arXiv subjects

Stephan Haas

Publications and source records attributed to Stephan Haas.

At least 37 records · Page 2Linked to original sources

arXiv2021

Bulk topological signatures of a quasicrystal

We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for the Fibonacci chain, we show that the total onsite charge oscillates when plotted in the appropriate coordinates, and the number of oscillations is given by the Chern number of the gap in which the Fermi level lies. We show that these oscillations have two distinct interpretations, obtained by extrapolating results from the two extreme limits of the Fibonacci chain -- the valence bond picture in the strong modulation limit, and perturbation around the periodic chain in the weak modulation limit. This effect is found to remain robust at moderate interactions, as well as in the presence of disorder. We conclude that experimental measurement of the real space charge distribution can yield information on topological properties in a straightforward way.

cond-mat.dis-nn↗

arXiv2021

Control of Plasmons in Topological Insulators via Local Perturbations

We use a fully quantum mechanical approach to demonstrate control of plasmonic excitations in prototype models of topological insulators by molecule-scale perturbations. Strongly localized surface plasmons are present in the host systems, arising from the topologically non-trivial single-particle edge states. A numerical evaluation of the RPA equations for the perturbed systems reveals how the positions and the internal electronic structure of the added molecules affect the degeneracy of the locally confined collective excitations, i.e., shifting the plasmonic energies of the host system and changing their spatial charge density profile. In particular, we identify conditions under which significant charge transfer from the host system to the added molecules occurs. Furthermore, the induced field energy density in the perturbed topological systems due to external electric fields is determined.

cond-mat.mes-hall↗

arXiv2021

Plasmonic Waveguides from Coulomb-Engineered Two-Dimensional Metals

Coulomb interactions play an essential role in atomically-thin materials. On one hand, they are strong and long-ranged in layered systems due to the lack of environmental screening. On the other hand, they can be efficiently tuned by means of surrounding dielectric materials. Thus all physical properties which decisively depend on the exact structure of the electronic interactions can be in principle efficiently controlled and manipulated from the outside via Coulomb engineering. Here, we show how this concept can be used to create fundamentally new plasmonic waveguides in metallic layered materials. We discuss in detail how dielectrically structured environments can be utilized to non-invasively confine plasmonic excitations in an otherwise homogeneous metallic 2D system by modification of its many-body interactions. We define optimal energy ranges for this mechanism and demonstrate plasmonic confinement within several nanometers. In contrast to conventional functionalization mechanisms, this scheme relies on a purely many-body concept and does not involve any direct modifications to the active material itself.

cond-mat.mes-hall↗

arXiv2021

Plasmons in Two-Dimensional Topological Insulators

We analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced charge-density distributions localized at the boundaries of the system are found in the topologically non-trivial phase, dispersing similarly as one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain. For two-dimensional bulk collective modes, we reveal regimes of enhanced inter-band wave function correlations, leading to characteristic hardening and softening of inter- and intra-band bulk plasmonic branches, respectively. In the two-dimensional Haldane Chern insulator model, chiral, uni-directional edge plasmons in nano-ribbon architectures are observed, which can be characterized by an effective Coulomb interaction cross section. Bulk collective excitations in the two-dimensional Haldane model are shown to be originated by single-particle band structure details in different topological phases.

cond-mat.mes-hall↗

arXiv2021

Control of Plasmons in Doped Topological Insulators via Basis Atoms

Collective excitations in topologically non-trivial systems have attracted considerable attention in recent years. Here we study plasmons in the Su-Schrieffer-Heeger model whose low-energy electronic band is only partially filled, such that the system is metallic. Using the random phase approximation, we calculate the intra- and inter-band polarization functions and determine the bulk plasmonic dispersion from the dielectric function within the random phase approximation. We find that the sub-lattice basis states strongly affect the polarization functions and therefore control the system's plasmonic excitations. By varying the real-space separation of these local orbitals, one can thus selectively enhance or suppress the plasmonic energies via a tunable trade-off between intra-band and inter-band screening processes. Specifically, this mechanism can be used to stabilize undamped high energy plasmons that have already been reported in related models. We propose scenarios on how to control and observe these effects in experiments.

