Stefan Walter

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.

We study synchronization of two dissipatively coupled Van der Pol oscillators in the quantum regime. Due to quantum noise strict frequency locking is absent and is replaced by a crossover from weak to strong frequency entrainment. We discuss the differences to the behavior of one quantum Van der Pol oscillator subject to an external drive. Moreover, we describe a possible experimental realization of two coupled quantum van der Pol oscillators in an optomechanical setting.

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 non-local fermionic zero mode. We further show that this teleportation mechanism leads to entanglement of the two oscillators over distances that can significantly exceed the coherence length of the superconductor.

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.

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 locking and frequency entrainment in close analogy to the classical case. We show that the quantum system exhibits frequency locking and that the synchronized (frequency-locked) region is reduced due to quantum noise.

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. This can be most efficiently achieved if the two oscillators are initially both prepared in their ground states. We propose two kinds of setups where the generation of entanglement can be realized by two different means. In the first setup, the oscillators are indirectly coupled via common fermionic reservoirs with long coherence times. While this setup gives valuable insight in the physics of this open quantum system, the second proposed setup, an Andreev entangler, represents a novel and feasible way of entangling two nanomechanical oscillators. In the Andreev entangler, a split Cooper-pair that coherently tunnels to each oscillator, mediates their coupling and thereby generates entanglement between them.

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.

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.

We propose and analyze different schemes to probe the quantum nature of nanoelectromechanical systems (NEMS) by a tunnel junction detector. Using the Keldysh technique, we are able to investigate the dynamics of the combined system for an arbitrary ratio of $eV/\hbar \Omega$, where V is the applied bias of the tunnel junction and $\Omega$ the eigenfrequency of the oscillator. In this sense, we go beyond the Markov approximation of previous works where these parameters were restricted to the regime $eV/\hbar \Omega\gg 1$. Furthermore, we also go beyond the Born approximation because we calculate the finite frequency current noise of the tunnel junction up to fourth order in the tunneling amplitudes. Interestingly, we discover different ways to probe both position and momentum properties of NEMS. On the one hand, for a non-stationary oscillator, we find a complex finite frequency noise of the tunnel junction. By analyzing the real and the imaginary part of this noise separately, we conclude that a simple tunnel junction detector can probe both position- and momentum-based observables of the non-stationary oscillator. On the other hand, for a stationary oscillator, a more complicated setup based on an Aharonov-Bohm-loop tunnel junction detector is needed. It still allows us to extract position and momentum information of the oscillator. For this type of detector, we analyze for the first time what happens if the energy scales $eV$, $\hbar \Omega$, and $k_B T$ take arbitrary values with respect to each other where T is the temperature of an external heat bath. Under these circumstances, we show that it is possible to uniquely identify the quantum state of the oscillator by a finite frequency noise measurement.

We numerically investigate the damping of Bloch oscillations in a one-dimensional lattice potential whose translational symmetry is broken in a systematic manner, either by making the potential bichromatic or by introducing scatterers at distinct lattice sites. We find that the damping strongly depends on the ratio of lattice constants in the bichromatic potential, and that even a small concentration of scatterers can lead to strong damping. Moreover, mean-field interactions are able to counteract aperiodicity-induced damping of Bloch oscillations.