Adiabatic quantum search with atoms in a cavity driven by lasers

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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.