arXiv subjects

Klaus Richter

Publications and source records attributed to Klaus Richter.

At least 91 records · Page 5Linked to original sources

arXiv2016

Multiparticle correlations in mesoscopic scattering: boson sampling, birthday paradox, and Hong-Ou-Mandel profiles

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of non-interacting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wavepackets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is then a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

quant-ph↗

arXiv2016

Canonical description of 1D few-body systems with short range interaction

We address the fundamental interplay between indistinguishability and interactions when discreteness effects are neglected in systems with strictly fixed number of particles. For this end we supplement cluster expansions (many-body canonical techniques where quantum statistics is treated exactly) with short-time/large volume dynamical information where interparticle forces are described non-perturbatively. This approach, specially suitable for the few-body case where it overcomes the inappropriate use of virial expansions, can be consistently combined with scaling considerations, minimal ground-state information and strong coupling expansions in such a way that a single interaction event provides most of the thermodynamic and spectral properties of 1D systems with short range interactions. Our analytical results, in excellent agreement with numerical simulations, show a form of universal integrability of interaction effects for arbitrary confinements.

quant-ph↗

arXiv2015

The semiclassical propagator in Fock space: dynamical echo and many-body interference

We present a semiclassical approach to many-body quantum propagation in terms of coherent sums over quantum amplitudes associated with the solutions of corresponding classical nonlinear wave equations. This approach adequately describes interference effects in the many-body space of interacting bosonic systems. The main quantity of interest, the transition amplitude between Fock states when the dynamics is driven by both single-particlecontributions and many-body interactions of similar magnitude, is non-perturbatively constructed in the spirit of Gutzwiller's derivation of the van Vleck propagator from the path integral representation of the time evolution operator, but lifted to the space of symmetrized many-body states. Effects beyond mean-field, here representing the classical limit of the theory, are semiclassically described by means of interfering amplitudes where the action and stability of the classical solutions enter. In this way, a genuinely many-body echo phenomenon, coherent backscattering in Fock space, is presented arising due to coherent quantum interference between classical solutions related by time reversal.

quant-ph↗

arXiv2015

Periodic Mean-Field Solutions and the Spectra of Discrete Bosonic Fields: Trace Formula for Bose-Hubbard Models

We consider the many-body spectra of interacting bosonic quantum fields on a lattice in the semiclassical limit of large particle number $N$. We show that the many-body density of states can be expressed as a coherent sum over oscillating long-wavelength contributions given by periodic, non-perturbative solutions of the, typically non-linear, wave equation of the classical (mean-field) limit. To this end we construct the semiclassical approximation for both the smooth and oscillatory part of the many-body density of states in terms of a trace formula starting from the exact path integral form of the propagator between many-body quadrature states. We therefore avoid the use of a complexified classical limit characteristic of the coherent state representation. While quantum effects like vacuum fluctuations and gauge invariance are exactly accounted for, our semiclassical approach captures quantum interference and therefore is valid well beyond the Ehrenfest time where naive quantum-classical correspondence breaks down. Remarkably, due to a special feature of harmonic systems with incommesurable frequencies, our formulas are generically valid also in the free-field case of non-interacting bosons.

quant-ph↗

arXiv2015

Gate tuneable beamsplitter in ballistic graphene

We present a beam splitter in a suspended, ballistic, multiterminal, bilayer graphene device. By using local bottomgates, a p-n interface tilted with respect to the current direction can be formed. We show that the p-n interface acts as a semi-transparent mirror in the bipolar regime and that the reflectance and transmittance of the p-n interface can be tuned by the gate voltages. Moreover, by studying the conductance features appearing in magnetic field, we demonstrate that the position of the p-n interface can be moved by $1\,μ$m. The herein presented beamsplitter device can form the basis of electron-optic interferometers in graphene.

cond-mat.mes-hall↗

arXiv2015

Guiding of Electrons in a Few Mode Ballistic Graphene Channel

In graphene, the extremely fast charge carriers can be controlled by electron-optical elements, such as waveguides, in which the transmissivity is tuned by the wavelength. In this work, charge carriers are guided in a suspended ballistic few-mode graphene channel, defined by electrostatic gating. By depleting the channel, a reduction of mode number and steps in the conductance are observed, until the channel is completely emptied. The measurements are supported by tight-binding transport calculations including the full electrostatics of the sample.

cond-mat.mes-hall↗

arXiv2015

Boson Sampling as Canonical Transformation: A semiclassical approach in Fock space

