arXiv subjects

Gerd Schön

Publications and source records attributed to Gerd Schön.

At least 19 recordsLinked to original sources

arXiv2019

Phonon spectral density in a GaAs/AlGaAs double quantum dot

We study phonon emission in a GaAs/AlGaAs double quantum dot by monitoring the tunneling of a single electron between the two dots. We prepare the system such that a known amount of energy is emitted in the transition process. The energy is converted into lattice vibrations and the resulting tunneling rate depends strongly on the phonon scattering and its effective phonon spectral density. We are able to fit the measured transition rates and see imprints of interference of phonons with themselves causing oscillations in the transition rates.

cond-mat.mes-hall↗

arXiv2019

Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors

A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and near-future quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a time-dependent Hamiltonian, where the - ideally short - fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasi-static errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities.

quant-ph↗

arXiv2019

Transport Signatures of a Majorana Qubit and Read-out-induced Dephasing

Motivated by recent proposals of Majorana qubits and the read-out of their quantum state we investigate a qubit setup formed by two parallel topological wires shunted by a superconducting bridge. The wires are further coupled to two quantum dots, which are also linked directly, thus creating an interference loop. The transport current through this system shows an interference pattern which distinguishes two basis states of the qubit in a QND measurement. We analyze various properties of the interference current and the read-out process, including the resulting dephasing and relaxation. We also analyze the effects of varying control parameters such as gate voltages on the current. The characteristic dependencies could serve as a signature of Majorana bound states.

quant-ph↗

arXiv2018

Mesoscopic electron transport and atomic gases, a review of Frank W. J. Hekking's scientific work

Frank W. J. Hekking performed his PhD work on "Aspects of Electron Transport in Semiconductor Nanostructures" at the TU Delft in 1992. He then worked as a postdoc at the University of Karlsruhe, the University of Minnesota, the Cavendish Laboratory at the University of Cambridge, and the Ruhr University at Bochum. In 1999 he joined the LPMMC (Laboratoire de Physique et Mod\' elisation des Milieux Condens\' es) in Grenoble and was appointed Professor at the Universit\' e Joseph Fourier and afterwards Universit\' e Grenoble Alpes. Frank Hekking was nominated as a member of the Institut Universitaire de France, for the periods 2002-2007 and 2012-2017. This review provides an overview of his scientific contributions to several fields of mesoscopic electron transport and superconductivity as well as atomic gases, and is organized along sections describing the different themes.

physics.hist-ph↗

arXiv2018

Effects of gate errors in digital quantum simulations of fermionic systems

Digital quantum simulations offer exciting perspectives for the study of fermionic systems such as molecules or lattice models. However, with quantum error correction still being out of reach with present-day technology, a non-vanishing error rate is inevitable. We study the influence of gate errors on simulations of the Trotterized time evolution of the quantum system with focus on the fermionic Hubbard model. Specifically, we consider the effect of stochastic over-rotations in the applied gates. Depending on the particular algorithm implemented such gate errors may lead to a time evolution that corresponds to a disordered fermionic system, or they may correspond to unphysical errors, e.g., violate particle number conservation. We substantiate our analysis by numerical simulations of model systems. In addition we establish the relation between the gate fidelity and the strength of the over-rotations in a Trotterized quantum simulation. Based on this we provide estimates for the maximum number of Trotter steps which can be performed with sufficient accuracy for a given algorithm. This in turn implies, apart from obvious limitations on the maximum time of the simulation, also limits on the system size which can be handled.

quant-ph↗

arXiv2018

Emulating the one-dimensional Fermi-Hubbard model by a double chain of qubits

The Jordan-Wigner transformation maps a one-dimensional spin-1/2 system onto a fermionic model without spin degree of freedom. A double chain of quantum bits with XX and ZZ couplings of neighboring qubits along and between the chains, respectively, can be mapped on a spin-full 1D Fermi-Hubbard model. The qubit system can thus be used to emulate the quantum properties of this model. We analyze physical implementations of such analog quantum simulators, including one based on transmon qubits, where the ZZ interaction arises due to an inductive coupling and the XX interaction due to a capacitive interaction. We propose protocols to gain confidence in the results of the simulation through measurements of local operators.

