Mixtures of ultracold gases: Fermi sea and Bose-Einstein condensate of lithium isotopes

This thesis presents studies of quantum degenerate atomic gases of fermionic $^6$Li and bosonic $^7$Li. Degeneracy is reached by evaporative cooling of $^7$Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, $^6$Li is sympathetically cooled by thermal contact with $^7$Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of $T/T_F=0.25(5)$ is achieved for $10^5$ fermions. For more than $\sim 300$ atoms, the $^7$Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments $^7$Li and $^6$Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A $^7$Li Bose-Einstein condensate (BEC) of $10^4$ atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are $T/T_C=T/T_F=0.2(1)$. The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to $|F=1,m_F=1\rangle$, the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of $1.1\,$mm is observed.