  We present the derivation of the frequency dependent scalar, vector, and
tensor dynamical polarizabilities for the two hyperfine levels of the 87Rb atom
5s ground state. Based on the characterization of the dynamical
polarizabilities, we analyze and measure the differential vector and tensor
light shift between the 5s ground state sub-levels with near-resonant,
stimulated Raman transitions. These results clarify that the tensor
polarizabilities for the ground states of alkali atoms are absent when the
light field is far-detuned from the atomic resonance and the total electronic
angular momentum J is a good quantum number. In the near resonant case, the
light shifts are non-trivial and the determination of the frequency dependent
vector and tensor dynamic polarizabilities will help to achieve higher
fidelities for applications of neutral atoms in quantum information and
precision measurements.