quant-ph↗

arXiv2017

Electron-assisted magnetization tunneling in single spin systems

Magnetic excitations of single atoms on surfaces have been widely studied experimentally in the past decade. Lately, systems with unprecedented magnetic stability started to emerge. Here, we present a general theoretical investigation of the stability of rare-earth magnetic atoms exposed to crystal or ligand fields of various symmetry and to exchange scattering with an electron bath. By analyzing the properties of the atomic wavefunction, we show that certain combinations of symmetry and total angular momentum are inherently stable against first or even higher order interactions with electrons. Further, we investigate the effect of an external magnetic field on the magnetic stability.

cond-mat.mes-hall↗

arXiv2017

Emulating Majorana fermions and their braiding by Ising spin chains

We analyse the control of Majorana zero-energy states by mapping the fermionic system onto a chain of Ising spins. Although the topological protection is lost for the Ising system, the mapping provides additional insight into the nature of the quantum states. By controlling the local magnetic field, one can separate the Ising chain into ferromagnetic and paramagnetic phases, corresponding to topological and non-topological sections of the fermionic system. In this paper we propose (topologically non-protected) protocols performing the braiding operation, and in fact also more general rotations. We first consider a T-junction geometry, but we also propose a protocol for a purely one-dimensional system. Both setups rely on an extra spin-1/2 coupler. By including the extra spin in the T-junction geometry, we overcome limitations due to the 1D character of the Jordan-Wigner transformation. In the 1D geometry the coupler, which controls one of the Ising links, should be manipulated once the ferromagnetic (topological) section of the chain is moved far away. We also propose experimental implementations of our scheme. One is based on a chain of flux qubits which allows for all needed control fields. We also describe how to translate our scheme for the 1D setup to a chain of superconducting wires hosting each a pair of Majorana edge states.

cond-mat.mes-hall↗

arXiv2017

Electronic Decoherence of Two-Level Systems in a Josephson Junction

The sensitivity of superconducting qubits allows for spectroscopy and coherence measurements on individual two-level systems present in the disordered tunnel barrier of an $\mathrm{Al/AlO_x/Al}$ Josephson junction. We report experimental evidence for the decoherence of two-level systems by Bogoliubov quasiparticles leaking into the insulating $\mathrm{AlO_x}$ barrier. We control the density of quasiparticles in the junction electrodes either by the sample temperature or by injecting them using an on-chip dc-SQUID driven to its resistive state. The decoherence rates were measured by observing the two-level system's quantum state evolving under application of resonant microwave pulses and were found to increase linearly with quasiparticle density, in agreement with theory. This interaction with electronic states provides a noise and decoherence mechanism that is relevant for various microfabricated devices such as qubits, single-electron transistors, and field-effect transistors. The presented experiments also offer a possibility to determine the location of the probed two-level systems across the tunnel barrier, providing clues about the fabrication step in which they emerge.

cond-mat.mes-hall↗

arXiv2016

Superconducting quantum metamaterials as active lasing medium: Effects of disorder

A metamaterial formed by superconducting circuits or quantum dots can serve as active lasing medium when coupled to a microwave resonator. For these artificial atoms, in contrast to real atoms, variations in their parameters cannot be avoided. In this paper, we examine the influence of disorder on such a multi-atom lasing setup. We find that the lasing process evolves into a self-organized stationary state that is quite robust against disorder. The reason is that photons created by those atoms which are in or close to resonance with the resonator stimulate the emission also of more detuned atoms. Not only the number of photons grows with the number of atoms, but also the width of the resonance as function of the detuning. Similar properties are found for other types of disorder such as variations in the individual coupling. We present relations how the allowed disorder scales with the number of atoms and confirm it by a numerical analysis. We also provide estimates for the sample-to-sample variations to be expected for setups with moderate numbers of atoms.

