arXiv subjects

Yaroslav Don

Publications and source records attributed to Yaroslav Don.

6 recordsLinked to original sources

arXiv2021

Winding Numbers and Topology of Aperiodic Tilings

We show that diffraction features of $1D$ quasicrystals can be retrieved from a single topological quantity, the Čech cohomology group, $\check{H}^{1}\cong\mathbb{Z}^2$, which encodes all relevant combinatorial information of tilings. We present a constructive way to calculate $\check{H}^{1}$ for a large variety of aperiodic tilings. By means of two winding numbers, we compare the diffraction features contained in $\check{H}^{1}$ to the gap labeling theorem, another topological tool used to label spectral gaps in the integrated density of states. In the light of this topological description, we discuss similarities and differences between families of aperiodic tilings, and the resilience of topological features against perturbations.

cond-mat.other↗

arXiv2021

Quantum tomography of entangled spin-multi-photon states

We present a novel method for quantum tomography of multi-qubit states. We apply the method to spin-multi-photon states, which we produce by periodic excitation of a semiconductor quantum-dot- confined spin every 1/4 of its coherent precession period. These timed excitations lead to the deterministic generation of strings of entangled photons in a cluster state. We show that our method can be used for characterizing the periodic process map, which produces the photonic cluster. From the measured process map, we quantify the robustness of the entanglement in the cluster. The 3-fold enhanced generation rate over previous demonstrations reduces the spin decoherence between the pulses and thereby increases the entanglement.

quant-ph↗

arXiv2020

Vacancies in Graphene : Dirac Physics and Fractional Vacuum Charges

The study of vacancies in graphene is a topic of growing interest. A single vacancy induces a localized stable charge of order unity interacting with other charges of the conductor through an unscreened Coulomb potential. It also breaks the symmetry between the two triangular graphene sublattices hence inducing zero energy states at the Dirac points. Here we show the fractional and pseudo-scalar nature of this vacancy charge. A continuous Dirac model is presented which relates zero modes to vacuum fractional charge and to a parity anomaly. This relation constitutes an Index theorem and is achieved by using particular chiral boundary conditions, which map the vacancy problem onto edge state physics. Vacancies in graphene thus allow to realize prominent features of $2+1$ quantum electrodynamics but without coupling to a gauge field. This essential difference makes vacancy physics relatively easy to implement and an interesting playground for topological switching.

cond-mat.mes-hall↗

arXiv2020

Relating Diffraction and Spectral Data of Aperiodic Tilings: Towards a Bloch theorem

The purpose of this paper is to show the relationship in all dimensions between the structural (diffraction pattern) aspect of tilings (described by Čech cohomology of the tiling space) and the spectral properties (of Hamiltonians defined on such tilings) defined by $K$-theory, and to show their equivalence in dimensions $\leq 3$. A theorem makes precise the conditions for this relationship to hold. It can be viewed as an extension of the "Bloch Theorem" to a large class of aperiodic tilings. The idea underlying this result is based on the relationship between cohomology and $K$-theory traces and their equivalence in low dimensions.

math-ph↗

arXiv2016

Numerical Study of Continuous and Discontinuous Dynamical Phase Transitions for Boundary Driven Systems

The existence and search for thermodynamic phase transitions is of unfading interest. In this paper, we present numerical evidence of dynamical phase transitions occurring in boundary driven systems with a constrained integrated current. It is shown that certain models exhibit a discontinuous transition between two different density profiles and a continuous transition between a time-independent and a time-dependent profile. We also checked that the KMP model does not exhibit phase transition in a range much larger than previously explored.

cond-mat.stat-mech↗

arXiv2016

Deterministic Generation of a Cluster State of Entangled Photons

We use semiconductor quantum dots, "artificial atoms," to implement a scheme for deterministic generation of long strings of entangled photons in a cluster state, an important resource for quantum information processing. We demonstrate a prototype device which produces strings of a few hundred photons in which the entanglement persists over 5 sequential photons. The implementation follows a proposal by Lindner and Rudolph (Phys. Rev. Lett. 2009) which suggested periodic timed excitation of a precessing electron spin as a mechanism for entangling the electron spin with the polarization of the sequentially emitted photons. In our realization, the entangling qubit is a quantum dot confined dark exciton. By performing full quantum process tomography, we obtain the process map which fully characterizes the evolution of the system, containing the dark exciton and n photons after n applications of the periodic excitations. Our implementation may greatly reduce the resources needed for quantum information processing.

quant-ph↗