Stefan Walter
ContactDepartment of PhysicsUniversity of Basel Klingelbergstrasse 82 CH4056 Basel, Switzerland

Research interests
 Nanoelectromechanical systems
 Nanooptomechanical systems
CV
since 01/2013  Postdoctoral associate with Christoph Bruder at the University of Basel. 
10/2009  12/2012  Ph.D. in Physics under supervision of Bjoern Trauzettel at the University of Wuerzburg 
08/2008  09/2009  MA in Physics under supervision of Adam Durst at Stony Brook University 
09/2007  08/2008  Studies of Physics at the University of Wuerzburg 
09/2005  09/2007  Studies of Nanoscience at the University of Wuerzburg 
Publications
Show all abstracts.1.  Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation 
Simon E. Nigg, Rakesh P. Tiwari, Stefan Walter, and Thomas L. Schmidt. arxiv:1411.3945
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.
 
2.  Quantum synchronization of two Van der Pol oscillators 
Stefan Walter, Andreas Nunnenkamp, and Christoph Bruder. Ann. Phys. (2014); arXiv:1406.7134.
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.
 
3.  Teleportationinduced entanglement of two nanomechanical oscillators coupled to a topological superconductor 
Stefan Walter and Jan Carl Budich. Phys. Rev. B 89, 155431 (2014); arXiv:1311.2765.
A onedimensional 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 tunnelcoupled to these Majorana modes. Most interestingly, we demonstrate that the combination of electronphonon 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 teleportation mechanism leads to entanglement of the two oscillators over distances that can significantly exceed the coherence length of the superconductor.
 
4.  Transport properties of double quantum dots with electronphonon coupling 
Stefan Walter, Björn Trauzettel, and Thomas L. Schmidt. Phys. Rev. B 88, 195425 (2013); arXiv:1309.6729.
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
electronphonon coupling and interdot 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.
 
5.  Quantum synchronization of a driven selfsustained oscillator 
Stefan Walter, Andreas Nunnenkamp, and Christoph Bruder. Phys. Rev. Lett. 112, 094102 (2014); arXiv:1307.7044.
Synchronization is a universal phenomenon that is important both in
fundamental studies and in technical applications. Here we investigate
synchronization in the simplest quantummechanical scenario possible, i.e., a
quantummechanical selfsustained 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 (frequencylocked) region is reduced due to quantum noise.
 
6.  Entanglement of nanoelectromechanical oscillators by Cooperpair tunneling 
Stefan Walter, Jan Carl Budich, Jens Eisert, and Björn Trauzettel. Phys. Rev. B 88, 035441 (2013); arXiv:1210.0665.
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 Cooperpair that coherently
tunnels to each oscillator, mediates their coupling and thereby generates
entanglement between them.
 
7.  Failure of protection of Majorana based qubits against decoherence 
Jan Carl Budich, Stefan Walter, and Björn Trauzettel. Phys. Rev. B 85, 121405(R) (2012); arXiv:1111.1734.
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.
 
8.  Detecting Majorana Bound States by Nanomechanics 
Stefan Walter, Thomas L. Schmidt, Kjetil Børkje, and Björn Trauzettel. Phys. Rev. B 84, 224510 (2011); arXiv:1108.2607.
We propose a nanomechanical detection scheme for Majorana bound states, which
have been predicted to exist at the edges of a onedimensional topological
superconductor, implemented, for instance, using a semiconducting wire placed
on top of an swave 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.
 
9.  Momentum and position detection in nanoelectromechanical systems beyond Born and Markov approximations 
Stefan Walter and Björn Trauzettel. Phys. Rev. B 83, 155411 (2011); arXiv:1012.4649.
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 nonstationary
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
momentumbased observables of the nonstationary oscillator. On the other hand,
for a stationary oscillator, a more complicated setup based on an
AharonovBohmloop 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.
 
10.  Bloch oscillations in lattice potentials with controlled aperiodicity 
Stefan Walter, Dominik Schneble, and Adam C. Durst. Phys. Rev. A 81, 033623 (2010); arXiv:0911.1108.
We numerically investigate the damping of Bloch oscillations in a
onedimensional 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,
meanfield interactions are able to counteract aperiodicityinduced damping of
Bloch oscillations.

Teaching
FS 2013: Übungen zur Elektrodynamik  Prof. Trautmann
Übungsblatt 1 (Abgabe Mo. 11.03.2013 bis 12:30 Uhr, Besprechung Mi. 13.03.2013) 
Übungsblatt 2 (Abgabe Mo. 18.03.2013 bis 12:30 Uhr, Besprechung Mi. 20.03.2013) 
Übungsblatt 3 (Abgabe Mo. 25.03.2013 bis 12:30 Uhr, Besprechung Mi. 27.03.2013) 
Übungsblatt 4 (Abgabe Di. 02.04.2013 bis 08:30 Uhr, Besprechung Mi. 03.04.2013) 
Übungsblatt 5 (Abgabe Mo. 08.04.2013 bis 12:30 Uhr, Besprechung Mi. 10.04.2013) 
Übungsblatt 6 (Abgabe Mo. 15.04.2013 bis 12:30 Uhr, Besprechung Mi. 17.04.2013) 
Übungsblatt 7 (Abgabe Mo. 22.04.2013 bis 12:30 Uhr, Besprechung Mi. 24.04.2013) 
Übungsblatt 8 (Abgabe Do. 02.05.2013 bis 12:30 Uhr, Besprechung Mi. 08.05.2013) 
Übungsblatt 9 (Abgabe Mo. 13.05.2013 bis 12:30 Uhr, Besprechung Mi. 15.05.2013) 
Übungsblatt 10 (Abgabe Di. 21.05.2013 bis 08:30 Uhr, Besprechung Mi. 22.05.2013) Nachtrag 
Übungsblatt 11 (Abgabe Mo. 27.05.2013 bis 12:30 Uhr, Besprechung Mi. 29.05.2013) Nachtrag 
Übungsblatt 12 BonusBlatt (Abgabe Mi. 05.06.2013 bis 12:00 Uhr) 
Übungsblatt 11 ist das letzte reguläre Übungsblatt.
Die Bestehensgrenze bleibt weiterhin bei 60%.
Es wird aber ein zusätzliches BonusBlatt geben, bei dem noch Punkte gesammelt werden können.