Resolving the problem of complex sound velocity in binary Bose mixtures with attractive intercomponent interactions

In 2015 Dmitry Petrov theoretically suggested that, in a binary mixture of bosons a quantum liquid droplet may arise due to the competition between attractive intercomponent and repulsive intracomponent forces. Although this prediction has been confirmed experimentally, the model by itself suffers from a serious conceptual problem: The low - lying excitation spectrum manifests a purely imaginary phonon velocity, $c_d^2 < 0$. In the present work, we develop a self consistent theory of two-component Bose systems with attractive interspecies interactions, which accurately takes into account pair correlations in terms of anomalous and mixed densities. We have shown that this procedure is able to resolve the problem of $c_d^2 < 0$. Limiting ourselves with a symmetric Bose mixture at zero temperature, we have found a region of stability in which a droplet can survive.