Related papers: Thouless quantum walks in topological flat bands
We propose a realistic cold-atom quantum setting where nontrivial energy-band topology induces non-reciprocal pumping. This is an intriguing non-Hermitian phenomenon that illustrates how topology, when assisted with atom loss, can act as a…
In many contexts, the interaction between particles gives rise to emergent and perhaps unanticipated physical phenomena. An example is the fractional quantum Hall effect, where interaction between electrons gives rise to fractionally…
The rotation of subspaces by a chosen angle is a fundamental quantum computing operation, with applications in error correction and quantum algorithms such as the Quantum Approximate Optimization Algorithm, the Variational Quantum…
Thouless's quantum adiabatic pumping is of fundamental interest to condensed-matter physics. It originally considered a zero-temperature equilibrium state uniformly occupying all the bands below a Fermi surface. In the light of recent…
We report the experimental detection of bulk topological invariants in nonunitary discrete-time quantum walks with single photons. The nonunitarity of the quantum dynamics is enforced by periodically performing partial measurements on the…
We propose a two-dimensional (2D) version of Thouless pumping that can be realized by using ultracold atoms in optical lattices. To be specific, we consider a 2D square lattice tight-binding model with an obliquely introduced superlattice.…
We establish the concept of topological pumping in one-dimensional systems with long-range couplings and apply it to the transport of a photon in quantum optical systems. In our theoretical investigation, we introduce an extended version of…
The discovery of the quantization of particle transport in adiabatic pumping cycles of periodic structures by Thouless [Phys. Rev. B 27, 6083 (1983)] linked the Chern number, a topological invariant characterizing the quantum Hall effect in…
Originating from the Hamiltonian of a single qubit system, the phenomenon of the avoided level crossing is ubiquitous in multiple branches of physics, including the Landau-Zener transition in atomic, molecular and optical physics, the band…
In view of the fundamental importance and many promising potential applications, non-Abelian statistics of topologically protected states have attracted much attention recently. However, due to the operational difficulties in solid-state…
In this paper we study continuous-time quantum walks on Cayley graphs of the symmetric group, and prove various facts concerning such walks that demonstrate significant differences from their classical analogues. In particular, we show that…
Although quantum walks exhibit peculiar properties that distinguish them from random walks, classical behavior can be recovered in the asymptotic limit by destroying the coherence of the pure state associated to the quantum system. Here I…
A quantum walk places a traverser into a superposition of both graph location and traversal "spin." The walk is defined by an initial condition, an evolution determined by a unitary coin/shift-operator, and a measurement based on the…
We address the question of symmetries of an important type of quantum walks. We introduce all the necessary definitions and provide a rigorous formulation of the problem. Using a thorough analysis, we reach the complete answer by presenting…
The development of non-Hermitian topological band theory has led to observations of novel topological phenomena in effectively classical, driven and dissipative systems. However, for open quantum many-body systems, the absence of a ground…
The notion of topological (Thouless) pumping in topological phases is traditionally associated with Laughlin's pump argument for the quantization of the Hall conductance in two-dimensional (2D) quantum Hall systems. It relies on magnetic…
Non-Hermitian topological edge states have many intriguing properties, but have so far mainly been discussed in terms of bulk-boundary correspondence. Here we propose to use a bulk property of diffusion coefficients for probing the…
We analyze a tight binding model of two coupled chains with strongly interacting fermions. Depending on the parameter $w$, the many body lowest energy band consists of either single particles or bound pairs. A topological quantum pump can…
We propose a new family of discrete-spacetime quantum walks capable to propagate on any arbitrary triangulations. Moreover we also extend and generalize the duality principle introduced by one of the authors, linking continuous local…
The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower dimensional time-dependent system maps into a higher dimensional one by combining the physical…