Fig. 4: Phase diagram and energy landscapes.
a Phase diagram as a function of as and atom number. The white region denotes a trap-bound BEC extended over several lattice sites. The colored regions denote quasi-2D self-bound solutions: a droplet (green), a soliton (blue), each either extended over several lattice sites (lighter shade) or localized (darker shade, >95% of the atoms are localized in the central lattice plane). Circles show the atom number from our experimental data points in Fig. 3a. The statistical uncertainties on the scattering length is smaller than the symbols size. a–c Energy landscapes as a function of the radial widths lx and ly, in units of the radial harmonic oscillator lengths xho = 0.50(1) μm and yho = 1.42(1) μm, respectively, with (left) and without (right) the radial harmonic trap, for (a) BEC (as, N) = (70 a0, 1.5 × 104), (b) droplet (as, N) = (65 a0, 1.5 × 104) and (c) soliton (as, N) = (51.5 a0, 0.4 × 104) regimes, with darker shading at the minima. d Radial width lx versus N for as = 51.5 a0. The dashed line indicates the soliton-to-droplet transition point, and the circles indicate the position of b, c.