We show that a theory of complex scattering between many-body (Fock) states can be constructed such that its classical limit is a canonical transformation thus encoding quantum interference in the semiclassical form of the associated unitary operator. Based on this idea, we study the different coherent effects expected under different choices of the many-body states and provide different representations of the associated transition probabilities. In this way, we derive exact relations and representations of the scattering process that can be used to attack timely problems related with Boson Sampling.

quant-ph↗

arXiv2015

Aspects of integrability in a classical model for non-interacting fermionic fields

In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system. Our main finding is that the classical system, contrary to the quantum system, is not integrablein general. Regarding this contrast it is clear that in general classical models for fermionic quantum systems have to be handled with care. Further numerical investigation of the system showed that there may be islands of stability in the phase space. We also investigated a similar model that is used in theoretical chemistry and found this one to be most probably integrable, although also here the integrability is not assured by the quantum-classical correspondence principle.

quant-ph↗

arXiv2015

Band gap and broken chirality in single-layer and bilayer graphene

Chirality is one of the key features governing the electronic properties of single- and bilayer graphene: the basics of this concept and its consequences on transport are presented in this review. By breaking the inversion symmetry, a band gap can be opened in the band structures of both systems at the K-point. This leads to interesting consequences for the pseudospin and, therefore, for the chirality. These consequences can be accessed by investigating the evolution of the Berry phase in such systems. Experimental observations of Fabry-Perot interference in a dual-gated bilayer graphene device are finally presented and are used to illustrate the role played by the band gap on the evolution of the pseudospin. The presented results can be attributed to the breaking of the chirality in the energy range close to the gap.

cond-mat.mes-hall↗

arXiv2015

Two-dimensional topological insulator edge state backscattering by dephasing

To understand the seemingly absent temperature dependence in the conductance of two-dimensional topological insulator edge states, we perform a numerical study which identifies the quantitative influence of the combined effect of dephasing and elastic scattering in charge puddles close to the edges. We show that this mechanism may be responsible for the experimental signatures in HgTe/CdTe quantum wells if the puddles in the samples are large and weakly coupled to the sample edges. We propose experiments on artificial puddles which allow to verify this hypothesis and to extract the real dephasing time scale using our predictions. In addition, we present a new method to include the effect of dephasing in wave-packet-time-evolution algorithms.

cond-mat.mes-hall↗

arXiv2015

Theory of spin-orbit induced spin relaxation in functionalized graphene

We perform a comparative study of the spin relaxation by spin-orbit coupling induced from adatoms (hydrogen and fluorine) in graphene. Two methods are applied, giving consistent results: a full quantum transport simulation of a graphene nanoribbon, and a T-matrix calculation using Green's functions for a single adatom in graphene. For hydrogenated graphene the dominant spin-orbit term for spin relaxation is PIA, the hitherto neglected interaction due to pseudospin inversion asymmetry. In contrast, in fluorinated graphene PIA and Rashba couplings destructively interfere, reducing the total spin relaxation rate. In this case we also predict a strong deviation from the expected 2:1 spin relaxation anisotropy for out- and in-plane spin orientations. Our findings should be useful to benchmark spin relaxation and weak localization experiments of functionalized graphene.

cond-mat.mes-hall↗

arXiv2015

Magnetotransport in disordered two-dimensional topological insulators: signatures of charge puddles

In this numerical study we investigate the influence and interplay of disorder, spin-orbit coupling and magnetic field on the edge-transport in HgTe/CdTe quantum wells in the framework of coherent elastic scattering. We show that the edge states remain unaffected by the combined effect of moderate disorder and a weak magnetic field at realistic spin-orbit coupling strengths. Agreement with the experimentally observed linear magnetic field dependence for the conductance of long samples is obtained when considering the existence of charge puddles.

cond-mat.mes-hall↗

arXiv2015

Snake Trajectories in Ultraclean Graphene p-n Junctions

Snake states are trajectories of charge carriers curving back and forth along an interface. There are two types of snake states, formed by either inverting the magnetic field direction or the charge carrier type at an interface. Whereas the former has been demonstrated in GaAs-AlGaAs heterostructures, the latter has become conceivable only with the advance of ballistic graphene where a gapless p-n interface governed by Klein tunneling can be formed. Such snake states were hidden in previous experiments due to limited sample quality. Here we report on magneto-conductance oscillations due to snake states in a ballistic suspended graphene p-n-junction which occur already at a very small magnetic field of 20mT. The visibility of 30% is enabled by Klein collimation. Our finding is firmly supported by quantum transport simulations. We demonstrate the high tunability of the device and operate it in different magnetic field regimes

