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We study the coupled atom-molecular quantized ring vortices of 87RbBose-Einstein Condensates (BEC) trapped in a rotating three dimensional (3D)anisotropic cylindrical trap both in time independent and time-dependentGross-Pitaevskii approaches. For atom to molecular conversion and vice-versatwo-photon Raman photoassociation scheme has been used. Atomic and molecularstationary state solutions show that the different number of nodes and crestsformed in the density profile (as a function of r and z) for differentcombinations of radial (n) and axial (nz) quantum numbers at a fixed azimuthalquantum number l=2, give rise to different structure around the 3D ring vortexcentered at r=0. We have considered both spontaneous and induced decays andcompared the results with those without considering the decays. The out ofphase oscillation of atomic and molecular numbers in two vortex states both inpresence and absence of external decays is the signature of coherence due tothe atom-molecular coupling. This coherence is also implemented in theevolution of coupled atomic and molecular vortices. Intensity of molecular ringvortices grows with progress in time in expense of that of atomic ring vorticesand vice versa. It is found that the intensity of the coupled atomic andmolecular ring vortices starts oscillation out of phase during evolution.Dependence of the atom-molecular conversion efficiency and the lifetime of thesystem on the laser intensity of photoassociation lasers and the total numberof atoms in two different vortex states reveals that formation ofatom-molecular coupled vortices and the efficiency of formation can becontrolled by varying these parameters. Linear stability analysis of vortexstates as a function of different system parameters shows that the atomicvortices are more stable than molecular vortices.

Investigation of 3D-Quantized Ring Vortices in Rotating Coupled Atom-Molecular BEC