Interacting matter waves quantum gases in box and shell geometries

Abstract

Bose-Einstein condensates are interacting quantum gases, that are used for a variety of applications ranging from basic scientific research to precision measurement devices. All this is possible due to the precise controllability of atom-atom interactions, via Feshbach resonances, as well as the interaction of atoms with optical and magnetic potentials. These achievements paved the way for the articles [1–3] presented in this thesis.

Due to good control of the scattering length via Feshbach resonances, we are able to analyze the effect of diffractive focusing for interacting systems. Strong interaction allows us to create the required box-shaped ground state, whereas small interaction is crucial to investigate the influence of interaction on diffractive focusing.

Moreover, by trapping two interacting Bose gases in an optical harmonic trap and tuning the inter-species interaction, we explore an alternative approach to create shell-shaped BECs. This scheme is shown to be more robust compared to the conventional method of rf-dressing. By compensating the gravitational sag and tuning the trap frequencies to the right value, this scheme has been successfully realized in experiments on Earth [4].

A shell without any external potential expands inwards and outwards, giving rise to fast destruction of the shell form of the BEC. To avoid this issue, we present schemes based on well-established methods, namely the delta kick and in-trap collimation, for extension of the free expansion times to several 100 ms. Additionally, we introduce and develop the one-dimensional analytical approach to describe the dynamics of a shell with a large radius and to predict the experimental outcomes.