Interferometry of non-Abelian band singularities and Euler class topology
- URL: http://arxiv.org/abs/2401.01928v2
- Date: Fri, 19 Jul 2024 11:18:38 GMT
- Title: Interferometry of non-Abelian band singularities and Euler class topology
- Authors: Oliver Breach, Robert-Jan Slager, F. Nur Ünal,
- Abstract summary: We experimentally probe non-Abelian braiding processes and charges in ultracold atomic systems.
We consider a coherent superposition of two bands that can be created by moving atoms through the band singularities.
Our results present a feasible avenue for measuring non-Abelian charges of band nodes and the direct experimental verification of braiding procedures.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In systems with a real Bloch Hamiltonian band nodes can be characterised by a non-Abelian frame-rotation charge. The ability of these band nodes to annihilate pairwise is path dependent, since by braiding nodes in adjacent gaps the sign of their charges can be changed. Here, we theoretically construct and numerically confirm two concrete methods to experimentally probe these non-Abelian braiding processes and charges in ultracold atomic systems. We consider a coherent superposition of two bands that can be created by moving atoms through the band singularities at some angle in momentum space. Analyzing the dependency of excitations on the frame charges, we demonstrate an interferometry scheme passing through two band nodes, which reveals the relative frame charges and allows for measuring the multi-gap topological invariant. The second method relies on a single wavepacket probing two nodes sequentially, where the frame charges can be determined from the band populations. Our results present a feasible avenue for measuring non-Abelian charges of band nodes and the direct experimental verification of braiding procedures, which can be applied in a variety of settings including the recently discovered anomalous non-Abelian phases arising under periodic driving.
Related papers
- Topological phases and edge modes of an uneven ladder [10.192360653612896]
We investigate the topological properties of a two-chain quantum ladder with uneven legs.
Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.
We propose that uneven ladders can be realized by spin-dependent optical lattices.
arXiv Detail & Related papers (2024-04-01T13:07:31Z) - Flat-band localization and interaction-induced delocalization of photons [0.0]
We experimentally construct an Aharonov-Bohm cage and observe the localization of a single photon.
Results mark the first experimental observation of a quantum walk that becomes delocalized due to interactions.
arXiv Detail & Related papers (2023-03-03T19:00:01Z) - Non-Abelian braiding of graph vertices in a superconducting processor [144.97755321680464]
Indistinguishability of particles is a fundamental principle of quantum mechanics.
braiding of non-Abelian anyons causes rotations in a space of degenerate wavefunctions.
We experimentally verify the fusion rules of the anyons and braid them to realize their statistics.
arXiv Detail & Related papers (2022-10-19T02:28:44Z) - Adaptive constant-depth circuits for manipulating non-abelian anyons [65.62256987706128]
Kitaev's quantum double model based on a finite group $G$.
We describe quantum circuits for (a) preparation of the ground state, (b) creation of anyon pairs separated by an arbitrary distance, and (c) non-destructive topological charge measurement.
arXiv Detail & Related papers (2022-05-04T08:10:36Z) - Tuning long-range fermion-mediated interactions in cold-atom quantum
simulators [68.8204255655161]
Engineering long-range interactions in cold-atom quantum simulators can lead to exotic quantum many-body behavior.
Here, we propose several tuning knobs, accessible in current experimental platforms, that allow to further control the range and shape of the mediated interactions.
arXiv Detail & Related papers (2022-03-31T13:32:12Z) - Multi-gap topology and non-Abelian braiding of phonons from first
principles [5.138204888245502]
Non-Abelian states of matter can encode information immune from environmental noise.
We show that phonons can carry non-Abelian frame charges at the band crossing points of their frequency spectrum.
Our work provides a new quasiparticle platform for realizable non-Abelian braiding in reciprocal space.
arXiv Detail & Related papers (2021-11-10T19:00:04Z) - Tight-Binding realization of non-abelian gauge fields: singular spectra
and wave confinement [0.0]
We present a geometric construction of a lattice that emulates the action of a gauge field on a fermion.
The emulation covers both abelian and non-abelian gauge fields.
arXiv Detail & Related papers (2021-06-09T22:15:24Z) - Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range.
For a large part of the presentation, infinite scattering length will be considered.
arXiv Detail & Related papers (2020-06-03T17:54:43Z) - Topological Euler class as a dynamical observable in optical lattices [0.0]
We show that the invariant $(xi)$ falls outside conventional symmetry-eigenvalue indicated phases.
We theoretically demonstrate that quenching with non-trivial Euler Hamiltonian results in stable monopole-antimonopole pairs.
Our results provide a basis for exploring new topologies and their interplay with crystalline symmetries in optical lattices beyond paradigmatic Chern insulators.
arXiv Detail & Related papers (2020-05-06T18:00:03Z) - Dynamical solitons and boson fractionalization in cold-atom topological
insulators [110.83289076967895]
We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities.
We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors.
Using a pumping argument, we show that it survives also for finite interactions.
arXiv Detail & Related papers (2020-03-24T17:31:34Z) - Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide.
For open boundary condition, we find exotic topological bound-pair edge states with radiative losses.
By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
arXiv Detail & Related papers (2020-02-24T04:44:12Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.