  A physical implementation of the adiabatic Grover search is theoretically
investigated in a system of N identical three-level atoms trapped in a single
mode cavity. Some of the atoms are marked through the presence of an energy gap
between their two ground states. The search is controlled by two partially
delayed lasers which allow a deterministic adiabatic transfer from an initially
entangled state to the marked states. Pulse schemes are proposed to satisfy the
Grover speedup either exactly or approximately, and the success rate of the
search is calculated.
