Polynomial effective density in quotient of $SL_2(Q_p) × SL_2(Q_p)$

We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of SL₂(Qₚ) in SL₂(Qₚ) × SL₂(Qₚ) for prime number $p > 3$. The proof is based on the use of Margulis function, a restricted projection theorem on Qₚ³, and spectral gap of the ambient space.