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C = 0). The conditional phase shift [Eq. (4)] can be achieved by repeated operation on the single atom of a Raman π pulse in the order (atom A) → (atom B) → (atom B) → (atom A), [rather than (atom A) → (atom B) → (atom A) → (atom B) as suggested in Ref. [4]]. Our four-photon protocol in a sense unites the four separate pulses into one with the use of large off-resonant detunings for all single-atom processes. In doing so, we end up with a protocol without the requirement for individual atom addressing.
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