Probing the Equation of State of Strongly Correlated Bose and Fermi Gases

We have developed and used a general method to probe with high precision the thermodynamics of homogeneous systems using trapped atomic gases. We have applied this technique to the two spin-component Fermi gas with short-range interactions. Using fermionic $^{6}$Li, one can explore a 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 Fermi liquid-type behaviour of the normal phase. We have extended this method to bosons using $^{7}$Li close to a Feshbach resonance. We have measured the EoS of the Bose gas as a function of interactions at very low temperature. For the first time in atomic Bose gases, we measured quantitatively the Lee-Huang-Yang beyond mean-field correction to the ground state energy. We compared the experimental in-situ density profiles with Monte-Carlo predictions for thermometry purpose. 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 properties of the hypothetical unitary Bose gas.