  We propose an implementation of the quantum search algorithm of a marked item
in an unsorted list of N items by adiabatic passage in a cavity-laser-atom
system. We use an ensemble of N identical three-level atoms trapped in a
single-mode cavity and driven by two lasers. In each atom, the same level
represents a database entry. One of the atoms is marked by having an energy gap
between its two ground states. Appropriate time delays between the two laser
pulses allow one to populate the marked state starting from an initial
entangled state within a decoherence-free adiabatic subspace. The time to
achieve such a process is shown to exhibit the Grover speedup.
