We consider pseudo-scalar and pseudo-vector interaction of atomic electrons with hypothetical dark matter particles (e.g., axions). These interactions lead to oscillating atomic parity non-conserving (PNC) amplitudes and/or oscillating electric dipole moments (EDM). In static
limit for PNC, existing atomic PNC experiments can be used to constrain time component of the pseudo-vector field.
Possible variation of fundamental constants is suggested by theories unifying gravity with other interactions. Evidence of the space/time variation of the fine structure constant alpha is found in
the quasar absorption spectra. Optical transitions in highly charged ions can be used as sensitive tools for studying time variation of alpha in laboratory.