  Fractional quantum Hall systems are among the most exciting strongly
correlated systems. Accessing them microscopically via quantum simulations with
ultracold atoms would be an important achievement toward a better understanding
of this strongly correlated state of matter. A promising approach is to confine
a small number of bosonic atoms in a quasi-two-dimensional rotating trap, which
mimics the magnetic field. For rotation frequencies close to the in-plane
trapping frequency, the ground state is predicted to be a bosonic analog of the
Laughlin state. Here, we study the problem of the adiabatic preparation of the
Laughlin state by ramping the rotation frequency and controlling the
ellipticity of the trapping potential. By employing adapted ramping speeds for
rotation frequency and ellipticity, and large trap deformations, we improve the
preparation time for high-fidelity Laughlin states by a factor of ten in
comparison to previous studies. With this improvement of the adiabatic protocol
the Laughlin state can be prepared with current experimental technology.
