Daniel Becker

We have developed a numerically exact approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the generating function of nonequilibrium observables of interest, e.g., the charge current or dynamical quantities of the central part. Self-energies due to the leads, being nonlocal in time, are fully taken into account within a finite memory time, thereby including non-Markovian effects. Numerical results are extra-polated first to vanishing (Trotter) time discretization and, second, to infinite memory time...

We propose a scheme to dynamically realize a quantum memory based on the toric code. The code is generated from qubit systems with typical two-body interactions (Ising, XY, Heisenberg) using periodic, NMR-like, pulse sequences. It allows one to encode the logical qubits without measurements and to protect them dynamically against the time evolution of the physical qubits. A weakly coupled cavity mode mediates a long-range attractive interaction between the stabilizer operators of the toric code, thereby suppressing the creation of thermal anyons. This significantly increases the lifetime of the memory compared to the code with noninteracting stabilizers. We investigate how the fidelity, with which the toric code is realized, depends on the period length T of the pulse sequence and the magnitude of possible pulse errors. We derive an optimal period T_opt that maximizes the fidelity.

We present a method for implementing stabilizer-based codes with encoding schemes of the operator quantum error correction paradigm, e.g., the "standard" five-qubit and CSS codes, on solid-state qubits with Ising or XY-type interactions. Using pulse sequences, we show how to dynamically generate the effective dynamics of the stabilizer Hamiltonian, the sum of an appropriate set of stabilizer operators for a given code. Within this approach, the encoded states (ground states of the stabilizer Hamiltonian) can be prepared without measurements and preserved against both the time evolution governed by the original qubit Hamiltonian, and errors caused by local sources.

The common spin Hamiltonians such as the Ising, XY, or Heisenberg model do not have ground states that are the graph states needed in measurement-based quantum computation. Various highly-entangled many-body states have been suggested as a universal resource for this type of computation, however, it is not easy to preserve these states in solid-state systems due to their short coherence times. Here we propose a scheme for generating a Hamiltonian that has a cluster state as ground state. Our approach employs a series of pulse sequences inspired by established NMR techniques and holds promise for applications in many areas of quantum information processing.

We study the non-equilibrium dynamics of a spinful single-orbital quantum dot with an incorporated quantum mechanical spin-1/2 magnetic impurity. Due to the spin degeneracy, double occupancy is allowed, and Coulomb interaction together with the exchange coupling of the magnetic impurity influence the dynamics. By extending the iterative summation of real-time path integrals (ISPI) to this coupled system, we monitor the time-dependent non-equilibrium current and the impurity spin polarization to determine features of the time-dependent non-equilibrium dynamics. We particulary focus on the deep quantum regime, where all time and energy scales are of the same order of magnitude and no small parameter is available. We observe a significant influence of the non-equilibrium decay of the impurity spin polarization both in the presence and in the absence of Coulomb interaction. The exponential relaxation is faster for larger bias voltages, electron-impurity interactions and temperatures. We show that the exact relaxation rate deviates from the corresponding perturbative result. In addition, we study in detail the impurity's back action on the charge current and find a reduction of the stationary current for increasing coupling to the impurity. Moreover, our approach allows us to systematically distinguish mean-field Coulomb and impurity effects from the influence of quantum fluctuations and flip-flop scattering, respectively. In fact, we find a local maximum of the current for a finite Coulomb interaction due to the presence of the impurity.

We investigate electronic- and spin transport through a single level quantum dot with magnetic impurity in a symmetric forward bias setup. On the quantum dot, electrons either interact with each other due to Coulomb interaction or with the spin 1/2 magnetic impurity. For certain configurations, the tunnel coupling to the leads induces an exponential relaxation of the impurity spin, which has been prepared in a polarized state initially. Furthermore, we study the influence of the nonequilibrium transport current on the relaxation dynamics. We obtain the respective numerical result by means of the iterative summation of path integral (ISPI) scheme. Within this approach, observables of interest are calculated from a functional derivative with respect to appropriate source terms in the Keldysh partition function. The real-time path integral extends over all possible paths (i) of the impurity spin and (ii) of the Ising like fluctuating spin fields we have to introduce in order to decouple the quartic interaction term of the Anderson model. The ISPI scheme allows us to sum up all paths including the time non-local self energies of the leads.

Transport through quantum dot systems covers a broad range of phenomena ranging from Coulomb blockade oscillations to the Kondo effect. The role of Coulomb interaction in transport processes has many facets. It influences the electronic structure of quantum dot systems, it introduces a strong dependence on the number of charge carriers in the confined system, and, last but not least, it enhances the appearance of spin effects. In this chapter, we review the different faces of Coulomb interaction on the electronic structure of few-particle quantum dot systems emphasizing the mutual interplay between quantum confinement, dimensionality, and charge interaction.

We present an exact analytical solution of the fundamental system of quasi-one-dimensional spin-1 bosons with infinite delta-repulsion. The eigenfunctions are constructed from the wave functions of non-interacting spinless fermions, based on Girardeau's Fermi-Bose mapping, and from the wave functions of distinguishable spins. We show that the spinor bosons behave like a compound of non-interacting spinless fermions and non-interacting distinguishable spins. This duality is especially reflected in the spin densities and the energy spectrum. We find that the momentum distribution of the eigenstates depends on the symmetry of the spin function. Furthermore, we discuss the splitting of the ground state multiplet in the regime of large but finite repulsion.

Non-equilibrium transport through a quantum dot with one spin-split single-particle level is studied in the cotunneling regime at low temperatures. The Coulomb diamond can be subdivided into parts differing in at least one of two respects: what kind of tunneling processes (i) determine the single-particle occupations and (ii) mainly contribute to the current. No finite systematic perturbation expansion of the occupations and the current can be found that is valid within the entire Coulomb diamond. We therefore construct a non-systematic solution, which is physically correct and perturbative in the whole cotunneling regime, while smoothly crossing-over between the different regions. With this solution the impact of an intrinsic spin-flip relaxation on the transport is investigated. We focus on peaks in the differential conductance that mark the onset of cotunneling-mediated sequential transport. It is shown that these peaks are maximally pronounced at a relaxation roughly as fast as sequential tunneling. The approach as well as the presented results can be generalized to quantum dots with few levels.