arXiv subjects

Fabian Hassler

Publications and source records attributed to Fabian Hassler.

At least 19 recordsLinked to original sources

arXiv2026

Probing proximity-induced superconductivity in bilayer graphene using gate-defined quantum dots

Van der Waals heterostructures offer a direct way of combining two-dimensional (2D) materials with different electronic properties, such as 2D semiconductors, metals, and superconductors, in a single device. Bilayer graphene (BLG) is particularly attractive in this context, as its electrically tunable band gap enables local control of tunnel barriers and quantum dots. Here, we realize an all-2D hybrid platform based on BLG proximitized by superconducting NbSe$_2$. Using local electrostatic gates, we define tunnel barriers and quantum dots at different distances from the lateral superconductor-semiconductor interface. The quantum dots serve as local spectroscopic probes of the proximitized BLG channel segment, forming tunable superconductor-quantum dot-normal conductor junction devices. Coulomb blockade and finite-bias spectroscopy reveal a proximity-induced superconducting gap of up to $80\,\mathrm{μeV}$ and allow to track its evolution with increasing distance from the NbSe$_2$ contact. We find that the local density of states remains suppressed over distances exceeding 1 $μ$m, consistent with superconducting proximity through a highly ballistic BLG channel. Our results show that BLG-superconductor hybrids offer a controllable platform where quantum dots and quantum point contacts can be well combined with superconductivity.

cond-mat.mes-hall↗

arXiv2026

DC Conductance of X-shaped Majorana Interferometer reveals Non-Abelian Anyon Statistics

We propose a four-terminal, X-shaped chiral Majorana interferometer with a central floating superconducting island, enabling the direct detection of the non-Abelian statistics of Ising anyons via the linear-response DC conductance tensor in charge transport experiments. Here, Ising anyons are realizable as edge vortices nucleated at Josephson line junctions defining the superconducting island, where both edge-vortex and Majorana-fermion tunneling processes can occur. We show that in such a multi-terminal Majorana interferometer, both the vacuum and the fermionic fusion channel for Ising anyons are possible. This is in contrast to two-arm interferometers, where only the vacuum fusion channel is accessible and the DC conductance contribution from edge vortices always vanishes. Using a low-energy effective theory derived via chiral bosonization, we find that in the X-shaped interferometer, the DC conductance tensor is completely isotropic, yielding a non-zero conductance when simultaneous edge-vortex and Majorana tunneling activates the fermionic fusion channel. Apart from conductance oscillations in a gate-tunable charge parameter, which display an offset related to the anyon topological spin, measuring a finite conductance can already provide direct evidence for non-Abelian statistics in this geometry.

quant-ph↗

arXiv2026

Photon counting beyond the rotating-wave approximation

Open quantum systems are often described by a Lindblad master equation, which relies on a set of approximations, most importantly the rotating-wave approximation which is only valid for weak damping. In the Lindblad setting, dissipative processes are described through jump operators, distinguishing between absorption and emission of photons. This enables the simple identification of emitted photons which provides a straightforward way to obtain the radiation statistics. Outside the rotating-wave limit, the Lindblad approach does not work. Open quantum systems can then be described by, e.g., the quantum Langevin equation. However, in this framework the number of emitted photons is not easily accessible. In this work, we point out how to obtain the photon counting statistics from a quantum Langevin equation and provide an expression for the photon current operator, for arbitrary systems coupled to linear environments. As an example, we employ the method to study the radiation statistics of a damped harmonic oscillator at finite temperature beyond the rotating-wave approximation. We show that even outside the rotating-wave limit, the most important contribution to the radiation statistics can be captured by an effective Lindblad equation, thus extending the range of possible applications of the Lindblad framework.

