arXiv subjects

Fabian Hassler

Publications and source records attributed to Fabian Hassler.

At least 73 records · Page 4Linked to original sources

arXiv2017

Aharonov-Bohm oscillations and magnetic focusing in ballistic graphene rings

We present low-temperature magnetotransport measurements on graphene rings encapsulated in hexagonal boron nitride. We investigate phase-coherent transport and show Aharonov-Bohm (AB) oscillations in quasi-ballistic graphene rings with hard confinement. In particular, we report on the observation of $h/e$, $h/2e$ and $h/3e$ conductance oscillations. Moreover we show signatures of magnetic focusing effects at small magnetic fields confirming ballistic transport. We perform tight binding calculations which allow to reproduce all significant features of our experimental findings and enable a deeper understanding of the underlying physics. Finally, we report on the observation of the AB conductance oscillations in the quantum Hall regime at reasonable high magnetic fields, where we find regions with enhanced AB oscillation visibility with values up to $0.7$%. These oscillations are well explained by taking disorder into account allowing for a coexistence of hard and soft-wall confinement.

cond-mat.mes-hall↗

arXiv2017

Quantum phase transitions of the Majorana toric code in the presence of finite Cooper-pair tunneling

The toric code based on Majorana fermions on mesoscopic superconducting islands is a promising candidate for quantum information processing. In the limit of vanishing Cooper-pair tunneling, it has been argued that the phase transition separating the topologically ordered phase of the toric code from the trivial one is in the universality class of (2+1)D-XY. On the other hand, in the limit of infinitely large Cooper-pair tunneling, the phase transition is in the universality class of (2+1)D-Ising. In this work, we treat the case of finite Cooper-pair tunneling and address the question of how the continuous XY symmetry breaking phase transition turns into a discrete $\mathbb{Z}_2$ symmetry breaking one when the Cooper-pair tunneling rate is increased. We show that this happens through a couple of tricritical points and first order phase transitions. Using a Jordan-Wigner transformation, we map the problem to that of spins coupled to quantum rotors and subsequently, propose a Landau field theory for this model that matches the known results in the respective limits. We calculate the effective field theories and provide the relevant critical exponents for the different phase transitions. Our results are relevant for predicting the stability of the topological phase in realistic experimental implementations.

cond-mat.mes-hall↗

arXiv2017

Measurement-induced entanglement of two transmon qubits by a single photon

On-demand creation of entanglement between distant qubits is a necessary ingredient for distributed quantum computation. We propose an entanglement scheme that allows for single-shot deterministic entanglement creation by detecting a single photon passing through a Mach-Zehnder interferometer with one transmon qubit in each arm. The entanglement production essentially relies on the fact that superconducting microwave structures allow to achieve strong coupling between the qubit and the photon. By detecting the photon via a photon counter, a parity measurement is implemented and the wave function of the two qubits is projected onto a maximally entangled state. Most importantly, the entanglement generation is heralded such that our protocol is not susceptible to photon loss due to the indivisible nature of single photons.

cond-mat.mes-hall↗

arXiv2016

Simulation of supersymmetric quantum mechanics in a Cooper-pair box shunted by a Josephson rhombus

Supersymmetries in quantum mechanics offer a way to obtain degeneracies in the excitation spectrum which do not originate from selection rules. The mechanism behind the degeneracies is the same as the one that leads to the miraculous cancellations of divergences in supersymmetric field theories found in the high energy physics context. Even though of importance, there is up to now no realistic proposal of non-integrable systems that show level degeneracies due to a supersymmetric structure. Here, we propose an implementation of a quantum-mechanical supersymmetry in a Cooper-pair box shunted by a Josephson junction rhombus which is effectively $π$-periodic in the superconducting phase difference. For a characteristic ratio between the strength of the $2π$- and the $π$-periodic junction, we find a two-fold degeneracy of all the energy levels all the way from the weak junction/charge qubit limit to the strong junction/transmon regime. We provide explicit values for the parameters of the rhombus and show that tuning in and out of the supersymmetric point is easily achieved by varying an external gate voltage. We furthermore discuss a microwave experiment to detect the supersymmetry and conclude that it could indeed be simulated with currently existing Josephson junction technology.

