Entanglement distribution in $V$ and $\Lambda$ systems

TL;DR

This paper analyzes entanglement distribution in V and Lambda three-level atomic systems by using tomography to determine the emitted radiation's quantum states, revealing differences in entanglement and measurement feasibility.

Contribution

It provides a complete description of entanglement in V systems and discusses the challenges of tomography in Lambda systems, highlighting new measurement considerations.

Findings

V systems exhibit weak entanglement and are mostly mixed states.

Atomic state tomography in Lambda systems requires anti-normal ordered operators.

Two photon states in Lambda systems can be determined outside dark states.

Abstract

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 $\Lambda$ 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.