cond-mat.mes-hall↗

arXiv2026

Quantum Synchronization of Fock States

Synchronization, a ubiquitous phenomenon in classical systems, has recently been extended to the quantum domain. Here, we show quantum synchronization of a bosonic mode exhibiting a Fock state-like limit cycle, manifesting as a steady state with a negative Wigner function. We demonstrate that this non-classical state can be phase-locked to an external drive, achieving synchronization within an Arnold tongue regime. We argue that synchronization is a dynamical property and fundamentally tied to the suppression of phase slips, which we show to occur with exponentially decreasing probability. We introduce a novel method to extract the phase slip rate from the Lindblad time evolution of the system. This work opens new avenues for understanding and manipulating non-classical synchronization dynamics.

quant-ph↗

arXiv2025

Interaction-induced strong zero modes in short quantum dot chains with time-reversal symmetry

We theoretically explore the emergence of strong zero modes in a two-site chain consisting of two quantum dots coupled due to a central dot that mediates electron hopping and singlet superconducting pairing. In the presence of time-reversal symmetry, the on-site Coulomb interaction leads to a three-fold ground-state degeneracy when tuning the system to a sweet spot as a function of the inter-dot couplings. This degeneracy is protected against changes of the dot energies in the same way as "poor man's'' Majorana bound states in short Kitaev chains. In the limit of strong interactions, this protection is maximal and the entire spectrum becomes triply degenerate, indicating the emergence of a ''poor man's'' version of a strong zero mode. We explain the degeneracy and protection by constructing corresponding Majorana Kramers-pair operators and $\mathbb{Z}_3$-parafermion operators. The strong zero modes share many properties of Majorana bound states in short Kitaev chains, including the stability of zero-bias peaks in the conductance and the behavior upon coupling to an additional quantum dot. However, they can be distinguished through finite-bias spectroscopy and the exhibit a different behavior when scaling to longer chains.

cond-mat.mes-hall↗

arXiv2024

Robust gap closing and reopening in topological-insulator Josephson junctions

In the seminal proposal by Fu and Kane, the superconducting proximity effect is used to realize topological superconductivity in the topological surface state (TSS) of a 3D topological insulator (TI). In a line Josephson junction made on the TI surface, the spin-momentum locking of the TSS guarantees the existence of a pair of spin-non-degenerate, perfectly transmitted Andreev modes. These modes lead to robust gap closing and parity alteration as a function of the superconducting phase difference $φ$ across the junction. Here, we report the observation of the predicted gap closing at $φ= (2n+1)π$ in a TI Josephson junction ($n$ integer), where the local density of states is probed via tunnel contacts and $φ$ is controlled by a flux loop. This phenomenon is robust for a wide range of chemical potentials, supporting its TSS origin. Under an applied perpendicular magnetic field, Josephson vortices form, making $φ$ position-dependent. In this case, the gap closing occurs locally at the Josephson vortex cores where $φ= (2n+1)π$, which we also observe. Our results confirm the fundamental role of spin-momentum locking in the Andreev physics in the TSS, which implies that the observed gap closing and reopening has a topological nature.

cond-mat.supr-con↗

arXiv2024

Topological quantum computing

These lecture notes offer a pedagogical yet concise introduction to topological quantum computing. The material focuses on topological superconductors and Majorana qubits. It concludes with a discussion of more general braiding phenomena. In particular, the notes delve into the non-Abelian braiding statistics of Ising and Fibonacci anyons. Although not comprehensive, this set provides a solid entry point for students and researchers interested in the field.

quant-ph↗

arXiv2024

Tunable diode effect in a superconducting tunnel junction with biharmonic drive

A Josephson diode is a superconducting circuit element that enables non-reciprocal transport, allowing a dissipationless supercurrent to preferentially flow in a single direction. Existing methods for achieving the required symmetry breaking mostly rely on specifically-designed materials or carefully-engineered circuits composed of multiple Josephson junctions. Here, we demonstrate that applying a biharmonic drive to a conventional superconducting tunnel-junction induces a diode effect through harmonic mixing processes that shift the supercurrent region. We show that, in a conventional tunnel junction, unity efficiency is achievable while maintaining a large supercurrent. Moreover, the relative phase between the two driving tones determines the directionality of the diode, which can be tuned in situ.

cond-mat.mes-hall↗

arXiv2024

The superconducting clock-circuit: Improving the coherence of Josephson radiation beyond the thermodynamic uncertainty relation

