Modulacijska nestabilnost nelinearne Schrödingerove jednadžbe sa sintetskim magnetskim poljem

master's thesis

• Title (english): Modulation instability in the nonlinear Schrödinger equation with a synthetic magnetic field
• Author: Ozana Čelan
• Mentor: Karlo Lelas (mentor)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2019-09-26, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Dinamika slabo međudjelujućih Bose Einsteinovih kondenzata i propagacija svjetlosti kroz nelinearan medij opisuju se nelinearnom Schrödingerovom jednadžbom. Modulacijska nestabilnost je fenomen karakterističan za sustave opisane tom jednadžbom i istraživan je u kontekstu Bose Einstein kondenzata i u kontekstu nelinearne optike. U novije vrijeme se razvijaju metode za kreiranje sintetskih magnetskih polja u tim sustavima u svrhu realizacije kvantnih emulatora. Mi smo u ovom radu teorijski istražili kako na modulacijsku nestabilnost utječe uvođenje homogenog sintetskog magnetskog polja u nelinearnu Schrödingerovu jednadžbu. Razvili smo dvije numeričke metode za vremensku evoluciju jednadžbe te pokazali da se modulacijska nestabilnost događa i u prisutnosti sintetskog magnetskog polja. Također, pokazali smo da će rezultati vremenske evolucije ovisiti o odabiru vektorskog potencijala s kojim opisujemo homogeno sintetsko magnetsko polje. Objasnili smo da do razlika u vremenskim evolucijama, za različite odabire vektorskog potencijala, dolazi zbog sintetskog električnog polja koje se javlja u trenutku uključivanja sintetskog magnetskog polja.

Abstract (english)

Dynamics of weakly interacting Bose Einstein condensates, and propagation of light through nonlinear media, are both described with the nonlinear Schrödinger equation. Modulation instability is a phenomenon characteristic for systems described with this equation and it was explored in the context of Bose Einstein condensates and in the context of nonlinear optics. Recently, new methods are being developed for creating homogeneous synthetic magnetic fields in these systems in order to create quantum emulators. In this work we theoretically explored how the implementation of the homogeneous synthetic magnetic field in nonlinear Schrödinger equation influences the modulation instability. We developed two numerical methods for the time evolution of the equation, and we showed that the modulation instability also occurs in the presence of homogeneous synthetic magnetic field. We also showed that the results of time evolution will depend on the choice of the vector potential used to describe the homogeneous synthetic magnetic field. We explained that the differences in time evolutions, for different choices of vector potential, occur because of the synthetic electric field which appears in the moment of activation of the homogeneous synthetic magnetic field.

• Keywords: modulacijska nestabilnost; nelinearna Schrödingerova jednadžba; Bose Einsteinov kondenzat; nelinearna optika; sintetsko magnetsko polje; baždarenje
• Keywords (english): modulation instability; nonlinear Schrödinger equation; Bose Einstein condensate; nonlinear optics; synthetic magnetic field; gauge
• Language: croatian
• URN:NBN: urn:nbn:hr:217:417678
• 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: 2020-09-26
• Created on: 2020-01-07 10:08:03