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The motivation of this work is to develop a methodology to create deeper bound tetramers starting from the loosely bound FL tetramers. We envisage extending the tools for photoassociation of ultracold atoms to produce molecules in the excited electronic states, and stimulated Raman adiabatic passage (STIRAP) transfer of weakly bound diatoms to deeply bound molecules in the ground vibronic state via an excited intermediate state. We investigate similar routes of creating deeply bound tetramers starting from weakly bound states or a pair of colliding diatoms. We consider static-electric field shielded alkali diatomic molecules initially in their ground electronic X1Σ+ + X1Σ+ pair state. We identify the excited electronic manifold X1Σ+ + b3Π0 for photoassociation and an intermediate state for STIRAP transfer to deeply bound states in the X+X manifold. For this, we develop shielding methods for X+b and predict Frank-Condon factors (FCFs) between FL states of X+b and X+X. We also predict photoassociation spectra for shielded molecules to form FL tetramers in X+b manifold. We obtain favourable FCFs between ground and excited tetramer states and promising photoassociation spectra. Our theoretical results should guide future experiments for stabilizing weakly bound ultracold tetramers.
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