Abstract
In previous lectures, we were interested in the link between two-body physics, described by the diffusion length, and the properties of an N-body system, addressed by Bogoliubov's method. This link was possible for a weakly interacting gas. The aim of these last two lectures is to explore the link " 2-body - N-body " without making any assumptions about the strength of the interactions. Specifically, we place no constraints on the value of the scattering length a, which can be adjusted to an arbitrarily large value for atomic species exhibiting Fano-Feshbach resonance. On the other hand, we always assume that the system is dilute, i.e. that the range of the potential is small compared with the distance between particles.
For the case of three-dimensional gases of interest here, the link " 2-body - N-body " was largely initiated by Shina Tan, who established universal relations for a two-component Fermi gas, with interactions described in the zero-span limit. These relations link microscopic quantities, such as the impulse distribution of the gas or its two-body correlation function, to macroscopic quantities, such as free energy or pressure. They involve a quantity called " contact ", a name justified by the fact that it is a measure of the probability of two particles being close to each other. The advantage of relations involving contact is that they do not require precise knowledge of the state of the system, which we would not be able to provide in the case of strong interactions.
In these two lectures (April 8 and 15, 2022), we first present in detail Tan's formalism for a Fermi gas. We then describe a series of experiments that have explored different facets of the contact, such as measuring the velocity distribution of gas particles, the response of the fluid to radio-frequency excitation, and the observation of atom losses induced by inelastic collisions. We conclude with a brief discussion of the possible extension of this formalism to the case of a Bose gas, highlighting the difficulty posed in this case by three-body processes. The study of this fascinating but difficult " three-body problem " will be the subject of a forthcoming series of lectures.
