Note that this light shift is not equal to twice the single atom light shifts. The single atom light-shifts are then cancelled by a global pulse that implements U = exp ⁡ ⁡ ( − − i ϕ ϕ 1 | 1 ⟩ ⟩ ⟨ ⟨ 1 | ) to get rid of the single qubit light shifts. The truth table for this gate is given to the right. This protocol leaves a total phase of ∫ ∫ ( E L S ( 2 ) ( t ) − − 2 E L S ( 1 ) ( t ) ) d t phase on the | 11 ⟩ ⟩ state. We can choose the pulses so that this phase equals π π , making it a controlled-Z gate. An extension to this gate was introduced to make it robust against errors in reference.