arXiv subjects

Ihor Vakulchyk

Publications and source records attributed to Ihor Vakulchyk.

6 recordsLinked to original sources

arXiv2023

Uniform Anderson Localization in One-Dimensional Floquet Maps

We study Anderson localization in a discrete-time quantum map dynamics in one dimension with nearest-neighbor hopping strength $θ$ and quasienergies located on the unit circle. We demonstrate that strong disorder in a local phase field yields a uniform spectrum gaplessly occupying the entire unit circle. The resulting eigenstates are exponentially localized. Remarkably this Anderson localization is universal as all eigenstates have one and the same localization length $L_{loc}$. We present an exact theory for the calculation of the localization length as a function of the hopping, $1/L_\text{loc}=\left|\ln\left(|\sin(θ)|\right)\right|$, that is tunable between zero and infinity by variation of the hopping $θ$.

cond-mat.dis-nn↗

arXiv2022

Non-Equilibrium Properties of Open Quantum Systems

We study two classes of open systems: discrete-time quantum walks (a type of Floquet-engineered discrete quantum map) and the Lindblad master equation (a general framework of dissipative quantum systems), focusing on the non-equilibrium properties of these systems. We study localization and delocalization phenomena, soliton-like excitations, and quasi-stationary properties of open quantum systems.

cond-mat.dis-nn↗

arXiv2020

Coherent topological polariton laser

Topological concepts have been applied to a wide range of fields in order to successfully describe the emergence of robust edge modes that are unaffected by scattering or disorder. In photonics, indications of lasing from topologically protected modes with improved overall laser characteristics were observed. Here, we study exciton-polariton microcavity traps that are arranged in a one-dimensional Su-Schrieffer-Heeger lattice and form a topological defect mode from which we unequivocally observe highly coherent polariton lasing. Additionally, we confirm the excitonic contribution to the polariton lasing by applying an external magnetic field. These systematic experimental findings of robust lasing and high temporal coherence are meticulously reproduced by a combination of a generalized Gross-Pitaevskii model and a Lindblad master equation model. Thus, by using the comparatively simple SSH geometry, we are able to describe and control the exciton-polariton topological lasing, allowing for a deeper understanding of topological effects on microlasers.

cond-mat.mes-hall↗

arXiv2019

Floquet Anderson Localization of Two Interacting Discrete Time Quantum Walks

We study the interplay of two interacting discrete time quantum walks in the presence of disorder. Each walk is described by a Floquet unitary map defined on a chain of two-level systems. Strong disorder induces a novel Anderson localization phase with a gapless Floquet spectrum and one unique localization length $ξ_1$ for all eigenstates for noninteracting walks. We add a local contact interaction which is parametrized by a phase shift $γ$. A wave packet is spreading subdiffusively beyond the bounds set by $ξ_1$ and saturates at a new length scale $ξ_2 \gg ξ_1$. In particular we find $ξ_2 \sim ξ_1^{1.2}$ for $γ=π$. We observe a nontrivial dependence of $ξ_2$ on $γ$, with a maximum value observed for $γ$-values which are shifted away from the expected strongest interaction case $γ=π$. The novel Anderson localization regime violates single parameter scaling for both interacting and noninteracting walks.

cond-mat.dis-nn↗

arXiv2019

Propagating large open quantum systems towards their steady states: cluster implementation of the time-evolving block decimation scheme

Many-body quantum systems are subjected to the Curse of Dimensionality: The dimension of the Hilbert space $\mathcal{H}$, where these systems live in, grows exponentially with systems' 'size' (number of their components, "bodies"). It means that, in order to specify a state of a quantum system, we need a description whose length grows exponentially with the system size. However, with some systems it is possible to escape the curse by using low-rank tensor approximations known as `matrix-product state/operator (MPS/O) representation' in the quantum community and `tensor-train decomposition' among applied mathematicians. Motivated by recent advances in computational quantum physics, we consider chains of $N$ spins coupled by nearest-neighbor interactions. The spins are subjected to an action coming from the environment. Spatially disordered interaction and environment-induced decoherence drive systems into non-trivial asymptotic states. The dissipative evolution is modeled with a Markovian master equation in the Lindblad form. By implementing the MPO technique and propagating system states with the time-evolving block decimation (TEBD) scheme (which allows to keep the length of the state descriptions fixed), it is in principle possible to reach the corresponding steady states. We propose and realize a cluster implementation of this idea. The implementation on four nodes allowed us to resolve steady states of the model systems with $N = 128$ spins.

cond-mat.stat-mech↗

arXiv2018

Universal Nonlinear Disordered Wave Packet Subdiffusion: 12 Decades

We use a novel unitary map toolbox -- discrete time quantum walks originally designed for quantum computing -- to implement ultrafast computer simulations of extremely slow dynamics in a nonlinear and disordered medium. Previous reports on wave packet spreading in Gross-Pitaevskii lattices observed subdiffusion with the second moment $m_2 \sim t^{1/3}$ (with time in units of a characteristic scale $t_0$) up to the largest computed times of the order of $10^8$. A fundamental question remained as to whether this process can continue ad infinitum, or has to slow down. Current experimental devices are not capable to even reach 1\textpertenthousand ~of the reported computational horizons. With our toolbox, we outperform previous computational results and observe that the universal subdiffusion persists over additional four decades reaching 'astronomic' times $2\cdot 10^{12}$. Such a dramatic extension of previous computational horizons suggests that subdiffusion is universal, and that the toolbox can be efficiently used to assess other hard computational many-body problems.

cond-mat.dis-nn↗