Theory of the inelastic lineshape for two-step sub-Doppler excitation

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Abstract
The inelastic lineshape expression for two-step sub-Doppler excitation of a four-level atomic or molecular system in the presence of a low-pressure perturber is derived by treating the collisional effects to first order. The degeneracies of the rotational levels and the tensorial coupling due to the laser fields and collisions have been fully taken into account by working with the irreducible tensorial components of the density matrix. Explicit expressions for the collision cross sections affecting the lineshape are derived using the Liouville-space formalism.