cond-mat.mes-hall↗

arXiv2016

Dual approach to circuit quantization using loop charges

The conventional approach to circuit quantization is based on node fluxes and traces the motion of node charges on the islands of the circuit. However, for some devices, the relevant physics can be best described by the motion of polarization charges over the branches of the circuit that are in general related to the node charges in a highly nonlocal way. Here, we present a method, dual to the conventional approach, for quantizing planar circuits in terms of loop charges. In this way, the polarization charges are directly obtained as the differences of the two loop charges on the neighboring loops. The loop charges trace the motion of fluxes through the circuit loops. We show that loop charges yield a simple description of the flux transport across phase-slip junctions. We outline a concrete construction of circuits based on phase-slip junctions that are electromagnetically dual to arbitrary planar Josephson junction circuits. We argue that loop charges also yield a simple description of the flux transport in conventional Josephson junctions shunted by large impedances. We show that a mixed circuit description in terms of node fluxes and loop charges yields an insight into the flux decompactification of a Josephson junction shunted by an inductor. As an application, we show that the fluxonium qubit is well approximated as a phase-slip junction for the experimentally relevant parameters. Moreover, we argue that the $0$-$π$ qubit is effectively the dual of a Majorana Josephson junction.

cond-mat.mes-hall↗

arXiv2016

Universal power-law decay of electron-electron interactions due to nonlinear screening in a Josephson junction array

Josephson junctions are the most prominent nondissipative and at the same time nonlinear elements in superconducting circuits allowing Cooper pairs to tunnel coherently between two superconductors separated by a tunneling barrier. Due to this, physical systems involving Josephson junctions show highly complex behavior and interesting novel phenomena. Here, we consider an infinite one-dimensional chain of superconducting islands where neighboring islands are coupled by capacitances. We study the effect of Josephson junctions shunting each island to a common ground superconductor. We treat the system in the regime where the Josephson energy exceeds the capacitive coupling between the islands. For the case of two offset charges on two distinct islands, we calculate the interaction energy of these charges mediated by quantum phase slips due to the Josephson nonlinearities. We treat the phase slips in an instanton approximation and map the problem onto a classical partition function of interacting particles. Using the Mayer cluster expansion, we find that the interaction potential of the offset charges decays with an universal inverse-square power law behavior.

cond-mat.mes-hall↗

arXiv2015

Exchange-interaction of two spin qubits mediated by a superconductor

Entangling two quantum bits by letting them interact is the crucial requirements for building a quantum processor. For qubits based on the spin of the electron, these two-qubit gates are typically performed by exchange interaction of the electrons captured in two nearby quantum dots. Since the exchange interaction relies on tunneling of the electrons, the range of interaction for conventional approaches is severely limited as the tunneling amplitude decays exponentially with the length of the tunneling barrier. Here, we present a novel approach to couple two spin qubits via a superconducting coupler. In essence, the superconducting coupler provides a tunneling barrier for the electrons which can be tuned with exquisite precision. We show that as a result exchange couplings over a distance of several microns become realistic, thus enabling flexible designs of multi-qubit systems.

cond-mat.mes-hall↗

arXiv2015

Second-order coherence of microwave photons emitted by a quantum point contact

Shot-noise of electrons that are transmitted with probability $T$ through a quantum point contact (biased at a voltage $V_0$) leads to a fluctuating current that in turn emits radiation in the microwave regime. By calculating the Fano factor $F$ for the case where only a single channel contributes to the transport, it has been shown that the radiation produced at finite frequency $ω_0$ close to $e V_0/\hbar$ and at low temperatures is nonclassical with sub-Poissonian statistics ($F<1$). The origin of this effect is the fermionic nature of the electrons producing the radiation, which reduces the probability of simultaneous emission of two or more photons. However, the Fano factor, being a time-averaged quantity, offers only limited information about the system. Here, we calculate the second-order coherence $g^{(2)}(τ)$ for this source of radiation. We show that due to the interference of two contributions, two photon processes (leading to bunching) are completely absent at zero temperature for $T=50\,\%$. At low temperatures, we find a competition of the contribution due to Gaussian current-current fluctuations (leading to bunching) with the one due to non-Gaussian fluctuations (leading to antibunching). At slightly elevated temperatures, the non-Gaussian contribution becomes suppressed whereas the Gaussian contributions remain largely independent of temperature. We show that the competition of the two contributions leads to a nonmonotonic behavior of the second-order coherence as a function of time. As a result, $g^{(2)}(τ)$ obtains a minimal value for times $τ^* \simeq ω_0^{-1}$. Close to this time, the second-order coherence remains below 1 at temperatures where the Fano factor is already above 1. We identify realistic experimental parameters that can be used to test the sub-Poissonian nature of the radiation.