cond-mat.mtrl-sci↗

arXiv2020

Topological Protection of Coherence in Noisy Open Quantum Systems

We consider topological protection mechanisms in dissipative quantum systems in the presence of quenched disorder, with the intent to prolong coherence times of qubits. The physical setting is a network of qubits and dissipative cavities whose coupling parameters are tunable, such that topological edge states can be stabilized. The evolution of a fiducial qubit is entirely determined by a non-Hermitian Hamiltonian which thus emerges from a bona-fide physical process. It is shown how even in the presence of disorder winding numbers can be defined and evaluated in real space, as long as certain symmetries are preserved. Hence we can construct the topological phase diagrams of noisy open quantum models, such as the non-Hermitian disordered Su-Schrieffer- Heeger dimer model and a trimer model that includes longer-range couplings. In the presence of competing disorder parameters, interesting re-entrance phenomena of topologically non-trivial sectors are observed. This means that in certain parameter regions, increasing disorder drastically increases the coherence time of the fiducial qubit.

quant-ph↗

arXiv2020

Achieving a quantum smart workforce

Interest in building dedicated Quantum Information Science and Engineering (QISE) education programs has greatly expanded in recent years. These programs are inherently convergent, complex, often resource intensive and likely require collaboration with a broad variety of stakeholders. In order to address this combination of challenges, we have captured ideas from many members in the community. This manuscript not only addresses policy makers and funding agencies (both public and private and from the regional to the international level) but also contains needs identified by industry leaders and discusses the difficulties inherent in creating an inclusive QISE curriculum. We report on the status of eighteen post-secondary education programs in QISE and provide guidance for building new programs. Lastly, we encourage the development of a comprehensive strategic plan for quantum education and workforce development as a means to make the most of the ongoing substantial investments being made in QISE.

physics.ed-ph↗

arXiv2020

Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real space Bogoliubov-de Gennes framework for three cases, namely, when states are i) extended, ii) localized or iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases i) and iii), stretched exponential in case ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable (case i) or of its logarithm (cases ii and iii). We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

cond-mat.supr-con↗

arXiv2020

Entanglement Properties of Disordered Quantum Spin Chains with Long-Range Antiferromagnetic Interactions

We examine the concurrence and entanglement entropy in quantum spin chains with random long-range couplings, spatially decaying with a power-law exponent $α$. Using the strong disorder renormalization group (SDRG) technique, we find by analytical solution of the master equation a strong disorder fixed point, characterized by a fixed point distribution of the couplings with a finite dynamical exponent, which describes the system consistently in the regime $α> 1/2$. A numerical implementation of the SDRG method yields a power law spatial decay of the average concurrence, which is also confirmed by exact numerical diagonalization. However, we find that the lowest-order SDRG approach is not sufficient to obtain the typical value of the concurrence. We therefore implement a correction scheme which allows us to obtain the leading order corrections to the random singlet state. This approach yields a power-law spatial decay of the typical value of the concurrence, which we derive both by a numerical implementation of the corrections and by analytics. Next, using numerical SDRG, the entanglement entropy (EE) is found to be logarithmically enhanced for all $α$, corresponding to a critical behavior with an effective central charge $c = {\rm ln} 2$, independent of $α$. This is confirmed by an analytical derivation. Using numerical exact diagonalization (ED), we confirm the logarithmic enhancement of the EE and a weak dependence on $α$. For a wide range of distances $l$, the EE fits a critical behavior with a central charge close to $c=1$, which is the same as for the clean Haldane-Shastry model with a power-la-decaying interaction with $α=2$. Consistent with this observation, we find using ED that the concurrence shows power law decay, albeit with smaller power exponents than obtained by SDRG.

