We calculate a probe response of a homogeneously broadened two-level transition in the presence of a strong pump. The derivation is carried out for a generalized interaction Hamiltonian, which gives a uniform account of both the Bloch - Siegert shift and dynamic Stark splitting. It is shown that the Bloch - Siegert shift can be viewed as an extreme situation of the dynamic Stark splitting, commonly known as light shift in the literature. Finally using a perturbative approach an analytical expression for the Bloch - Siegert shift is obtained, which is compared with the previous results.
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Wei et al. (1997) studied this question.
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