Two-photon-assisted collisions in ultracold gases of polar molecules

We present a theoretical formalism to treat the ultracold dynamics of a pair of colliding polar molecules submitted to two laser fields. We express the dressed Hamiltonian including the dipole-dipole interaction of the colliding molecular pair, both in their ground and electronic excited states, as well as their interaction with the two laser fields. We apply adiabatic elimination of the electronic excited state to reduce the size of the dressed-state basis in which the dressed Hamiltonian is expressed. In an application, we investigate the feasibility of two-photon collisional shielding between two $^{23}\mathrm{Na}^{39}\mathrm{K}$ molecules, which could be favored by the Raman resonance condition suppressing unwanted spontaneous emission and photon scattering. We demonstrate the influence of laser Rabi frequencies on the dynamics through the computation of elastic, inelastic, and reactive collision rates, which is still insufficient to ensure noticeable shielding.