cond-mat.dis-nn↗

arXiv2020

Detection of Topology via Entanglement Oscillations

We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using exact diagonalization and the strong disorder renormalization group method, we demonstrate that this approach gives results in agreement with the use of traditional topological invariants, especially in cases where topological order is known to persist in the presence of off-diagonal bond disorder. The entanglement gap is then used to analyze classes of quantum systems with alternating bond types, allowing us to construct their topological phase diagrams. The validity of these phase diagrams is verified in limiting cases of dominant bond types, where the solution is known.

cond-mat.str-el↗

arXiv2019

Localized Plasmons in Topological Insulators

We investigate in a fully quantum-mechanical manner how the many-body excitation spectrum of topological insulators is affected by the presence of long-range Coulomb interactions. In the one-dimensional Su-Schrieffer-Heeger model and its mirror-symmetric variant strongly localized plasmonic excitations are observed which originate from topologically non-trivial single-particle states. These \textit{"topological plasmons"} inherit some of the characteristics of their constituent topological single-particle states, but they are not equally well protected against disorder due to the admixture of non-topological bulk single-particle states in the polarization function. The strength of the effective Coulomb interactions is also shown to have strong effects on the plasmonic modes. Furthermore, we show how external modifications via dielectric screening and applied electric fields with distinct symmetries can be used to study topological plasmons, thus allowing for experimental verification of our atomistic predictions.

cond-mat.mtrl-sci↗

arXiv2019

Induced superconducting pair correlations in a quasicrystal coupled to a BCS superconductor

In this report, we describe the proximity effect which arises when a quasicrystal is placed in contact with a superconductor. We consider the simplest known model of a quasicrystal, the 1D Fibonacci chain, for which all states are known to be critical. A hybrid ring is made by connecting a finite piece of such a Fibonacci chain to a BCS-type superconductor. Solving the resulting Bogoliubov-de Gennes equations self-consistently, we show that the proximity effect in the Fibonacci chain is long ranged, and that the induced superconducting order carries information on topological properties, namely, the winding numbers of edge states of the Fibonacci chain.

cond-mat.supr-con↗

arXiv2019

The Proximity Effect in a Superconductor-Quasicrystal Hybrid Ring

We compute the real-space profile of the superconducting order parameter (OP) in a hybrid ring that consists of a 1D superconductor connected to a Fibonacci chain using a self-consistent approach. In our study, the strength of the penetration, as measured by the order parameter at the center of the quasicrystal, depends on the structural parameter $ϕ$, or phason angle, that characterizes different realizations of the Fibonacci chains of a given length. We show that the penetration strength dependence on $ϕ$ reflects properties of the topological edge states of the Fibonacci chain. We show that the induced superconducting order parameter averaged over all chains has a power law decay as a function of distance from the S-N interface. More interestingly, we show that there are large OP fluctuations for individual chains and that the penetration strength in a finite Fibonacci chain can be significantly $larger$ than in a normal periodic conductor for special values of $ϕ$.

cond-mat.supr-con↗

arXiv2018

Threshold Response to Stochasticity in Morphogenesis

During development of biological organisms, multiple complex structures are formed. In many instances, these structures need to exhibit a high degree of order to be functional, although many of their constituents are intrinsically stochastic. Hence, it has been suggested that biological robustness ultimately must rely on complex gene regulatory networks and clean-up mechanisms. Here we explore developmental processes that have evolved inherent robustness against stochasticity. In the context of the Drosophila eye disc, multiple optical units, ommatidia, develop into crystal-like patterns. During the larva-to-pupa stage of metamorphosis, the centers of the ommatidia are specified initially through the diffusion of morphogens, followed by the specification of R8 cells. Establishing the R8 cell is crucial in setting up the geometric, and functional, relationships of cells within an ommatidium and among neighboring ommatidia. Here we study a mathematical model of these spatio-temporal processes in the presence of stochasticity, defining and applying measures that quantify order within the resulting spatial patterns. We observe a universal sigmoidal response to increasing transcriptional noise. Ordered patterns persist up to a threshold noise level in the model parameters. As the noise is further increased past a threshold point of no return, these ordered patterns rapidly become disordered. Such robustness in development allows for the accumulation of genetic variation without any observable changes in phenotype. We argue that the observed sigmoidal dependence introduces robustness allowing for sizable amounts of genetic variation and transcriptional noise to be tolerated in natural populations without resulting in phenotype variation.

