Abstract
This lecture began with a description of experimental measurements of the Lee-Huang-Yang (LHY) energy in dilute atomic gases. We then moved on to measurements of the excitation spectrum, with the now-classic results obtained at the Weizmann Institute, which are very well described by the Bogoliubov approach. We also looked at more recent experiments at Boulder and Cambridge, which have extended the measurement range to k-wavenumbers of the order of 1/a, where a is the scattering length. The final part of this lecture was devoted to the ground state of a mixture of two quantum gases, 1 and 2. Depending on the values of the three interaction parameters gij with i, j = 1,2, this mixture can be miscible or immiscible within the framework of mean-field theory. In particular, immiscibility occurs when the dispersion relation of the homogeneous mixture gives rise to complex frequencies, leading to exponential divergences from a small initial perturbation. Following a proposal by Dmitry Petrov, we then showed how LHY effects, beyond the mean field, can be used to stabilize this mixture in the form of quantum droplets.