In the field of superconducting electronics, the on-chip generation of AC radiation is essential for further advancements. Although a Josephson junction can emit AC radiation from a purely DC voltage bias, the coherence of this radiation is significantly limited by Johnson-Nyquist noise. We relate this limitation to the thermodynamic uncertainty relation (TUR) in the field of stochastic thermodynamics. Recent findings indicate that the thermodynamic uncertainty relation can be broken by a classical pendulum clock. We demonstrate how the violation of the TUR can be used as a design principle for radiation sources by showing that a superconducting clock circuit emits coherent AC radiation from a DC bias.

cond-mat.mes-hall↗

arXiv2024

Non-Abelian anyon statistics through AC conductance of a Majorana interferometer

Demonstrating the non-Abelian Ising anyon statistics of Majorana zero modes in a physical platform still represents a major open challenge in physics. We here show that the linear low-frequency charge conductance of a Majorana interferometer containing a floating superconducting island can reveal the topological spin of quantum edge vortices. The latter are associated with chiral Majorana fermion edge modes and represent "flying" Ising anyons. We describe possible device implementations and outline how to detect non-Abelian anyon braiding through AC conductance measurements.

cond-mat.str-el↗

arXiv2024

Superbunched radiation of a tunnel junction due to charge quantization

A chaotic light source is characterized by the fact that many independent emitters radiate photons with a random optical phase. This is similar compared to a tunnel junction where many independent channels are able to emit photons due to a coupling to an electromagnetic environment. However, in a recent experiment it has been observed that a tunnel junction can deviate from the expectation of chaotic light and is able to emit strongly correlated, superbunched photons. Motivated by this, we study the correlation of the radiation and show that the superbunching originates from the emission of multiple photons which is possible due to the quantization of charge.

cond-mat.mes-hall↗

arXiv2023

Tuning the supercurrent distribution in parallel ballistic graphene Josephson junctions

We report on a ballistic and fully tunable Josephson junction system consisting of two parallel ribbons of graphene in contact with superconducting MoRe. By electrostatic gating of the two individual graphene ribbons we gain control over the real space distribution of the superconducting current density, which can be continuously tuned between both ribbons. We extract the respective gate dependent spatial distributions of the real space current density by employing Fourier- and Hilbert transformations of the magnetic field induced modulation of the critical current. This approach is fast and does not rely on a symmetric current profile. It is therefore a universally applicable tool, potentially useful for carefully adjusting Josephson junctions.

cond-mat.mes-hall↗

arXiv2023

Two-point spectroscopy of Fibonacci topoelectrical circuits

Topoelectrical circuits are meta-material realizations of topological features of condensed matter systems. In this work, we discuss experimental methods that allow a fast and straightforward detection of the spectral features of these systems from the two-point impedance of the circuit. This allows to deduce the full spectrum of a topoelectrical circuit consisting of N sites from a single two-point measurement of the frequency resolved impedance. In contrast, the standard methods rely on $N^2$ measurements of admittance matrix elements with a subsequent diagonalization on a computer. We experimentally test our approach by constructing a Fibonacci topoelectrical circuit. Although the spectrum of this chain is fractal, i.e., more complex than the spectra of periodic systems, our approach is successful in recovering its eigenvalues. Our work promotes the topoelectrical circuits as an ideal platform to measure spectral properties of various (quasi)crystalline systems.

cond-mat.mes-hall↗

arXiv2023

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries

Open quantum systems that interact with a Markovian environment can be described by a Lindblad master equation. The generator of time-translation is given by a Liouvillian superoperator $\mathcal{L}$ acting on the density matrix of the system. As the Fock space for a single bosonic mode is already infinite-dimensional, the diagonalization of the Liouvillian has to be done on the creation- and annihilation-superoperators, a process called `third quantization'. We propose a method to solve the Liouvillian for quadratic systems using a single symplectic transformation. We show that the non-Hermitian effective Hamiltonian of the system, next to incorporating the dynamics of the system, is a tool to analyze its symmetries. As an example, we use the effective Hamiltonian to formulate a $\mathcal{PT}$-`symmetry' of an open system. We describe how the inclusion of source terms allows us to obtain the cumulant generating function for observables such as the photon current.

