Soliton-to-droplet crossover in a dipolar Bose gas in one and two dimensions

We analyze a system of dipolar atoms confined in geometries of quasi low dimensionality. Due to the long-range and anisotropic nature of dipolar interactions, the system supports both stable solitons and quantum droplets. In quasi-one-dimensional geometries, the transition between these states is known to manifest either as a first-order phase transition, associated with bistability, or as a smooth crossover. We investigate this transition by calculating the structure factor and showing that the response of the breathing mode provides an experimentally accessible probe. In addition, we identify regions of both bistability and smooth crossover in quasi-two-dimensional geometries. Finally, we connect our findings to previous experimental results and delineate the conditions under which two-dimensional dipolar bright solitons can be realized.