The correction $\epsilon_\mathrm{LHY}$ originates from a zero-point energy of the vacuum of Bogoliubov’s quasiparticles. Since it depends on a higher power of the density, as compared to the leading mean-field terms, its contribution to the energy is negligible in most circumstances. However, for the Bose-Bose mixture, at the edge of the stability, close to the collapse threshold, the mean-field energy vanishes, and the quantum fluctuations start to dominate. As predicted in [@Petrov15], these fluctuations contribute additional energy, called the LHY correction [@Larsen63; @Sacha08; @Petrov15], and stabilize the system and lead to the formation of quantum droplets.

Quantum droplets were first observed in Dysprosium and Erbium BECs [@Kadau16; @Ferrier16a; @Ferrier16b; @Schmitt16; @Chomaz16], in which the dipole-dipole interactions between atoms is significant. This anisotropic interaction, depending on the relative position of atoms and the orientation of their magnetic dipole moments, can be attractive or repulsive. The competition of attraction and repulsion, similarly to the two-component mixtures, might bring the system to the stability edge, making it vulnerable to quantum fluctuations. The original scenario from Ref. [@Petrov15], was realized in the recent experiments with two-component Potassium BECs [@Cabrera17; @Fattori17; @Cheiney18].

Quantum droplets can also exists in low-dimensional systems [@Petrov16]. Due to the expected 