We present a quantum-Monte-Carlo--based density functional to describe droplet formation and supersolidity in dipolar systems. The usual Lee-Huang-Yang term, accounting for quantum correlations in the conventional extended Gross-Pitaevskii equation (eGPE), has been substituted by the correlation energy evaluated with quantum Monte Carlo. We demonstrate the ability of our functional to reproduce existing experimental data for the minimum critical number of atoms
Nc required for droplet formation.
Nc is a challenging quantity for theoretical predictions, and the eGPE provides only a qualitative description of it, mainly when it is applied to dysprosium. We also use our approach to characterize the BEC-supersolid transition. The quantum-Monte-Carlo--based functional can be easily implemented in any existing eGPE code, improving the description of dipolar systems without increasing the computational cost.
The purpose of this paper is to study the dynamics of solutions to an extended Gross–Pitaevskii equation that models the formation of droplets in a dipolar Bose–Einstein condensate (BEC). The formation of these droplets has been recently discovered by driving the BEC into the strongly dipolar regime. Surprisingly, instead of collapsing, the system formed stable droplets. So far, no rigorous mathematical explanation has been proved. To the best of our knowledge, only experimental results have been obtained. The goal of this paper is to validate this breakthrough discovery. Many predictions/ conjectures properties of these droplets have been stated by some research groups in physics and engineering. In particular, it has been claimed that the stability of these droplets is a consequence of the presence of the damping term in the extended Gross–Pitaevskii equation under study. This term describes the three-body loss process. To accurately model the dynamics of formation of these droplets, it is necessary to consider a time-dependent harmonic trapping potential as well as other terms with different types of nonlinearity among them that describe the Lee–Huang–Yang (LHY). This presents some challenges that will be solved in this paper.