cond-mat.mes-hall↗

arXiv2015

Dephasing due to quasiparticle tunneling in fluxonium qubits: a phenomenological approach

The fluxonium qubit has arisen as one of the most promising candidate devices for implementing quantum information in superconducting devices, since it is both insensitive to charge noise (like flux qubits) and insensitive to flux noise (like charge qubits). Here, we investigate the stability of the quantum information to quasiparticle tunneling through a Josephson junction. Microscopically, this dephasing is due to the dependence of the quasiparticle transmission probability on the qubit state. We argue that on a phenomenological level the dephasing mechanism can be understood as originating from heat currents, which are flowing in the device due to possible effective temperature gradients, and their sensitivity to the qubit state. The emerging dephasing time is found to be insensitive to the number of junctions with which the superinductance of the fluxonium qubit is realised. Furthermore, we find that the dephasing time increases quadratically with the shunt-inductance of the circuit which highlights the stability of the device to this dephasing mechanism.

cond-mat.mes-hall↗

arXiv2015

Changing anyonic ground degeneracy with engineered gauge fields

For systems of lattice anyons like Majorana and parafermions, the unconventional quantum statistics determines a set of global symmetries (e.g., fermion parity for Majoranas) admitting no relevant perturbations. Any operator that breaks these symmetries explicitly would violate locality if added to the the Hamiltonian. As a consequence, the associated quasi-degeneracy of topologically non-trivial phases is protected, at least partially, by locality via the symmetries singled out by quantum statistics. We show that it is possible to bypass this type of protection by way of specifically engineered gauge fields, in order to modify the topological structure of the edge of the system without destroying the topological order completely. To illustrate our ideas in a concrete setting, we focus on the $\Z_6$ parafermion chain. Starting in the topological phase of the chain (sixfold ground degeneracy), we show that a gauge field with restricted dynamics acts as a relevant perturbation, driving a transition to a phase with threefold degeneracy and $\Z_3$ parafermion edge modes. The transition from the $\Z_3$ to the topologically trivial phase occurs on a critical line in the three-state Potts universality class. We also investigate numerically the emergence of Majorana edge modes when the $\Z_6$ chain is coupled to a differently restricted gauge field.

cond-mat.mes-hall↗

arXiv2015

Majorana-assisted nonlocal electron transport through a floating topological superconductor

The nonlocal nature of the fermionic mode spanned by a pair of Majorana bound states in a one-dimensional topological superconductor has inspired many proposals aiming at demonstrating this property in transport. In particular, transport through the mode from a lead attached to the left bound state to a lead attached to the right will result in current cross-correlations. For ideal zero modes on a grounded superconductor, the cross-correlations are however completely suppressed in favor of purely local Andreev reflection. In order to obtain a non-vanishing cross-correlation, previous studies have required the presence of an additional global charging energy. Adding nonlocal terms in the form of a global charging energy to the Hamiltonian when testing the intrinsic nonlocality of the Majorana modes seems to be conceptually troublesome. Here, we show that a floating superconductor allows to observe nonlocal current correlations in the absence of charging energy. We show that the non-interacting and the Coulomb-blockade regime have the same peak conductance $e^2/h$ but different shot-noise power; while the shot noise is sub-Poissonian in the Coulomb-blockade regime in the large bias limit, Poissonian shot noise is generically obtained in the non-interacting case.

cond-mat.supr-con↗

arXiv2015

Strongly interacting Majorana modes in an array of Josephson junctions

An array of superconducting islands with semiconducting nanowires in the right regime provides a macroscopic implementation of Kitaev's toy model for Majorana wires. We show that a capacitive coupling between adjacent islands leads to an effective interaction between the Majorana modes. We demonstrate that even though strong repulsive interaction eventually drive the system into a Mott insulating state the competition between the (trivial) band-insulator and the (trivial) Mott insulator leads to an interjacent topological insulating state for arbitrary strong interactions.