cond-mat.mes-hall↗

arXiv2016

Decoherence of a quantum two-level system by spectral diffusion

We study the dephasing of an individual high-frequency tunneling two-level system (TLS) due to its interaction with an ensemble of low-frequency thermal TLSs which are described by the standard tunneling model (STM). We show that the dephasing by the bath of TLSs explains both the dependence of the Ramsey dephasing rate on an externally applied strain as well as its order of magnitude, as observed in a recent experiment [J. Lisenfeld et al.]. However, the theory based on the STM predicts the Hahn-echo protocol to be much more efficient, yielding too low echo dephasing rates, as compared to the experiment. Also the strain dependence of the echo dephasing rate predicted by the STM does not agree with the measured quadratic dependence, which would fit to a high-frequency white noise environment. We suggest that few fast TLSs which are coupled much more strongly to the strain fields than the usual TLSs of the STM give rise to such a white noise. This explains the magnitude and strong fluctuations of the echo dephasing rate observed in the experiment.

cond-mat.dis-nn↗

arXiv2016

Lasing and transport in a multi-level double quantum dot system coupled to a microwave oscillator

We study a system of two quantum dots, each with several discrete levels, which are coherently coupled to a microwave oscillator. They are attached to electronic leads and coupled to a phonon bath, both leading to inelastic processes. For a simpler system with a single level in each dot it has been shown that a population inversion can be created by electron tunneling, which in a resonance situation leads to lasing-type properties of the oscillator. In the multi-level system several resonance situations may arise, some of them relying on a sequence of tunneling processes which also involve non-resonant, inelastic transitions. The resulting photon number in the oscillator and the current-voltage characteristic are highly sensitive to these properties and accordingly can serve as a probe for microscopic details.

cond-mat.mes-hall↗

arXiv2016

Decoherence and Decay of Two-level Systems due to Non-equilibrium Quasiparticles

It is frequently observed that even at very low temperatures the number of quasiparticles in superconducting materials is higher than predicted by standard BCS-theory. These quasiparticles can interact with two-level systems, such as superconducting qubits or two-level systems (TLS) in the amorphous oxide layer of a Josephson junction. This interaction leads to decay and decoherence of the TLS, with specific results, such as the time dependence, depending on the distribution of quasiparticles and the form of the interaction. We study the resulting decay laws for different experimentally relevant protocols.

cond-mat.mes-hall↗

arXiv2016

Decoherence spectroscopy with individual two-level tunneling defects

Recent progress with microfabricated quantum devices has revealed that an ubiquitous source of noise originates in tunneling material defects that give rise to a sparse bath of parasitic two-level systems (TLSs). For superconducting qubits, TLSs residing on electrode surfaces and in tunnel junctions account for a major part of decoherence and thus pose a serious roadblock to the realization of solid-state quantum processors. Here, we utilize a superconducting qubit to explore the quantum state evolution of coherently operated TLSs in order to shed new light on their individual properties and environmental interactions. We identify a frequency-dependence of TLS energy relaxation rates that can be explained by a coupling to phononic modes rather than by anticipated mutual TLS interactions. Most investigated TLSs are found to be free of pure dephasing at their energy degeneracy points, around which their Ramsey and spin-echo dephasing rates scale linearly and quadratically with asymmetry energy, respectively. We provide an explanation based on the standard tunneling model, and identify interaction with incoherent low-frequency (thermal) TLSs as the major mechanism of the pure dephasing in coherent high-frequency TLS.

