Anyons, Zitterbewegung and dynamical phase transitions in topologically nontrivial systems

doctoral thesis

• Title (croatian): Anyoni, Zitterbewegung i dinamički fazni prijelazi u topološki netrivijalnim sustavima
• Author: Frane Lunić
• Mentor: Hrvoje Buljan (mentor)
• Mentor: Dario Jukić (komentor)
• Committee member: Karlo Lelas (predsjednik povjerenstva)
• Committee member: Robert Pezer (član povjerenstva)
• Committee member: Hrvoje Buljan (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2022-07-07, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics
• Universal decimal classification (UDC): 53 - Physics

Abstract

Nontrivial topology in physical systems is the driving force behind many interesting phenomena. Notably, phases of matter must be classified in part by their topological properties. Phases with topological (nonlocal) order, such as the fractional quantum Hall effect (QHE), can support anyonic excitations obeying fractional statistics with potential application in topological quantum computing. States lacking intrinsic topological order can still belong to topological phases, provided certain symmetries are imposed. On their own, these symmetry-protected phases do not support anyons, but they can still have other interesting features, such as protected boundary states. In this thesis we present an original research into several topologically nontrivial systems. First, we present the experimental and theoretical results on light propagation in the valley modes of inversion-symmetry broken honeycomb lattices (HCL). We find that a rotating spiral pattern, leading to Zitterbewegung, arises in the intensity profile of the beam as a result of the nontrivial topology of the HCL valleys. Next, we present the numerical demonstration of dynamical topological phase transitions driven by nonlinearity of the photonic medium, which occur in soliton SSH lattices. The phase transitions, marked by the appearance of topological edge states in the band gap, occur due to the setup which enables continually changing relative values of the intracell and intercell soliton couplings. Finally, we propose a scheme for creating and manipulating synthetic anyons in a noninteracting system by perturbing it with specially tailored localized probes. The external probes are needed because noninteracting systems do not possess the kind of topological order required to support anyonic excitations. We start from a noninteracting 2D electron gas in a uniform magnetic field, which is in an integer QHE state, and introduce thin solenoids carrying a fractional magnetic flux. We present the solution for a suitable ground state, and demonstrate the fractional braiding statistics in the coordinates of the solenoids.

Abstract (croatian)

U ovoj disertaciji proučavali smo više tema koje objedinjuje utjecaj topologije na fiziku sustava. Glavni cilj bio je prezentacija originalnih članaka [52,53,18], no pritom smo predstavili i neke bitnije teme vezane za topološku kvantnu materiju uključujući IQHE, FQHE, anyone i SPT faze. IQHE i FQHE, iako različiti, su povezani, a obje pojave su bitna pozadina za naše sintetičke anyone. Dok IQHE služi kao temelj za naš model, Laughlinove kvazičestice u FQHE-u daju inspiraciju za ideju perturbacije sustava lokaliziranim frakcijskim solenoidnim probama. U sklopu prezentacije prvog članka prikazali smo utjecaj netrivijalne topologije dolinskog stupnja slobode saćaste rešetke na propagaciju svjetla kroz fotonički kristal. Ovaj utjecaj se manifestira kroz pojavu „vorteks” komponente koja u interferenciji s "nevorteks" komponentom uzrokuje rotirajući spiralni uzorak u profilu intenziteta te s njim povezanu pojavu Zitterbewegunga. Ove pojave smo vidjeli u rezultatima eksperimenta i u teorijskim proračunima. U sljedećem dijelu predstavili smo rezultate numeričke studije evoluirajuće solitonske SSH rešetke koja je moguća zahvaljujući nelinearnosti fotoničkog medija. Uočili smo periodičku pojavu rubnih stanja u spektralnom procijepu s faznim profilom topoloških rubnih stanja koja signalizira topološke fazne prijelaze. Ovakvi topološki fazni prijelazi primjer su emergentne nelinearne topološke pojave. U posljednjem dijelu predlažemo realizaciju sintetičkih anyona perturbacijom neinteragirajućeg sustava posebnim lokaliziranim probama. Naši sintetički anyoni se razlikuju od emergentnih frakcijskih kvazičestica kakve se javljaju u sustavima poput FQHE-a, no realizacija ovog modela je poželjna jer bi njegov neabelovski pandan mogao biti podloga za topološka kvantna računala. Sustavi ultrahladnih atoma sa sintetičkim vektorskim potencijalima su obećavajuća platforma za ovu namjenu.

• Keywords: Berry phase; Berry curvature; topology; topological quantum matter; photonics; Zitterbewegung; symmetry broken honeycomb lattice; valley degree of freedom; SSH model; optical solitons; nonlinearity; anyons; fractional statistics; topological quantum computation; quantum Hall effect; synthetic anyons
• Keywords (croatian): Berryjeva faza; Berryjeva zakrivljenost; topologija; topološka kvantna materija; fotonika; Zitterbewegung; saćasta rešetka s narušenom simetrijom; dolinski stupanj slobode; SSH model; optički solitoni; nelinearnost; anyoni; frakcijska statistika; topološko kvantno računanje; kvantni Hallov efekt; sintetički anyoni
• Language: english
• URN:NBN: urn:nbn:hr:217:171115
• Promotion: 2022
• Study programme: Title: Physics; Study programme type: university; Study level: postgraduate; Academic / professional title: doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika (doktor/doktorica znanosti, područje prirodnih znanosti, polje fizika)
• Type of resource: Text
• Extent: 106 str.
• File origin: Born digital
• Access conditions: Open access
• Created on: 2022-08-26 11:45:18