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A scheme is presented to perform an entangling gate between two atomicensembles or Bose-Einstein condensates in a optical cavity with a commonoptical mode. The method involves using a generalized Stimulated RamanAdiabatic Passage (STIRAP) to adiabatically evolve the ground state. We showthat dark states exist for any atom number within the cavities, and find thatthe operation produces an unusual type of evolution where the minimum of thenumber of atoms between two levels transitions to another state. This producesa unconventional type of entangling Hamiltonian which creates a phase dependingon the minimum operation. We analyze its reliability under a variety ofconditions ranging from the ideal decoherence-free case to that includingphoton loss and spontaneous emission. Ways of combating decoherence areanalyzed and the amount of entanglement that is generated is calculated.

Adiabatic entangling gate of Bose-Einstein condensates based on the minimum function