Coherently prepared nondegenerate Y-shaped four-level correlated emission laser: A source of tripartite entangled light

A detailed derivation of the master equation of the cavity radiation of a coherently prepared $Y$-shaped four-level correlated emission laser is presented. The outline of the procedures that can be employed in analytically solving the stochastic differential equations and the rate equations of various correlations are also provided. It is shown that coherently preparing the atoms in the upper two energy levels and the lower, initially, can lead to a genuine continuous variable tripartite entanglement. Moreover, preparing the atoms in the coherent superposition, other than the possible maximum or minimum, of the upper two energy levels, leaving the lower unpopulated, may lead to a similar observation. With the possibility of the atom at the intermediate energy level to take three different transition roots guided by the induced coherence, this system in general is found to encompass versatile options for practical utilization. In particular, coupling at least one of the dipole forbidden transitions by an external radiation is expected to enhance the degree of detectable entanglement.