Related papers: Second-order topological insulator in a coinless d…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
The quantum walk was originally proposed as a quantum mechanical analogue of the classical random walk, and has since become a powerful tool in quantum information science. In this paper, we show that discrete time quantum walks provide a…
Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected…
Phases of matter with non-trivial topological order are predicted to exhibit a variety of exotic phenomena, such as the existence robust localized bound states in 1D systems, and edge states in 2D systems, which are expected to display…
We present a protocol to implement discrete-time quantum walks and simulate topological insulator phases in cavity-based quantum networks, where the single photon is the quantum walker and the cavity input-output process is employed to…
Quantum walks are versatile simulators of topological phases and phase transitions as observed in condensed matter physics. Here, we utilize a step dependent coin in quantum walks and investigate what topological phases we can simulate with…
We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the…
The search for exotic new topological states of matter in widely accessible materials, for which the manufacturing process is mastered, is one of the major challenges of the current topological physics. Here we predict higher order…
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of…
Quantum walks constitute a versatile platform for simulating transport phenomena on discrete graphs including topological material properties while providing a high control over the relevant parameters at the same time. To experimentally…
We simulate various topological phenomena in condense matter, such as formation of different topological phases, boundary and edge states, through two types of quantum walk with step-dependent coins. Particularly, we show that…
Quantum walks, whose dynamics is prescribed by alternating unitary coin and shift operators, possess topological phases akin to those of Floquet topological insulators, driven by a time-periodic field. While there is ample theoretical work…
Discrete-time quantum walks have been shown to simulate all known topological phases in one and two dimensions. Being periodically driven quantum systems, their topological description, however, is more complex than that of closed…
The dimensionality of the internal coin space of discrete-time quantum walks has a strong impact on the complexity and richness of the dynamics of quantum walkers. While two-dimensional coin operators are sufficient to define a certain…
Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop classification of second-order point-gap topological phases protected by reflection…
We have recently proposed a two-dimensional quantum walk where the requirement of a higher dimensionality of the coin space is substituted with the alternance of the directions in which the walker can move [C. Di Franco, M. Mc Gettrick, and…
Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern…
We suggest a method for engineering a quantum walk, with cold atoms as walkers, which presents topologically non-trivial properties. We derive the phase diagram, and show that we are able to produce a boundary between topologically distinct…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
We study the simulation of the topological phases in three subsequent dimensions with quantum walks. We are mainly focused on the completion of a table for the protocols of the quantum walk that could simulate different family of the…