In this project we focus on the transfer of electrons between two electrostatically defined semiconductor quantum dots (QDs). We use local Schottky barriers on top of a GaAs/AlGaAs heterostructure to form individual QDs and quantum point contacts (QPCs) which act as local charge sensors. We use one QD as electron emitter and detect with the second one (see Figure).

Using single QDs we can individually change the injection and detection energy of our electrons and spectroscopically investigate the effects and interactions involved in transferring electrons. An external perpendicular magnetic field helps guiding the electrons, but strongly increases the interaction. Many body effects and interactions are of crucial importance.

With charge sensing of single electrons we can understand the transfer of single electrons in a time resolved manner and tackle fundamental problems in quantum mechanics concerning the measurement process as well as dephasing and coherence effects.

(Lev Ginzburg, Carolin Gold)

In our group we use two setups to perform scanning gate microscopy at millikelvin-temperatures.

This measurement technique uses a voltage-biased scanning probe tip as a mobile, local perturbation.
During the measurements, the tip is scanned at constant height to the sample surface while recording the non-local conductance through the sample.

Our main topics of investigations are ballistic electron flow and the fractional quantum Hall effect on high mobility GaAs materials. Also different materials, such as graphene, are investigated.

(Szymon Hennel, Giorgio Nicoli, Marc Röösli)

The fractional quantum Hall effect is associated with correlated incompressible ground states of high mobility two-dimensional electron gases subject to very low temperatures and strong magnetic fields. Of particular interest is the state emerging in the second Landau level at the even-denominator filling factor ν = 5/2. This state is conjectured to be described by the Pfaffian ground state and is potentially useful in the realization of topological quantum computation owing to its possibly non-Abelian statistics.

In this project, we study bulk and edge properties of fractional quantum Hall states in nanoscale devices defined in ultra high mobility GaAs/AlGaAs heterostructures by optical and electron beam lithography techniques.

In one of our recent works (Fig. 1), we have studied the breaking of particle-hole symmetry in non-equilibrium transport in the second Landau level.

One of our current goals is to probe the statistics of ν = 5/2 in interferometry experiments. An electronic Fabry-Pérot interferometer device is shown in Fig. 2, together with an interference pattern observed in the integer quantum Hall state at filling ν = 10.

The wave-particle duality in quantum mechanics describes how objects may possess properties of both waves and particles [1]. Demonstrations of this duality reside at the foundation of modern physics research with pioneering experiments displaying its validity for elementary particles and testing its limits for larger systems [2-4].

Our experiment consists of two mesoscopic-scale building blocks:

- A single electron (particle) localized in an electrostatic confinement potential, a so-called quantum dot.
- An electronic standing wave, bound between the quantum dot and a spherical mirror at a distance of two micrometers.

In our experiment [5], we observe pairing of these two constituents which in itself conforms to a demonstration of a wave coupled to a particle. Interestingly, we find that the mechanism inducing this pairing is the spin of the involved electrons, i.e. the magnetic moments of the localized electron and the electronic wave in the cavity.

In view of quantum engineering applications, custom shaped cavity modes might prove a welcome addition to the ensemble of existing low-dimensional structures like quantum dots and quantum wires. In particular for employing spins for quantum information processing, the demonstration of micrometer-ranged spin-pairing holds great promise for entangling spatially separated spin-qubits.

[1]: L. de Broglie, Thesis, Paris, 1924, Ann. de Physique (10) 3, 22 (1925)

[2]: I. Estermann and O. Stern, Zeitschrift für Physik 61 (1-2), 95-125 (1930)

[3]: M. Arndt et al., Nature 401 (6754): 680-682 (1999)

[4]: Y. Couder and E. Fort, PRL 97, 154101 (2006)

[5]: C. Rössler et al., PRL 115, 166603 (2015)

(Jonne Koski, Benedikt Kratochwil, Andreas Landig)

In this project we explore the physics of semiconductor quantum dots coupled to superconducting microwave resonators.

Figure (a) presents the discrete energy levels of a double quantum dot interacting with a photon of the resonator and figure (b) a typical double dot structure we use.

We focus on investigating the coherent coupling of the two systems for example by measuring the photons emitted by the inelastic tunneling of single charges in the double dot. See figure (c), where two resonances are observed.