cond-mat.str-el↗

arXiv2015

Microwave readout of Majorana qubits

Majorana qubits offer a promising way to store and manipulate quantum information by encoding it into the state of Majorana zero modes. As the information is stored in a topological property of the system, local noise cannot lead to decoherence. Manipulation of the information is achieved by braiding the zero modes. The measurement, however, is challenging as the information is well hidden and thus inherently hard to access. Here, we discuss a setup for measuring the state of a Majorana qubit by employing standard tools of microwave engineering. The basic physical effect that we employ is the fact that a voltage-biased Josephson junction hosting Majorana fermions allows photons to be emitted and absorbed at half the Josephson frequency. We show that in the dispersive regime, our setup allows us to perform a quantum nondemolition measurement and to reach the quantum limit. An appealing feature of our setup is that the interaction of the Majorana qubit with the measurement device can be turned on and off at will by changing the dc bias of the junction.

cond-mat.mes-hall↗

arXiv2015

Measurement and dephasing of a flux qubit due to heat currents

We study a flux qubit, made of a superconducting loop interrupted by three Josephson junctions, which is subject to a temperature gradient. We show that the heat current induced by the temperature gradient, being sensitive to the superconducting phase differences at the junctions, depends significantly on the state of the qubit. We furthermore investigate the impact of the heat current on the coherence properties of the qubit state. We have found that even small temperature gradients can lead to dephasing times of the order of microseconds for the Delft-qubit design.

cond-mat.mes-hall↗

arXiv2014

Supersymmetry in the Majorana Cooper-Pair Box

Over the years, supersymmetric quantum mechanics has evolved from a toy model of high energy physics to a field of its own. Although various examples of supersymmetric quantum mechanics have been found, systems that have a natural realization are scarce. Here, we show that the extension of the conventional Cooper-pair box by a 4pi-periodic Majorana-Josephson coupling realizes supersymmetry for certain values of the ratio between the conventional Josephson and the Majorana- Josephson coupling strength. The supersymmetry we find is a "hidden" minimally bosonized supersymmetry that provides a non-trivial generalization of the supersymmetry of the free particle and relies crucially on the presence of an anomalous Josephson junction in the system. We show that the resulting degeneracy of the energy levels can be probed directly in a tunneling experiment and discuss the various transport signatures. An observation of the predicted level degeneracy would provide clear evidence for the presence of the anomalous Josephson coupling.

cond-mat.mes-hall↗

arXiv2014

Majorana Qubits

Contribution to the 44th IFF Spring School held at the Forschungszentrum Jülich in 2013 on "Quantum Information Processing". The notes include a pedagogic (but incomplete) introduction to Majorana fermions; especially paying attention to the usefulness for quantum information purposes. It contains an introduction to topological aspects of superconductors, braiding, physical implementations, and measurement of the quantum information using superconducting qubits.

quant-ph↗

arXiv2013

Majorana fermions coupled to electromagnetic radiation

We consider a voltage-biased Josephson junction between two nanowires hosting Majorana zero modes which occur as topological protected zero-energy excitations at the junction. We show that two Majorana fermions localized at the junction, even though being neutral particles, interact with the electromagnetic field and generate coherent radiation similar to the conventional Josephson radiation. Within a semiclassical analysis of the radiation field, we find that the optical phase gets locked to the superconducting phase difference and that the radiation is emitted at half the Josephson frequency. In order to confirm the coherence of the radiation, we study correlations of the radiation emitted by two spatially-separated junctions in a d.c.-SQUID geometry taking into account decoherence due to spontaneous state-switches as well as due to quasi-particle poisoning.

cond-mat.mes-hall↗

arXiv2013

Effects of non-equilibrium noise on a quantum memory encoded in Majorana zero modes

In order to increase the coherence time of topological quantum memories in systems with Majorana zero modes, it has recently been proposed to encode the logical qubit states in non-local Majorana operators which are immune to localized excitations involving the unpaired Majorana modes. In this encoding, a logical error only happens when the quasi-particles, subsequent to their excitation, travel a distance of the order of the spacing between the Majorana modes. Here, we study the decay time of a quantum memory encoded in a clean topological nanowire interacting with an environment with a particular emphasis on the propagation of the quasi-particles above the gap. We show that the non-local encoding does not provide a significantly longer coherence time than the local encoding. In particular, the characteristic speed of propagation is of the order of the Fermi velocity of the nanowire and not given by the much slower group velocity of quasi-particles which are excited just above the gap.

cond-mat.mes-hall↗