Belzig, Wolfgang
0000-0002-5109-2203 Berufsbeschreibung
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Ground state topology of a four-terminal superconducting double quantum dot
In recent years, various classes of systems were proposed to realize topological states of matter. One of them are multiterminal Josephson junctions where topological Andreev bound states are constructed in the synthetic space of superconducting phases. Crucially, the topology in these systems results in a quantized transconductance between two of its terminals comparable to the quantum Hall effect. In this work, we study a double quantum dot with four superconducting terminals and show that it has an experimentally accessible topological regime in which the non-trivial topology can be measured. We also include Coulomb repulsion between electrons which is usually present in experiments and show how the topological region can be maximized in parameter space.
Quantum-correlated photons generated by nonlocal electron transport
Since the realization of high-quality microwave cavities coupled to quantum dots, one can envisage the possibility to investigate the coherent interaction of light and matter in semiconductor quantum devices. Here we study a parallel double quantum dot device operating as single-electron splitter interferometer, with each dot coupled to a local photon cavity. We explore how quantum correlation and entanglement between the two separated cavities are generated by the coherent transport of a single electron passing simultaneously through the two different dots. We calculate the covariance of the cavity occupations by use of a diagrammatic perturbative expansion based on Keldysh Green's functions to the fourth order in the dot-cavity interaction strength, taking into account vertex diagrams. In this way, we demonstrate the creation of entanglement by showing that the classical Cauchy-Schwarz inequality is violated if the energy levels of the two dots are almost degenerate. For large level detunings or a single dot coupled to two cavities, we show that the inequality is not violated.
Tunneling processes between Yu-Shiba-Rusinov bound states
Very recent experiments have reported the tunneling between Yu-Shiba-Rusinov (YSR) bound states at the atomic scale. These experiments have been realized with the help of a scanning tunneling microscope where a superconducting tip is functionalized with a magnetic impurity and is used to probe another magnetic impurity deposited on a superconducting substrate. In this way it has become possible to study for the first time the spin-dependent transport between individual superconducting bound states. Motivated by these experiments, we present here a comprehensive theoretical study of the tunneling processes between YSR bound states in a system in which two magnetic impurities are coupled to superconducting leads. Our theory is based on a combination of an Anderson model with broken spin degeneracy to describe the impurities and nonequilibrium Green's function techniques to compute the current-voltage characteristics. This combination allows us to describe the spin-dependent transport for an arbitrary strength of the tunnel coupling between the impurities. We first focus on the tunnel regime and show that our theory naturally explains the experimental observations of the appearance of current peaks in the subgap region due to both the direct and thermal tunneling between the YSR states in both impurities. Then, we study in detail the case of junctions with increasing transparency, which has not been experimentally explored yet, and predict the occurrence of a large variety of (multiple) Andreev reflections mediated by YSR states that give rise to a very rich structure in the subgap current. In particular, we predict the occurrence of multiple Andreev reflections that involve YSR states in different impurities. These processes have no analog in single-impurity junctions, and they are manifested as current peaks with negative differential conductance for subgap voltages. Overall, our work illustrates the unique physics that emerges when the spin degree of freedom is added to a system with superconducting bound states.
Non-classical current noise and light emission of an ac-driven tunnel junction
The nonsymmetrized current noise is crucial for the analysis of light emission in nanojunctions. The latter represent non-classical photon emitters whose description requires a full quantum approach. It was found experimentally that light emission can occur with a photon energy exceeding the applied dc voltage, which intuitively should be forbidden due to the Pauli principle. This overbias light emission cannot be described by the single-electron physics, but can be explained by two-electron or even three-electron processes, correlated by a local resonant mode in analogy to the well-known dynamical Coulomb blockade (DCB). Here, we obtain the nonsymmetrized noise for junctions driven by an arbitrarily shaped periodic voltage. We find that when the junction is driven, the overbias light emission exhibits intriguingly different features compared to the dc case. In addition to kinks at multiples of the bias voltage, side kinks appear at integer multiples of the ac driving frequency. Our work generalizes the DCB theory of light emission to driven tunnel junctions and opens the avenue for engineered quantum light sources, which can be tuned purely by applied voltages.
