We derive a theoretical description for dilute Bose gases as a loop expansion in terms of composite-field propagators by rewriting the Lagrangian in terms of auxiliary fields related to the normal and anomalous densities. We demonstrate that already in leading order this nonperturbative approach describes a large interval of coupling-constant values, satisfies Goldstone's theorem, yields a Bose-Einstein transition that is second order, and is consistent with the critical temperature predicted in the weak-coupling limit by the next-to-leading-order large-N expansion.
We discuss the equilibrium properties of dilute Bose gases using a nonperturbative formalism based on auxiliary fields related to the normal and anomalous densities. We show analytically that for a dilute Bose gas of weakly interacting particles at zero temperature, the leading-order auxiliary field (LOAF) approximation leads to well-known analytical results. Close to the critical point the LOAF predictions are the same as those obtained using an effective field theory in the large-
N approximation. We also report analytical approximations for the LOAF results in the unitarity limit, which compare favorably with our numerical results. LOAF predicts that the equation of state for the Bose gas in the unitarity limit is
E/(pV)=1, unlike the case of the Fermi gas when
E/(pV)=3/2.
An ultracold Bose-Fermi gas mixture of 40K and 87Rb atoms has tunable interspecies interactions and therefore provides a fantastic platform for exploring not only few-body physics such as Feshbach molecule formation and Efimov trimers, but also many-body physics including Bose polarons, quantum Hall physics and so on. In this thesis, I present experimental evidence of Bose polarons in cold atoms obtained using radio-frequency spectroscopy to measure the excitation spectrum of fermionic 40K impurities resonantly interacting with a BEC of 87Rb atoms. These Bose polarons originate from the dressing of an impurity coupled to its environment, which is an important paradigm in quantum many-body physics. I also present initial work that launches an exciting new direction for our experiment, which is exploring rotating quantum gases. Goals for this work include studying both rotating Bose and Fermi superfluids with tunable interactions as well as working toward rapidly rotating quantum gases in the quantum Hall regime. For these goals, a new all-optical trap for rotating gases was designed, implemented, and tested using a 87Rb Bose-Einstein condensate.