physics.bio-ph↗

arXiv2017

Topological Protection of Coherence in a Dissipative Environment

One dimensional topological insulators are characterized by edge states with exponentially small energies. According to one generalization of topological phases to non-Hermitian systems, a finite system in a non-trivial topological phase displays surface states with exponentially long life times. In this work we explore the possibility of exploiting such non-Hermitian topological phases to enhance the quantum coherence of a fiducial qubit embedded in a dissipative environment. We first show that a network of qubits interacting with lossy cavities can be represented, in a suitable super-one-particle sector, by a non-Hermitian "Hamiltonian" of the desired form. We then study, both analytically and numerically, one-dimensional geometries with up to three sites per unit cell, and up to a topological winding number $W=2$. For finite-size systems the number of edge modes is a complicated function of $W$ and the system size $N$. However we find that there are precisely $W$ modes localized at one end of the chain. In such topological phases the quibt's coherence lifetime is exponentially large in the system size. We verify that, for $W>1$, at large times, the Lindbladian evolution is approximately a non-trivial unitary. For $W=2$ this results in Rabi-like oscillations of the qubit's coherence measure.

quant-ph↗

arXiv2017

Healing of Defects in Random Antiferromagnetic Spin Chains

We study the effects of a weakened link in random antiferromagnetic spin chains. We show that healing occurs, and that homogeneity is restored at low energy, in a way that is qualitatively similar to the fate of impurities in clean ferromagnetic spin chains, or in Luttinger liquids with attractive interactions. Healing in the random case occurs even without interactions, and is characteristic of the random singlet phase. Using real space renormalization group and exact diagonalization methods, we characterize this universal healing crossover by studying the entanglement across the weak link. We identify a crossover healing length $L^*$ that separates a regime where the system is cut in half by the weak link from a fixed point where the spin chain is healed. Our results open the way to the study of impurity physics in disordered spin chains.

cond-mat.dis-nn↗

arXiv2015

Small quench dynamics as a probe for trapped ultracold atoms

Finite systems of bosons and/or fermions described by the Hubbard model can be realized using ultracold atoms confined in optical lattices. The ground states of these systems often exhibit a coexistence of compressible superfluid and incompressible Mott insulating regimes. We analyze such systems by studying the out-of-equilibrium dynamics following a weak sudden quench of the trapping potential. In particular, we show how the temporal variance of the site occupations reveals the location of spatial boundaries between compressible and incompressible regions. The feasibility of this approach is demonstrated for several models using numerical simulations. We first consider integrable systems, hard-core bosons (spinless fermions) confined by a harmonic potential, where space separated Mott and superfluid phases coexist. Then, we analyze a nonintegrable system, a $J-V-V'$ model with coexisting charge density wave and superfluid phases. We find that the temporal variance of the site occupations is a more effective measure than other standard indicators of phase boundaries such as a local compressibility. Based on these examples, we argue that analyzing temporal fluctuations is a valuable experimental tool for exploring phase boundaries in trapped atom systems.

cond-mat.quant-gas↗

arXiv2014

Two-dimensional percolation with multiple seeds

We study non-uniform percolation in a two-dimensional cluster growth model with multiple seeds. With increasing concentration of seeds, the percolation threshold is found to increase monotonically, while the exponents for correlation length, order parameter, and average cluster size, keep invariant. The scaling law for an infinite square lattice keeps working for any nonzero concentration of seeds. Abnormal finite-size scaling behaviours happen at low concentration of seeds.

cond-mat.dis-nn↗