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Large cross-phase shifts among three slow weak pulses via triple electromagnetically induced transparency

We propose a scheme to generate triple electromagnetically induced transparency (TEIT) where EIT is induced simultaneously for three weak slow light pulses. We calculate the complex polarizibilities and group velocities of the three slow light pulses in the weak field limit by means of the full Hamiltonian approach. It is shown that strong cross-phase modulation can be realized and large cross-phase shifts on the order of π radians can be generated for three slow weak pulses even if light pulses of ultrasmall energies, i.e. single photons, are involved. It is indicated that under certain conditions the three slow weak pulses can reach matching of group velocities in a single species of 87Rb atoms.