  Quantum many-body phases offer unique properties and emergent phenomena,
making them an active area of research. A promising approach for their
experimental realization in model systems is to adiabatically follow the ground
state of a quantum Hamiltonian from a product state of isolated particles to
one that is strongly-correlated. Such protocols are relevant also more broadly
in coherent quantum annealing and adiabatic quantum computing. Here we explore
one such protocol in a system of ultracold atoms in an optical lattice. A fully
magnetized state is connected to a correlated zero-magnetization state (an
xy-ferromagnet) by a many-body spin rotation, realized by sweeping the detuning
and power of a microwave field. The efficiency is characterized by applying a
reverse sweep with a variable relative phase. We restore up to 50% of the
original magnetization independent of the relative phase, evidence for the
formation of correlations. The protocol is limited by the many-body gap of the
final state, which is inversely proportional to system size, and technical
noise. Our experimental and theoretical studies highlight the potential and
challenges for adiabatic preparation protocols to prepare many-body eigenstates
of spin Hamiltonians.
