Theory for Self-Bound States of Dipolar Bose-Einstein Condensates

We investigate the self-bound states of dipolar Dy condensates with the Gaussian-state ansatz which improves the conventional coherent-state ansatz with multimode squeezed coherent states. We show that the self-bound states consist of the experimentally observed self-bound liquid phase and the unobserved self-bound gas phase. The numerically obtained gas-liquid boundary is in good agreement with experimental data. Our theory also allows one to extract the real part of the three-body coupling constant of the Dy atoms from the particle number distribution of the condensates. In particular, we results show that the self-bound states are stabilized by the short-range three-body repulsion. Our study shed a different light to understand the self-bound droplets of Bose-Einstein condensates.