quant-ph↗

arXiv2023

On chip AC driving for dual Shapiro steps

A single Josephson junction in the phase-slip regime exhibits Bloch oscillations in the voltage when biased with a DC current $I_\text{DC}$. The frequency of the oscillation is given by $πI_\text{DC}/e$, with $e$ the elementary charge, linking the current to the frequency via fundamental constants of nature. If an additional AC drive is applied, the Bloch oscillations may synchronize with the external drive. This leads to the emergence of dual Shapiro steps at fixed current in the $IV$ characteristics of the device. For applications as a current standard, frequencies of the order of 10\,GHz are required. These are challenging to implement experimentally without detrimental effects due to stray capacitances. Here, we propose to employ an additional Josephson junction with a DC voltage bias as an on chip AC source due to the AC Josephson effect. We study the back action of the Bloch oscillations on the Josephson oscillations and identify a parameter regime in which it is minimized. Furthermore, we find that the back action can even be utilized to further enhance the driving signal which can lead to increased widths of the resulting dual Shapiro steps. Finally, we show dual Shapiro steps for a set of realistic experimental parameters at finite temperatures.

cond-mat.mes-hall↗

arXiv2023

Time-dependent driving and topological protection in the fractional Josephson effect

The control of any type of quantum hardware invariably necessitates time-dependent driving. If the basis depends on the control parameter, the presence of a time-dependent control field yields an extra term in the Schrödinger equation that is often neglected. Here, we examine the effect of this term in a flux-controlled Majorana junction. We show that a time-varying flux gives rise to an electromotive force which is amplified when truncating to the junction's low-energy degrees of freedom. As a result, it compromises the robustness of the ground-state degeneracy present in the absence of the drive. The resulting flattening of the energy spectrum can be measured by a strong suppression of the dc supercurrent.

cond-mat.supr-con↗

arXiv2023

On chip synchronization of Bloch oscillations in a strongly coupled pair of small Josephson junctions

Bloch oscillations are a fundamental phenomenon linking the adiabatic transport of Cooper pairs to time. Here, we investigate synchronization of the Bloch oscillations in a strongly coupled system of sub-100 nm Al/AlOx/Al Josephson junctions in high-ohmic environment composed of highly inductive meanders of granulated aluminum and high-ohmic titanium microstrips. We observe a pronounced current mirror eff ect in the coupled junctions and demonstrate current plateaus, akin to the fi rst dual Shapiro step in microwave experiments. These fi ndings suggest that our circuit design holds promise for realizing protected Bloch oscillations and precise Shapiro steps of interest for current metrology.

cond-mat.mes-hall↗

arXiv2023

Counting interacting electrons in one dimension

The calculation of the full counting statistics of the charge within a finite interval of an interacting one-dimensional system of electrons is a fundamental, yet as of now unresolved problem. Even in the non-interacting case, charge counting turns out to be more difficult than anticipated because it necessitates the calculation of a nontrivial determinant and requires regularization. Moreover, interactions in a one-dimensional system are best described using bosonization. However, this technique rests on a long-wavelength approximation and is a priori inapplicable for charge counting due to the sharp boundaries of the counting interval. To mitigate these problems, we investigate the counting statistics using several complementary approaches. To treat interactions, we develop a diagrammatic approach in the fermionic basis, which makes it possible to obtain the cumulant generating function up to arbitrary order in the interaction strength. Importantly, our formalism preserves charge quantization in every perturbative order. We derive an exact expression for the noise and analyze its interaction-dependent logarithmic cutoff. We compare our fermionic formalism with the results obtained by other methods, such as the Wigner crystal approach and numerical calculations using the density-matrix renormalization group. Surprisingly, we show good qualitative agreement with the Wigner crystal for weak interactions, where the latter is in principle not expected to apply.

cond-mat.str-el↗