cond-mat.supr-con↗

arXiv2015

Majorana fermion fingerprints in spin-polarised scanning tunneling microscopy

We calculate the spatially resolved tunneling conductance of topological superconductors (TSCs) based on ferromagnetic chains, measured by means of spin-polarised scanning tunneling microscopy (SPSTM). Our analysis reveals novel signatures of MFs arising from the interplay of their strongly anisotropic spin-polarisation and the magnetisation content of the tip. We focus on the deep Yu-Shiba-Rusinov (YSR) limit where only YSR bound states localised in the vicinity of the adatoms govern the low-energy as also the topological properties of the system. Under these conditions, we investigate the occurence of zero/finite bias peaks (ZBPs/FBPs) for a single or two coupled TSC chains forming a Josephson junction. Each TSC can host up to two Majorana fermions (MFs) per edge if chiral symmetry is preserved. Here we retrieve the conductance for all the accessible configurations of the MF number of each chain. Our results illustrate innovative spin-polarisation-sensitive experimental routes for arresting the MFs by either restoring or splitting the ZBP in a predictable fashion via: i) weakly breaking chiral symmetry, e.g. by the SPSTM tip itself or by an external Zeeman field and ii) tuning the superconducting phase difference of the TSCs, which is encoded in the 4$π$-Josephson coupling of neighbouring MFs.

cond-mat.mes-hall↗

arXiv2015

Magnetic adatoms as memory bits: A quantum master equation analysis

Due to underlying symmetries the ground states of magnetic adatoms may be highly stable, which opens perspectives for application as single-atom memory. A specific example is a single holmium atom (with $J=8$) on a platinum (111) surface for which exceptionally long lifetimes were observed in recent scanning tunneling microscopy studies. For control and read-out the atom must be coupled to electronic contacts. Hence the spin dynamics of the system is governed by a quantum master equation. Our analysis shows that in general it cannot be reduced to a classical master equation in the basis of the unperturbed crystal-field Hamiltonian. Rather, depending on parameters and control fields, "environment induced superselection" principles choose the appropriate set of basis states, which in turn determines the specific relaxation channels and lifetimes. Our simulations suggest that in ideal situations the lifetimes should be even longer than observed in the experiment. We, therefore, investigate the influence of various perturbations. We also study the initialization process of the state of the Ho atom by applied voltage pulses and conclude that fast, high fidelity preparation, on a $100\,\text{ns}$ timescale, should be possible.

cond-mat.mes-hall↗

arXiv2015

Magnetic order on a topological insulator surface with warping and proximity-induced superconductivity

We determine the nature of the magnetic order on the surface of a topological insulator (TI) which develops due to hexagonal warping and the resulting Fermi surface (FS) nesting in the presence of a repulsive Hubbard interaction. For this purpose we investigate the spin susceptibility and derive a Landau theory to compare the different accessible phases. For a nearly hexagonal FS and sufficiently strong interaction the magnetic ground state is formed by a skyrmion lattice, i.e., by a superposition of three helical spin density waves which preserves C$_3$ symmetry. The magnetic ground state is topologically nontrivial with a nonzero skyrmion charge, which can be stabilized and controlled by an applied magnetic field. By bringing the TI in proximity to a conventional superconductor one can engineer a C$_3$-symmetric topological superconductor. We explore the modification of the phase diagram as well as the mutual influence between the skyrmion structure and a multipolar distribution of supercurrents, which can provide information about the underlying skyrmion charge.

cond-mat.mes-hall↗

arXiv2014

Circular-polarization sensitive metamaterial based on triple quantum-dot molecules

We propose a new type of a chiral metamaterial based on an ensemble of artificial molecules formed by three identical quantum-dots in a triangular arrangement. A static magnetic field oriented perpendicular to the plane breaks mirror symmetry, rendering the molecules sensitive to the circular polarization of light. By varying the orientation and magnitude of the magnetic field one can control the polarization and frequency of the emission spectrum. We identify a threshold frequency, Ω, above which we find strong birefringence. In addition, a Kerr rotation and circularly polarized lasing action can be implemented. We investigate the single-molecule lasing properties for different energy-level arrangements and demonstrate the possibility of circular polarization conversion. Finally, we analyze the effect of weak stray electric fields or deviations from the equilateral triangular geometry.

cond-mat.mes-hall↗