This thesis describes a collection of experiments that explore interacting ultracold Bose gases, both in and out of equilibrium. Our experiments are performed using a gas of
39K or
87Rb confined in the uniform potential of an optical box trap, a novel testbed for quantum many-body phenomena. Our work focuses on weakly interacting non-equilibrium systems, moderately interacting systems that are still in equilibrium, and the unitary Bose gas which is both strongly interacting and eludes equilibrium. We begin with studies of weakly-interacting gases far from equilibrium, which feature ties to nonlinear wave phenomena. Highlights of our experiments include the direct measurement of turbulent-cascade fluxes, which (alongside realizing a tuneable dissipation scale) allow us to demonstrate the zeroth law of turbulence, and the first observation of weak collapse, a general type of nonlinear wave collapse predicted over 40 years ago. We then turn to moderately strong interactions, confronting existing theories of interacting quantum fluids. One of our most important results is the first quantitative measurement of the quantum depletion of a Bose–Einstein condensate, confirming a 70-year-old theory first developed to describe liquid helium. The culmination of our work explores the unitary Bose gas, where interparticle interactions are as strong as allowed by the laws of quantum mechanics. This strongly-correlated state promises tantalizing possibilities, including emergent universal behavior set solely by the gas density and novel forms of superfluidity. However, the strong interactions also lead to a complex interplay between coherent and dissipative dynamics. By disentangling these two processes, we have caught a glimpse of the promises that the unitary Bose gas holds. In particular, we observe the emergence of universal behavior, and find that the gas features a well defined quasi-equilibrium state, with a non-zero condensed fraction.
Following up on recent calculations, we investigate the leading- and next-to-leading-order semiclassical approximation to the virial coefficients of a two-species fermion system with a contact interaction. Using the analytic result for the second-order virial coefficient as a renormalization condition, we derive expressions for up to the seventh-order virial coefficient $\mathrm{\ensuremath{\Delta}}{b}_{7}$. Our results at leading order, though approximate, furnish simple analytic formulas that relate $\mathrm{\ensuremath{\Delta}}{b}_{n}$ to $\mathrm{\ensuremath{\Delta}}{b}_{2}$ for arbitrary dimension, providing a glimpse into the behavior of the virial expansion across dimensions and coupling strengths. As an application, we calculate the pressure and Tan's contact of the two-dimensional attractive Fermi gas and examine the radius of convergence of the virial expansion as a function of the coupling strength.