Sintetički magnetizam za ultrahladne atomske plinove

master's thesis

• Title (english): Synthetic magnetism for ultracold atomic gases
• Author: Tomislav Jajtić
• Mentor: Hrvoje Buljan (mentor)
• Committee member: Hrvoje Buljan (predsjednik povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Davor Horvatić (član povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2018-06-12, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom radu pokazali smo da je u sustav ultrahladnih atomskih plinova, ograničenog na dvije dimenzije (u xy ravnini), moguće upisati vektorski potencijal zavojnice koristeći lasersku zraku koja se propagira u z-smjeru. Prvo smo pokazali da sustav ultrahladnih atomskih plinova čije stanje ovisi o vanjskim parametrima λ i koji evoluira adijabatski dobiva geometrijsku fazu ∮ A · dλ, gdje je A sintetički vektorski potencijal istog oblika kao i vektorski potencijal zavojnice A ~ ^φ/r. Pokazali smo da je A posljedica interakcije svjetlosti i atoma i da trebamo laserske zrake s vrtlozima koje imaju fazu eimφ da bi dobili A željenog oblika. Nakon toga pogledali smo kompozitne čestice u dvodimenzionalnom prostoru koje se sastoje od zavojnice i nabijene čestice. Te čestice zovu se anyoni i imaju necjelobrojnu statistiku, što zapravo znači da dobivaju fazu koja nije ni 0 (bozoni) ni π (fermioni) kada se jedan anyon zavrti oko drugog identičnog takvog. Pogledali smo dvije takve laserske zavojnice upisane u Bose-Einsteinov kondenzat koji se nalazi u vanjskom skalarnom potencijalu harmoničkog oscilatora. Na zamjenu pozicija zavojnica dobili smo fazu koja nije ni 0 ni π, ali vidjeli smo i da ta faza ovisi o udaljenosti medu zavojnicama što znači da to nije topološka faza.

Abstract (english)

Here we have shown it is possible to imprint a solenoidal vector field to a system of ultracold atomic gases confined to two dimensions in the xy plane using a laser beam propagating in the z-direction. First we have shown a system of ultracold atomic gases, whose state depends on external parameters λ and whose evolution is adiabatic, acquires a geometric phase ∮ A · dλ, where A is the synthetic vector potential of the same form as the solenoidal vector field A ~ ^φ/r. We have also shown A is a result of the light-matter interaction. Optical vortex laser beam, i.e. a laser beam with a phase eimφ, is needed forAto take the form that of a solenoidal vector field. Then we have introduced a composite particle in two-dimensional space consisting of a flux tube (a solenoid) and a charged particle. These composite particles are called anyons and have non-integer statistics. Non-integer statistics here (and elsewhere as per the author’s knowledge) meaning they acquire a phase that is neither 0 (like bosons) or π (like fermions) when one anyon comes a full circle around another identical one. We have put 2 such laser flux tubes imprinted in a Bose-Einstein condensate in an external scalar potential that of a harmonic oscillator and spun them around. Turns out, the phase we get actually is non-integer, but it shows dependence on the distance between the flux tubes and is, therefore, not topological.

• Keywords: geometrijska faza; Berryjeva faza; laserske zrake s vrtlozima; sintetički vektorski potencijal; anyoni
• Keywords (english): geometric phase; Berry phase; optical vortex; synthetic vector potential; anyon
• Language: croatian
• URN:NBN: urn:nbn:hr:217:760265
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access; Embargo expiration date: 2019-06-12
• Created on: 2018-07-13 14:14:58