Future work will also focus on spin physics in the circuit QED architecture. We will address the electron spin with microwave fields by coupling the charge and spin degrees of freedom with the inhomogeneous magnetic field of a micromagnet [3].

The study of the interaction between the electromagnetic field of such resonators and semiconductor quantum dots marks an important step toward hybrid quantum information processing, in which the advantages of different systems, like a long relaxation time of the individual qubit and interaction between distant qubits, could be exploited in one device.

[1]: A. Stockklauser et al., PRL 115, 046802 (2015)

[2]: T. Frey et al., PRL 108, 046807 (2012)

[3]: M. Pioro-Ladrière et al., Nature 4, 776-779 (2008)

(Annika Kurzmann)

We study time-resolved tunnelling of single electrons in n-type GaAs/AlGaAs quantum dot systems.

A single quantum dot coupled to a single lead provides a controllable and easily tunable testbed for out-of-equilibrium thermodynamics measurements on the microscopic level of a single electron. By applying a feedback mechanism, which allows for measuring the tunnel rates between the quantum dot and the lead, we study the filling of electrons into the quantum dot ground and excited states. While alternate filling of spin-up and spin-down electrons is found for the first few electrons, the case of many electrons is still to be tested.

We aim to find more information about the level composition of a QD by analyzing the tunnel dynamics between two coupled quantum dots (DQD).

In a finite magnetic field, we measure Pauli spin blockade (PSB) for even numbers of electrons occupying the DQD, agreeing with the spin-pair filling found for the single QD. Real-time measurements of the PSB allow for extracting the spin-flip rate of electrons while tunneling or within a single dot and we want to gain insight into the spin-orbit and hyperfine interaction, respectively.

We use the feedback mechanism to measure the interdot tunneling rates far away from the resonance with the aim to study the phononic environment.

[1]: A. Hofmann et al., arXiv: 1504.04949

(Marius Eich, Rebekka Garreis, Yongjin Lee, Riccardo Pisoni, Peter Rickhaus, Chuyao Tong)

Patterned graphene nanodevices are an interesting playground for nano- and quantum-electronics [1]. We currently focus on two topics: combining graphene and Gallium Arsenide and electrostatical gating of bilayer graphene.

The combination of electronic devices made of different material systems, such as graphene on GaAs/AlGaAs heterostructures, offers unique opportunities for studying the coupling of charge carriers with strongly differing energy-momentum relations. We have demonstrated mutual capacitive coupling and charge detection between graphene and GaAs nanostructures (see device schematic in left figure) [2]. Using shallower heterostructures, Coulomb drag in such hybrid nanostructures or tunneling coupling between quasi-relativistic charge carriers in graphene with massive electrons in GaAs could be investigated.

Bilayer graphene is a unique material for both fundamental physics and applications, because its band structure can be tuned by electrical gating. For instance, dual-gated heterojunctions of bilayer graphene show a change of the degeneracies of Landau levels in the high displacement field regime as a result of a Lifshitz transition (right figure) [3]. Inducing a band gap in bilayer graphene might also provide a way to electrostatically engineer nanostructures in graphene, such as spin qubits. Graphene is a promising material for such applications, because both the small spin-orbit coupling and the nuclear spin-free ^{12}C isotope presumably lead to long spin coherence times.

**References:**

[1]: D. Bischoff et al., Appl. Phys. Rev. 2, 031301 (2015)

[2]: P. Simonet et al., Appl. Phys. Lett. 107, 023105 (2015)

[3]: A. Varlet et al., PRL 113, 116602 (2014)

(Matija Karalic, Zijin Lei, Christopher Mittag)

The double quantum well system InAs/GaSb with the peculiar type-II band alignment is a prospective topological insulator candidate. Due to the spatially separate InAs and GaSb quantum wells, gate tunability is expected in the form of a rich phase diagram with both trivial and topological insulator phases. The latter entails counterpropagating helical edge states, which manifest themselves in the quantum spin Hall effect.

We are interested in exploring the nature of the proposed edge states with nonlocal transport measurements (Figure 1). Preliminary experiments on standard Hall bars (Figure 2) in the mesoscopic regime confirm edge transport.