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This thesis presents experimental work to investigate the properties of ultracold rubidium atoms in multiple-radiofrequency dressed potentials and detailed theoretical calculations to understand this system. The use of multiple frequencies rather than a single dressing frequency increases the complexity of the spectrum, and we present theoretical calculations that predict all possible transitions as well as the corresponding strengths. Extensive measurements for dressing with a single and multiple frequencies have verified these predictions, observing transitions up to tenth order in the probe field. We observe previously unknown transitions even for the single-frequency case and have uncovered further transitions which we explain by the non-linearity of the Zeeman effect even at our small field strengths. These results are used to understand the absorption spectrum as the potential transforms from a single to a double well in order to split a Bose-Einstein condensate. This is important for applications since spurious noise leads to atom loss if it is resonant with a transition between eigenstates. We present a new method of splitting, replacing adiabatic ramps with a projection, that reduces the duration of the ramps as well as the spectrum of resonances throughout the ramps, thus reducing losses. The new experimental techniques will allow observation of the thermalisation of a two-dimensional quantum system using ultracold gases. We discuss how multiple-radiofrequency dressed potentials can be used to confine ultracold atoms in two dimensions, and subsequently split the trapped cloud into two parallel sheets. After a varying hold time, the atoms can be released and overlapped to produce interference fringes. Analysis of the fringes determines how the relative phase between the two sheets thermalises. Information can be accumulated to determine the probability distribution of the integrated contrast, which can then be compared to the equilibrium distribution to determine if and how the relative phase thermalises. This promises to answer key questions in non-equilibrium physics. |
