3D analogue. Three-dimensional droplets are formed when the mean-field approach predicts a collapse of the system, i.e., interspecies attraction is sufficiently strong. However, in lower dimensions, the two- and one-dimensional droplets can be formed in an overall repulsive system, which liquefies while squeezed, and does not need any trapping potential in the not confined direction(s) anymore.

In our paper, we study the formation of droplets at the dimensional crossover from 3D to quasi-2D, and 3D to quasi-1D. In this regime, which was not previously explored in the literature, we find new kind of stable droplets which are formed only due to quantum fluctuations, when the mean-field interaction vanishes. Our results are also important for experiments for which the access to quasi-1D or quasi-2D regimes is demanding. Since such experiments are always performed in 3D under conditions of tight confinement the kinematics may be low-dimensional to a large extent. The elimination of excitations, however, in the confined direction(s) is not complete, and the proper description requires inclusion of corrections. In particular, we show that the access to quasi-1D is significantly more demanding than to quasi-2D, therefore, our results are especially important for these experiments since in most circumstances only the crossover 