How can we move from the individual to the collective, from the microscopic to the macroscopic ? Does our knowledge of the constituents of ordinary matter, atoms and molecules, enable us to predict the behavior of a large assembly of particles ? In this year's lecture, we will tackle this question for ultra-cold quantum fluids, for which the distance between particles is less than the de Broglie length.
We'll first study the weak interaction regime, for which the distance between particles remains greater than the diffusion length characterizing interactions in the ultra-cold regime. We'll show that this regime can be treated quantitatively by the Bogoliubov method and its Lee-Huang-Yang corrections, and present recent experimental results that have confirmed these theoretical predictions.
We then turn to the case of strongly interacting particles, so that the scattering length becomes greater than the distance between particles. We will show that it is still possible to relate the microscopic characteristics of the fluid, its two-body correlation function for example, to its macroscopic properties described by its equation of state. We will present the " contact " formalism, which applies to both bosonic and fermionic fluids, and describe a series of recent experiments that have validated this formalism.