Stefan Walter

Failure of protection of Majorana based qubits against decoherence

Qubit realizations based on Majorana bound states have been considered promising candidates for quantum information processing which is inherently inert to decoherence. We put the underlying general arguments leading to this conjecture to the test from an open quantum system perspective. It turns out that, from a fundamental point of view, the Majorana qubit is as susceptible to decoherence as any local paradigm of a qubit.

Quantum synchronization of a driven self-sustained oscillator.

Synchronization is a universal phenomenon that is important both in fundamental studies and in technical applications. Here we investigate synchronization in the simplest quantum-mechanical scenario possible, i.e., a quantum-mechanical self-sustained oscillator coupled to an external harmonic drive. Using the power spectrum we analyze synchronization in terms of frequency entrainment and frequency locking in close analogy to the classical case. We show that there is a steplike crossover to a synchronized state as a function of the driving strength. In contrast to the classical case, there is a finite threshold value in driving. Quantum noise reduces the synchronized region and leads to a deviation from strict frequency locking.

Interface structure and stabilization of metastable B2-FeSi/Si(111) studied with low-energy electron diffraction and density functional theory

We present a combined experimental and theoretical investigation of the interface between a B2-type FeSi film and Si(111). Using an ultra-thin B2-FeSi film grown on Si(111), the interface is still reached by electrons, so quantitative low-energy electron diffraction (LEED) could be applied to determine the bonding geometry experimentally. As a result, the local configuration at the shallow buried interface is characterized by near-substrate Fe atoms being 8-fold coordinated to Si atoms and by the silicide unit cell being rotated by 180° with respect to the Si unit cell (B8 configuration). The interface energetics were explored by total-energy calculations using density functional theory (DFT). The B8-type interface proves to be the most stable one, consistent with the experimental findings. The atomic geometries obtained experimentally (LEED) and theoretically (DFT) agree within the limits of errors. Additionally, the calculations explain the stabilization of the B2 phase, which is unstable as bulk material: the analysis of the elastic behaviour reveals a reversed energy hierarchy of B2 and the bulk stable B20 phase when epitaxial growth on Si(111) is enforced.

The role of an energy-dependent inner potential in quantitative low-energy electron diffraction

Recent apparent discrepancies between results from low-energy electron and X-ray diffraction concerning a reduced in-plane lattice parameter of Cu(100) are resolved in favour of an uncontracted surface. We show that neglecting the energy dependence of the inner potential in the electron intensity analysis simulates reduced structural parameters when a precision level of about 0.01 A is reached. As today this level is frequently claimed, our finding is of general relevance, in particular when the in-plane lattice parameter is not precisely known, as in epitaxial growth, for example.

Quantum synchronization of two Van der Pol oscillators

Synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime is studied. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. The differences to the behavior of one quantum Van der Pol oscillator subject to an external drive are discussed. Moreover, a possible experimental realization of two coupled quantum Van der Pol oscillators in an optomechanical setting is described.

Detecting Majorana bound states by nanomechanics

We propose a nanomechanical detection scheme for Majorana bound states, which have been predicted to exist at the edges of a one-dimensional topological superconductor, implemented, for instance, using a semiconducting wire placed on top of an s-wave superconductor. The detector makes use of an oscillating electrode, which can be realized using a doubly clamped metallic beam, tunnel coupled to one edge of the topological superconductor. We find that a measurement of the nonlinear differential conductance provides the necessary information to uniquely identify Majorana bound states.

Teleportation-induced entanglement of two nanomechanical oscillators coupled to a topological superconductor

A one-dimensional topological superconductor features a single fermionic zero mode that is delocalized over two Majorana bound states located at the ends of the system. We study a pair of spatially separated nanomechanical oscillators tunnel coupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electron-phonon coupling and a finite charging energy on the mesoscopic topological superconductor can lead to an effective superexchange between the oscillators via the nonlocal fermionic zero mode. We further show that this electron teleportation mechanism leads to entanglement of the two oscillators over distances that can significantly exceed the coherence length of the superconductor.

Transport properties of double quantum dots with electron-phonon coupling

We study transport through a double quantum dot system in which each quantum dot is coupled to a phonon mode. Such a system can be realized, e.g., using a suspended carbon nanotube. We find that the interplay between strong electron-phonon coupling and inter-dot tunneling can lead to a negative differential conductance at bias voltages exceeding the phonon frequency. Various transport properties are discussed, and we explain the physics of the occurrence of negative differential conductance in this system.

Entanglement of nanoelectromechanical oscillators by Cooper-pair tunneling

We demonstrate that entanglement of two macroscopic nanoelectromechanical resonators—coupled to each other via a common detector, a tunnel junction—can be generated by running a current through the device. We introduce a setup that overcomes generic limitations of proposals suggesting to entangle systems via a shared bath. At the heart of the proposal is an Andreev entangler setup, representing an experimentally feasible way of entangling two nanomechanical oscillators. Instead of relying on the coherence of a (fermionic) bath, in the Andreev entangler setup, a split Cooper pair that coherently tunnels to each oscillator mediates their coupling and thereby induces entanglement between them. Since entanglement is in each instance generated by Markovian and non-Markovian noisy open system dynamics in an out-of-equilibrium situation, we argue that the present scheme also opens up perspectives to observe dissipation-driven entanglement in a condensed-matter system.

Quantum-coherent phase oscillations in synchronization

Recently, several studies have investigated synchronization in quantum-mechanical limit-cycle oscillators. However, the quantum nature of these systems remained partially hidden, since the dynamics of the oscillators phase was overdamped and therefore incoherent. We show that there exist regimes of underdamped and even quantum-coherent phase motion, opening up new possibilities to study quantum synchronization dynamics. To this end, we investigate the Van der Pol oscillator (a paradigm for a self-oscillating system) synchronized to an external drive. We derive an effective quantum model which fully describes the regime of underdamped phase motion and additionally allows us to identify the quality of quantum coherence. Finally, we identify quantum limit cycles of the phase itself.