Frequency comb from a single driven nonlinear nanomechanical mode
Phononic frequency combs have attracted increasing attention both as a qualitatively new type of nonlinear phenomena in vibrational systems and from the point of view of applications. It is commonly believed that at least two modes must be involved in generating a comb. We demonstrate that a comb can be generated by a single nanomechanical mode driven by a resonant monochromatic drive. The comb emerges where the drive is still weak, so the anharmonic part of the mode potential energy remains small. We relate the experimental observation to a negative nonlinear friction induced by the resonant drive, which makes the vibrations at the drive frequency unstable. We directly map the measured trajectories of the emerging oscillations in the rotating frame and show how these oscillations lead to the frequency comb in the laboratory frame. The results go beyond nanomechanics and suggest a qualitatively new approach to generating tunable frequency combs in single-mode vibrational systems. They demonstrate new sides of the interplay of conservative and dissipative nonlinearities in driven systems.
Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems
Topological phases of matter became a new standard to classify quantum systems in many cases, yet key quantities like the quantum geometric tensor providing local information about topological properties are still experimentally hard to access. In non-Abelian systems this accessibility to geometric properties can be even more restrictive due to the degeneracy of the states. We propose universal protocols to determine quantum geometric properties in non-Abelian systems. First, we show that for a weak resonant driving of the local parameters the coherent Rabi oscillations are related to the quantum geometric tensor. Second, we derive that in a Landau-Zener like transition the final probability of an avoided energy crossing is proportional to elements of the non-Abelian quantum geometric tensor. Our schemes suggest a way to prepare eigenstates of the quantum metric, a task that is difficult otherwise in a degenerate subspace.
Ground-state quantum geometry in superconductor–quantum dot chains
Multiterminal Josephson junctions constitute engineered topological systems in arbitrary synthetic dimensions defined by the superconducting phases. Microwave spectroscopy enables the measurement of the quantum geometric tensor, a fundamental quantity describing both the quantum geometry and the topology of the emergent Andreev bound states in a unified manner. In this work we propose an experimentally feasible multiterminal setup of N quantum dots connected to N + 1 superconducting leads to study nontrivial topology in terms of the many-body Chern number of the ground state. Moreover, we generalize the microwave spectroscopy scheme to the multiband case and show that the elements of the quantum geometric tensor of the noninteracting ground state can be experimentally accessed from the measurable oscillator strengths at low temperature.
Engineering the speedup of quantum tunneling in Josephson systems via dissipation
We theoretically investigate the escape rate occurring via quantum tunneling in a system affected by tailored dissipation. Specifically, we study the environmental assisted quantum tunneling of the superconducting phase in a current-biased Josephson junction. We consider Ohmic resistors inducing dissipation both in the phase and in the charge of the quantum circuit. We find that the charge dissipation leads to an enhancement of the quantum escape rate. This effect appears already in the low Ohmic regime and also occurs in the presence of phase dissipation that favors localization. Inserting realistic circuit parameters, we address the question of its experimental observability and discuss suitable parameter spaces for the observation of the enhanced rate.
Exponential speedup of incoherent tunneling via dissipation
We study the escape rate of a particle in a metastable potential in presence of a dissipative bath coupled to the momentum of the particle. Using the semiclassical bounce technique, we find that this rate is exponentially enhanced. In particular, the influence of momentum dissipation depends on the slope of the barrier that the particle is tunneling through. We investigate also the influence of dissipative baths coupled to the position, and to the momentum of the particle, respectively. In this case the rate exhibits a non-monotonic behavior as a function of the dissipative coupling strengths. Remarkably, even in presence of position dissipation, momentum dissipation can enhance exponentially the escape rate in a large range of the parameter space. The influence of the momentum dissipation is also witnessed by the substantial increase of the average energy loss during inelastic (environment-assisted) tunneling.
Second Chern Number and Non-Abelian Berry Phase in Topological Superconducting Systems
Topology ultimately unveils the roots of the perfect quantization observed in complex systems. The 2D quantum Hall effect is the celebrated archetype. Remarkably, topology can manifest itself even in higher-dimensional spaces in which control parameters play the role of extra, synthetic dimensions. However, so far, a very limited number of implementations of higher-dimensional topological systems have been proposed, a notable example being the so-called 4D quantum Hall effect. Here we show that mesoscopic superconducting systems can implement higher-dimensional topology and represent a formidable platform to study a quantum system with a purely nontrivial second Chern number. We demonstrate that the integrated absorption intensity in designed microwave spectroscopy is quantized and the integer is directly related to the second Chern number. Finally, we show that these systems also admit a non-Abelian Berry phase. Hence, they also realize an enlightening paradigm of topological non-Abelian systems in higher dimensions.