cond-mat.mes-hall↗

arXiv2015

Scalable Tight-Binding Model for Graphene

Artificial graphene consisting of honeycomb lattices other than the atomic layer of carbon has been shown to exhibit electronic properties similar to real graphene. Here, we reverse the argument to show that transport properties of real graphene can be captured by simulations using "theoretical artificial graphene." To prove this, we first derive a simple condition, along with its restrictions, to achieve band structure invariance for a scalable graphene lattice. We then present transport measurements for an ultraclean suspended single-layer graphene pn junction device, where ballistic transport features from complex Fabry-Pérot interference (at zero magnetic field) to the quantum Hall effect (at unusually low field) are observed and are well reproduced by transport simulations based on properly scaled single-particle tight-binding models. Our findings indicate that transport simulations for graphene can be efficiently performed with a strongly reduced number of atomic sites, allowing for reliable predictions for electric properties of complex graphene devices. We demonstrate the capability of the model by applying it to predict so-far unexplored gate-defined conductance quantization in single-layer graphene.

cond-mat.mes-hall↗

arXiv2014

Signatures of spin-preserving symmetries in two-dimensional hole gases

We investigate ramifications of the persistent spin helix symmetry in two-dimensional hole gases in the conductance of disordered mesoscopic systems. To this end we extend previous models by going beyond the axial approximation for III-V semiconductors. For heavy-hole subbands we identify an exact spin-preserving symmetry analogous to the electronic case by analyzing the crossover from weak antilocalization to weak localization and spin transmission as a function of extrinsic spin-orbit interaction strength.

cond-mat.mes-hall↗

arXiv2014

A Statistical Benchmark for BosonSampling

Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood quantum statistical effects, the coherent superposition of many-particle amplitudes rapidly overburdens classical computing devices - essentially by creating extremely complicated interference patterns, which also challenge experimental resolution. With the advent of controlled many-particle interference experiments, optical set-ups that can efficiently probe many-boson wave functions - baptised BosonSamplers - have therefore been proposed as efficient quantum simulators which outperform any classical computing device, and thereby challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, there remains one crucial problem: How to certify that a given experimental measurement record is an unambiguous result of sampling bosons rather than fermions or distinguishable particles, or of uncontrolled noise? In this contribution, we describe a statistical signature of many-body quantum interference, which can be used as an experimental (and classically computable) benchmark for BosonSampling.

quant-ph↗

arXiv2014

Fabry-Pérot interference in gapped bilayer graphene with broken anti-Klein tunneling

We report the experimental observation of Fabry-Pérot (FP) interference in the conductance of a gate-defined cavity in a dual-gated bilayer graphene (BLG) device. The high quality of the BLG flake, combined with the device's electrical robustness provided by the encapsulation between two hexagonal boron nitride layers, allows us to observe ballistic phase-coherent transport through a $1$μm-long cavity. We confirm the origin of the observed interference pattern by comparing to tight-binding calculations accounting for the gate-tunable bandgap. The good agreement between experiment and theory, free of tuning parameters, further verifies that a gap opens in our device. The gap is shown to destroy the perfect reflection for electrons traversing the barrier with normal incidence (anti-Klein tunneling). The broken anti-Klein tunneling implies that the Berry phase, which is found to vary with the gate voltages, is always involved in the FP oscillations regardless of the magnetic field, in sharp contrast with single-layer graphene.

cond-mat.mes-hall↗

arXiv2014

The semiclassical propagator in fermionic Fock space

We present a rigorous derivation of a semiclassical propagator for anticommuting (fermionic) degrees of freedom, starting from an exact representation in terms of Grassmann variables. As a key feature of our approach the anticommuting variables are integrated out exactly, and an exact path integral representation of the fermionic propagator in terms of commuting variables is constructed. Since our approach is not based on auxiliary (Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic determinants yielding a standard form $\int {\cal D}[ψ,ψ^{*}] {\rm e}^{i R[ψ,ψ^{*}]}$ with real actions for the propagator. These two features allow us to provide a rigorous definition of the classical limit of interacting fermionic fields and therefore to achieve the long-standing goal of a theoretically sound construction of a semiclassical van Vleck-Gutzwiller propagator in fermionic Fock space. As an application, we use our propagator to investigate how the different universality classes (orthogonal, unitary and symplectic) affect generic many-body interference effects in the transition probabilities between Fock states of interacting fermionic systems.

physics.chem-ph↗