Fakultät für Physik - Digitale Hochschulschriften der LMU - Teil 05/05

This thesis advances and applies matrix product state (MPS) based algorithms to the solution of dynamical mean-field theory (DMFT) and its variants. The advances enable to solve quantum many-body problems in and out of equilibrium that were previously out of reach for any

numerical treatment. In equilibrium, this concerns in particular the computation of the electronic --- such as insulating, metallic,

spin-freezed and many other --- phases of highly complex realistic models for correlated materials. In non-equilibrium, this concerns in

particular the understanding of the fundamental mechanisms of the relaxation behavior of quantum many-body systems on short and intermediate time scales.

Electron spins confined in quantum dots (QDs) are among the leading contenders for implementing quantum information processing. In this Thesis we address two of the most significant technological challenges towards developing a scalable quantum information processor based on spins in quantum dots: (i) decoherence of the electronic spin qubit due to the surrounding nuclear spin bath, and (ii) long-range spin-spin coupling between remote qubits. To this end, we develop novel strategies that turn the unavoidable coupling to the solid-state environment (in particular, nuclear spins and phonons) into a valuable asset rather than a liability.

In the first part of this Thesis, we investigate electron transport through single and double QDs, with the aim of harnessing the (dissipative) coupling to the electronic degrees of freedom for the creation of coherence in both the transient and steady-state behaviour of the ambient nuclear spins. First, we theoretically show that intriguing features of coherent many-body physics can be observed in electron transport through a single QD. To this end, we first develop a master-equation-based formalism for electron transport in the Coulomb-blockade regime assisted by hyperfine (HF) interaction with the nuclear spin ensemble in the QD. This general tool is then used to study the leakage current through a single QD in a transport setting. When starting from an initially uncorrelated, highly polarized state, the nuclear system experiences a strong correlation buildup, due to the collective nature of the coupling to the central electron spin. We demonstrate that this results in a sudden intensity burst in the electronic tunneling current emitted from the QD system, which exceeds the maximal current of a corresponding classical system by several orders of magnitude. This gives rise to the new paradigm of electronic superradiance. Second, building upon the insight that the nuclear spin dynamics are governed by collective interactions giving rise to coherent effects such as superradiance, we propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics is shown to lead to intriguing effects such as multistability and criticality in the steady-state solutions.

In the second part of this Thesis, our focus turns towards the realization of long-range spin-spin coupling between remote qubits. We propose a universal, on-chip quantum transducer based on surface acoustic waves in piezo-active materials. Because of the intrinsic piezoelectric (and/or magnetostrictive) properties of the material, our approach provides a universal platform capable of coherently linking a broad array of qubits, including quantum dots, trapped ions, nitrogen-vacancy centers or superconducting qubits. The quantized modes of surface acoustic waves lie in the gigahertz range, can be strongly confined close to the surface in phononic cavities and guided in acoustic waveguides. We show that this type of surface acoustic excitations can be utilized efficiently as a quantum bus, serving as an on-chip, mechanical cavity-QED equivalent of microwave photons and enabling long-range coupling of a wide range of qubits.

In summary, this thesis provides contributions towards developing a scalable quantum information processor based on spins in quantum dots in two different aspects. The first part is dedicated to a deeper understanding of the nuclear spin dynamics in quantum dots. In the second part we put forward a novel sound-based strategy to realize long-range spin-spin coupli

Ultrafast electron diffraction is a pump--probe technique that allows the visualisation of molecular dynamics with atomic scale resolution. However, the fastest electronic and atomic dynamics in light-driven matter transformations are, as yet, unmeasureable with this technique. This is because the temporal resolution in ultrafast electron diffraction is limited by difficulties in producing the shortest electron pulses, caused by the electron charge, via Coulomb repulsion (space charge), and rest mass, via vacuum dispersion of the electron wavefunction. Space charge effects and a finite energy bandwidth both lead to temporal broadening of electron pulses. Methods to compress such pulses in microwave fields have been developed, but these are fundamentally limited by the achievable temporal synchronisation of the employed microwave with the excitation laser pulses.

This work is aimed at breaking this limitation and thereby advancing ultrafast electron diffraction towards the ultimate temporal resolution of any realistic light--matter interaction. Firstly, a high-resolution optical-microwave phase detector based on optical interferometry is designed for operation around the 800-nm wavelength of Ti:sapphire lasers best suited for sample excitation. The phase detector provides a resolution of 3 fs and the capability of functioning as an integral component in a phase-locked loop for synchronising a low-noise dielectric resonator oscillator with the Ti:sapphire laser.

