When polarized light is absorbed by an atom, the excited atomic system carries information about the initial polarization of light. For the light that carries an orbital angular momentum, or the twisted light, the polarization states are described by eight independent parameters, as opposed to three Stokes parameters for plane waves. We use a parameterization of the spin-density matrix of the twisted light in terms of vector and tensor polarization, in analogy with massive spin-1 particles, and derive formulae that define atoms response to specific polarization components of the twisted light. It is shown that for dipole ($Sto P$) atomic transitions, the atoms polarization is in one-to-one correspondence with polarization of the incident light; this relation is violated, however, for the transitions of higher multipolarity ($Sto D$, $Sto F$, etc.) We pay special attention to contributions of the longitudinal electric field into the matrix elements of atomic transitions.
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