Ultracold Bose systems studied by Quantum Monte Carlo methods

Istražena su svojstva interagirajućih ultrahladnih bozonskih sustava korištenjem kvantnih Monte Carlo simulacija. Ispitana je suprafluidnost i Bose-Einsteinova kondenzacija vrlo rijetkih dvokomponentnih bozonskih mješavina u ovisnosti o temperaturi. Ovisno o interakcijama, sustav može biti u tri različita režima: miješanom, separiranom u dvije nakupine i separiranom u ljuskastom režimu. Uočena je anizotropnost suprafluidnosti u slučaju separacije u obliku dviju nakupina. Također je uočen i prijelaz pri kojem udio suprafluida postaje manji od udjela Bose- Einsteinovog kondenzata za svaki režim. Nadalje smo istražili svojstva jednodimenzionalnih jakointeragirajućih bozonskih sustava u periodičnim potencijalima. Detaljno je prikazan prijelaz suprafluida u Mottov izolator u režimima robusnog i fragilnog suprafluida. Istražili smo prijelaz iz jednodimenzionalnog u dvodimenzionalni sustav helija-4 unutar nanopore. Analizirali smo skaliranje suprafluidnosti s umnoškom temperature i duljine simulacijske ćelije te slaganje rezultata s teorijskim opisom. Uočen je prijelaz sustava helija-4 iz jednodimenzionalnog u dvodimenzionalni s povećanjem linijske gustoće unutar nanopore radijusa R = 4 Å što je vidljivo u ponašanju korelacijskih funkcija i suprafluidnosti.The properties of interacting ultracold Bose systems were investigated using quantum Monte Carlo simulations. The superfluidity and Bose-Einstein condensation of very dilute two species trapped bosons mixtures as a function of temperature were investigated. Depending on the interactions, the system can be in three different modes: mixed, separated into two blobs, and separated in a shell regime. Anisotropy of superfluidity was observed in the case of two blobs. A transition was also observed in which the superfluidity fraction becomes smaller than the condensate fraction for each regime. We further investigated the properties of one dimensional strongly interacting bosonic systems in periodic potentials. The transition of the superfluid to the Mott insulator phase in the robust and fragile superfluid regimes is shown in detail. We investigated transition from a one-dimensional system to a two-dimensional one of helium-4 in the nanopore. We analyzed the scaling of the helium-4 superfluidity with the product of the temperature and the length of the simulation cell and the agreement of the results with the theoretical predictions. The transition of the helium-4 system from one-dimensional to two-dimensional with an increase in the linear density within the nanopores of radius R = 4 Å was observed, which is visible in the behavior of the correlation function and suprafluidity