Can vortex quantum droplets be realized experimentally?

C reation of stable self-trapped vortex states (alias vortex solitons) in Bose-Einstein condensates (BECs) in free space is a challenging problem [1].To date, an experimental demonstration of this possibility is missing.A new powerful platform for the realization of various self-trapped states is offered by quantum droplets (QDs), i.e., stable localized modes maintained by the balance of mean-field (MF) interactions and corrections to them induced by quantum fluctuations [2].Recent theoretical predictions [3, 4] and experimental demonstrations [5-10] suggest various possibilities for the creation of novel fundamental and vortical patterns, as summarized in reviews [11-13].In particular, QDs with embedded vorticity were theoretically investigated in detail [14-21].This story starts with the original experimental realization of BECs [22][23][24], which has made it possible to probe properties of quantum matter that are otherwise difficult to access.By observing macroscopic quantum phenomena manifested by BECs, researchers gain valuable insights into the underlying physical phenomena and mechanisms [25][26][27][28][29][30][31][32][33][34][35][36].In experimental settings, the BEC lifetime is usually short, as the condensates are prone to spatial expansion or collapse, in the cases of the repulsive and attractive inter-atomic interactions, respectively [37].The lifetime may be substantially extended by means of a trapping potential which confines the condensate [1,25,26].It is relevant to stress that the natural interaction between atoms is repulsive, due to the fact that colliding hard particles bounce back from each other.The interaction may be switched to attraction by dint of the Feshbach-