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A detailed derivation of the master equation of the cavity radiation of acoherently prepared $Y$-shaped four-level correlated emission laser ispresented. The outline of the procedures that can be employed in analyticallysolving the stochastic differential equations and the rate equations of variouscorrelations are also provided. It is shown that coherently preparing the atomsin the upper two energy levels and the lower, initially, can lead to a genuinecontinuous variable tripartite entanglement. Moreover, preparing the atoms inthe coherent superposition, other than the possible maximum or minimum, of theupper two energy levels, leaving the lower unpopulated, may lead to a similarobservation. With the possibility of the atom at the intermediate energy levelto take three different transition roots guided by the induced coherence, thissystem in general is found to encompass versatile options for practicalutilization. In particular, coupling at least one of the dipole forbiddentransitions by an external radiation is expected to enhance the degree ofdetectable entanglement.

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