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Entanglement distribution in $V$ and $Λ$ systems

We determine the two mode fock state of the radiation emitted by $V$ type three level atomic systems using the method of tomography described in our previous work. Utilizing the knowledge of the atomic/two photon state we provide a complete description of the entanglement distribution in the full parameter space in the case of the $V$ system. The $V$ system shows weak entanglement and is predominantly in a mixed state in two dimensional subspace. Unlike the case of $V$ and the ladder systems, atomic state tomography of the $Λ$ system requires the measurement of anti-normal ordered operators and more importantly, there is no equivalence between the atomic and the two photon density matrix. Tomography of this atomic state is not possible with existing types of measurements. However the two photon state may be determined when it is not in a dark state.