-consistent Green's function approach, accounting for disorder in the Mn--doped regions and unwanted spin-flips at heterointerfaces on phenomenological ground. We find that the magnetization in GaMnAs layers can be controlled by an external electric bias. The underlying mechanism is identified as spin-selective hole tunneling in and out of the Mn-doped quantum wells, whereby the applied bias determines both hole population and spin polarization in these layers. In particular we predict that, near resonance, ferromagnetic order in the Mn doped quantum wells is destroyed. The interplay of both magnetic and transport properties combined with structural design potentially leads to several interrelated physical phenomena, such as dynamic spin filtering, electrical control of magnetization in individual magnetic layers, and, under specific bias conditions, to self-sustained current and magnetization oscillations (magneticmulti-stability). Relevance to recent experimental results is discussed.

cond-mat.mes-hall↗

arXiv2011

Bias-induced destruction of ferromagnetism and disorder effects in GaMnAs heterostructures

The magneto-electric properties of resonant tunneling double barrier structures using GaMnAs for the quantum well is investigated within a self-consistent Green's function approach and a tight-binding electronic structure model. The magnetic state of the well is determined self-consistently by the tunneling current which controls the hole spin density and, hence, the degree of exchange splitting of the subbands inside the well. Prompted by recent experiments we compare model systems of increasing defect concentration (substitutional disorder) regarding their I-V curve, magnetic state, and spin polarization. We predict that, near resonance, the ferromagnetic order which may be present at zero bias in the GaMnAs well tends to be destroyed. Resonance peaks are found to be more sensitive to disorder than ferromagnetic ordering and spin polarization of the steady-state current.

cond-mat.mes-hall↗

arXiv2010

Proposal for a ferromagnetic multiwell spin oscillator

The highly nonlinear coupling of transport and magnetic properties in a multiwell heterostructure, which comprises ferromagnetic quantum wells made of diluted magnetic semiconductors, is theoretically investigated. The interplay of resonant tunneling and carrier-mediated ferromagnetism in the magnetic wells induces very robust, self-sustained current and magnetization oscillations. Over a large window of steady bias voltages the spin polarization of the collector current is oscillating between positive and negative values, realizing a spin oscillator device.

cond-mat.mes-hall↗

arXiv2010

Electric g Tensor Control and Spin Echo of a Hole-Spin Qubit in a Quantum Dot Molecule

The feasibility of high-fidelity single-qubit operations of a hole spin in a quantum dot molecule by electric g tensor control is demonstrated. Apart from a constant external magnetic field the proposed scheme allows for an exclusively electric control of the hole spin. Realistic electric gate bias profiles are identified for various qubit operations using process-tomography-based optimal control. They are shown to be remarkably robust against decoherence and dissipation arising from the interaction of the hole with host-lattice nuclear spins and phonons, with a fidelity loss of $\approx$ 1 percent for gate operation times of $\approx 10$ ns. Spin-echo experiments for the hole spin are modeled to explore dephasing mechanisms and the role of pulse-timing imperfections on the gate fidelity loss is discussed.

cond-mat.mes-hall↗

arXiv2009

Optimal Control for Open Quantum Systems: Qubits and Quantum Gates

This article provides a review of recent developments in the formulation and execution of optimal control strategies for the dynamics of quantum systems. A brief introduction to the concept of optimal control, the dynamics of of open quantum systems, and quantum information processing is followed by a presentation of recent developments regarding the two main tasks in this context: state-specific and state-independent optimal control. For the former, we present an extension of conventional theory (Pontryagin's principle) to quantum systems which undergo a non-Markovian time-evolution. Owing to its importance for the realization of quantum information processing, the main body of the review, however, is devoted to state-independent optimal control. Here, we address three different approaches: an approach which treats dissipative effects from the environment in lowest-order perturbation theory, a general method based on the time--evolution superoperator concept, as well as one based on the Kraus representation of the time-evolution superoperator. Applications which illustrate these new methods focus on single and double qubits (quantum gates) whereby the environment is modeled either within the Lindblad equation or a bath of bosons (spin-boson model). While these approaches are widely applicable, we shall focus our attention to solid-state based physical realizations, such as semiconductor- and superconductor-based systems. While an attempt is made to reference relevant and representative work throughout the community, the exposition will focus mainly on work which has emerged from our own group.

quant-ph↗

arXiv2009

Time-optimal performance of Josephson charge qubits: A process tomography approach

A process tomography based optimization scheme for open quantum systems is used to determine the performance limits of Josephson charge qubits within current experimental means. The qubit is modeled microscopically as an open quantum system taking into account state leakage, as well as environment-induced dephasing based on experimental noise spectra. Within time-optimal control theory, we show that the competing requirements for suppression of state leakage and dephasing can be met by an external control of the effective qubit-environment interaction, yielding minimal gate fidelity losses of around $ΔF \approx 10^{-3}$ under typical experimental conditions.

cond-mat.supr-con↗

arXiv2007

Bell-state preparation for electron spins in a semiconductor double quantum dot

A robust scheme for state preparation and state trapping for the spins of two electrons in a semiconductor double quantum dot is presented. The system is modeled by two spins coupled to two independent bosonic reservoirs. Decoherence effects due to this environment are minimized by application of optimized control fields which make the target state to the ground state of the isolated driven spin system. We show that stable spin entanglement with respect to pure dephasing is possible. Specifically, we demonstrate state trapping in a maximally entangled state (Bell state) in the presence of decoherence.

cond-mat.mes-hall↗