Gil, Pedro dos Santos2026-01-132026-01-132025http://hdl.handle.net/10400.5/116579Tese de Mestrado, Física (Física Nuclear e Partículas), 2025, Universidade de Lisboa, Faculdade de CiênciasWe consider a Bose-Einstein condensate loaded into an optical cavity subject to the combined action of an external potential and a cavity mode with mutually incommensurate periods. This configuration enables the localization of matter waves even in the absence of attractive two-body interactions. We analyze the families of the corresponding localized modes for both red- and bluedetuned atomic and cavity resonances in relatively shallow lattices. The parameter regimes supporting localization are identified. The system is found to exhibit multi-stability, previously discussed in terms of bistability, manifesting as distinct photon numbers under otherwise identical conditions. In addition, the system may display ”strict” bistability, characterized by two different atomic density distributions corresponding to the same photon number. The stability of the localized modes is examined.application/pdfengCavity QEDBose–Einstein condensatesquasi-periodic potentialslocalizationmaster thesis204175208