Furthermore, we demonstrate a separate, novel, passive synchronisation technique through direct microwave extraction of a harmonic of the laser repetition rate by photodetection. A record-low residual phase noise over nine frequency decades (mHz--MHz) is achieved through implementation of an optical-mode filter which circumvents thermal noise problems at low pulses energies to simultaneously reduce detrimental amplitude-to-phase noise conversion in the photodetection process. An amplification chain is designed to achieve a microwave power suitable for electron compression while preserving this excellent phase noise. Rigorous out-of-loop characterisation of the synchronisation with the optical-microwave phase detector shows a root-mean-square (rms) timing stability of 4.8 fs. This superior synchronisation has allowed the generation of 12 fs (rms) electron pulses, the shortest to our knowledge.

Lastly, stability of the laser--electron synchronisation over many hours is also demonstrated on a sub-five-femtosecond scale through in-situ measurement and subsequent compensation for the entire range of possible long-term drifts. This shows that incorporating these techniques can allow ultrafast electron diffraction experiments to observe the fastest reversible atomic-scale light--matter interaction dynamics.

In this thesis we study geometric corrections to the low-energy effective actions of string theory. More concretely, we compute higher-derivative corrections to the couplings of three-dimensional, N = 2 supergravity theories and interpret the induced α′-corrections in N = 1, minimal supergravity theories in four dimensions, in the framework of F-theory. These allow for chiral spectra and are therefore phenomenological relevant. We analyzed higher-derivative corrections to M-theory, accessible through its low-energy effective theory, given by eleven-dimensional supergravity. The next to leading order terms to eleven-dimensional supergravity carry eight-derivatives, and are suppressed by lM6 compared to the classical terms, with lM being the eleven-dimensional Planck-Length - the only scale in eleven dimensions. These corrections are lifted from IIA supergravity corrections, which are derived from string scattering amplitudes.

The common theme of this thesis is to compactify the bosonic sector of the eleven-dimensional supergravity action, including all known eight-derivative corrections, on a supersymmetric background to find a 3d, N = 2 theory, which then can be lifted to a 4d, N = 1 theory. This goal is approached in several steps.

In the classical reduction of eleven-dimensional supergravity the metric background is a direct product of the external space, consisting of two space and one time dimension and the internal eight spacelike-dimensional Calabi-Yau manifold. However, when considering higher-derivative corrections the background has to be altered by introducing a dependence of the external space on the warp- factor, which is a function of the internal space. We find an explicit warped background solution to the eleven-dimensional E.O.M.’s including non-vanishing flux. To check the background for its supersymmetry features one would need to consider the eleven-dimensional gravitino variations at this order in lM . However, these are not known, which leads us to propose higher-order lM -corrected gravitino variations consistent with our background solution.

As a next step we dimensionally reduce the bosonic sector of the eleven-dimensional supergravity action including all eight-derivative terms on this warped background and analyze the resulting three- dimensional theory. In this context the interplay of the warp-factor and the higher-derivative terms is of crucial importance. To identify the N = 2 properties of the resulting three-dimensional theory obtained by dimensional reduction, we compare it to the canonical from of three-dimensional N = 2 supergravtiy. We conclude that the reduced action is compatible with N = 2 supersymmetry and give a proposal for the K ̈ahler potential and the complex coordinates, which receive lM6 corrections. Besides a warp-factor contribution, the K ̈ahler potential receives a correction proportional to the third Chern-

2

form of the zeroth order internal background, being the Calabi-Yau fourfold. The complex coordinates are defined as divisor-integrals and are corrected by a warp-factor dependent term as well as one related to the non-harmonic part of the fourth Chern-form, of the zeroth order Calabi-Yau manifold. Thus the couplings of the resulting theory receive besides the warp-factor, in particular geometric corrections of order lM6 .

In the first part of this thesis we study a simplified setup, only considering a subset of the relevant eight-derivative corrections in eleven dimensions. Furthermore, we do compactify on the classical background, consisting of the internal Calabi-Yau fourfold without warping and fluxes, to gain a three-dimensional theory. However, we use the M/F-theory duality to uplift the yielded corrections, which results in corrections to the couplings of the four-dimensional theory. In the weak coupling limit we find that these are sourced by the self-intersection curves of D7-branes.