Researchers have explored methods for controlling the evolution of dipolar Bose-Einstein condensates (BECs), where the long-range and anisotropic magnetic dipole-dipole interaction plays a crucial role. These BECs exhibit superfluid and supersolid phases, the latter characterized by a modulation in the ground state density. Preparing this modulated supersolid state is an experimental challenge, as unwanted excitations arise during the finite-time evolution required to induce qualitative changes in the density wavefunction.

To overcome these difficulties, the study proposes using "shortcuts to adiabaticity" techniques to control the time-dependent evolution of dipolar BECs. They focus on modulating the interatomic scattering length, a parameter that can be precisely tuned in contemporary experiments. Two main approaches were explored: a variational technique based on the Euler-Lagrange equations for a separable ansatz describing the evolution of the superfluid state, and a direct optimization protocol to study the transition from the superfluid to the supersolid phase.

The developed protocols aim to minimize excitation generation and improve the fidelity of the process, i.e., the accuracy with which the desired state is achieved. The effectiveness of these methods is discussed in relation to the evolution time, suggesting that carefully designed time-dependent control can enable the efficient and robust preparation of supersolid states in dipolar BECs, opening new avenues for research into exotic quantum matter.