The quantum many-body problem is at the heart of some of the most formidable open problems in modern physics, such as high-T
c superconductivity or the behaviour of neutron stars. Ultracold atomic systems can now be used to simulate model Hamiltonians of condensed matter or nuclear physics, in very well-controlled environnement. In this thesis, we have developed a general method to probe the thermodynamics of homogeneous quantum systems using trapped atomic gases. These measurements are directly compared to the predictions of theories of the quantum many-body problem. We have applied this technique to the spin-
1/2 Fermi gas and the Bose with short-range interactions. Using fermionic
6Li, we explored a part of the wide parameter space by changing the interaction strength, the spin-population imbalance or the temperature of the gas. This system exhibits remarkably rich physics, such as normal/superfluid phase transitions (that can be of thermal or quantum character) or a Fermi liquid-type behaviour of the normal phase. We have also used this method to probe a Bose gas of
7Li atoms close to a Feshbach resonance. We have measured the Equation of State of the Bose gas as a function of interactions at very low temperature. For the first time, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground-state energy of the system, first predicted in 1957. We compared the experimental results to Quantum Monte-Carlo calculations. We have extended this study using out-of-equilibrium measurements of the Bose gas in the strongly interacting regime, which gives a first hint on the properties of the hypothetical unitary Bose gas.
A dilute Bose-Einstein condensate (BEC) near a Feshbach resonance provides experimental physics with a clean and controllable system to investigate strongly interacting many-body systems. The ability to tune the scattering length allows BECs to be projected onto strong interactions from an initial weakly interacting state. However, historically, studying a bulk 3D strongly interacting BEC has been diffcult, as these systems are inherently unstable due to three-body inelastic collisions. Thus, 2D, 1D, lattice confined, and two component Fermi gases were used to explore the strong interactions in an ultracold gas. In this thesis, I present the first measurement of a strongly interacting 3D 85Rb BEC. I introduce our experimental system and the techniques we used to probe the BEC. I first report on probes of a BEC in the weakly interacting regime. To probe a spherical 85Rb BEC with strong interactions we implemented a novel experimental technique that allowed us to quickly change the interactions, bypassing inelastic losses. We projected the BEC onto unitarity, where the scattering length diverges and the interactions are infinite, in order to observe dynamics and the unexpectedly long lifetime of the gas. Additionally, we observe a universality of the gas with respect to the length scale set by the interparticle spacing.
A powerful set of universal relations, centered on a quantity called the contact, connects the strength of short-range two-body correlations to the thermodynamics of a many-body system with zero-range interactions. We report on measurements of the contact, using rf spectroscopy, for an (85)Rb atomic Bose-Einstein condensate (BEC). For bosons, the fact that contact spectroscopy can be used to probe the gas on short time scales is useful given the decreasing stability of BECs with increasing interactions. A complication is the added possibility, for bosons, of three-body interactions. In investigating this issue, we have located an Efimov resonance for (85)Rb atoms with loss measurements and thus determined the three-body interaction parameter. In our contact spectroscopy, in a region of observable beyond-mean-field effects, we find no measurable contribution from three-body physics.