Density-matrix description of partially coherent spin-orbit wave packets produced in short-laser-pulse photodetachment

We investigate orbital alignment dynamics within the valence shell of atoms in coherently excited $j=3/2,1/2$ fine-structure manifolds generated by short-pulse photodetachment of F$^-$, Cl$^-$ and Br$^-$ anions. Using Keldysh-type theory, we calculate the density matrix of the residual atoms generated by few-cycle pulses, whose elements determine the populations and coherence among the electronic states. Our calculations demonstrate that the degree of atomic coherence can be represented by a near universal function of the ratio between the pulse duration $\tilde{\tau}_p$ and the beat period $\tau_{j'j}$ of the atomic system, which allows one to characterize the coherence generated in atomic states.