Recoil-induced resonances in pump-probe spectroscopy

When a pump field and probe field simultaneously drive an electronic-state atomic transition, the probe field absorption spectrum can consist of an absorption peak centered near Δ’=0 and amplification peak centered near Δ’=2Δ (Δ and Δ’ are the pump and probe field detunings from the atomic transition frequency, respectively). This type of spectrum is seen in the limit ‖Δ‖≫χ≫Γ, where χ is the Rabi frequency associated with the pump field and 2Γ is the homogeneous width associated with the atomic transition. For atoms cooled below the recoil limit of laser cooling, the qualitative nature of the probe absorption spectrum can undergo a dramatic change. Provided that the recoil splitting ${\mathrm{\omega }}_{\mathit{k}}$ is larger than the homogeneous decay rate (as might occur in the case of a forbidden transition), the absorption and amplification features each split into an absorption-amplification doublet. In addition, structure is found in the probe absorption spectrum near Δ’=Δ; this structure consists of two absorption-amplification doublets. Both doublets can be resolved if ${\mathrm{\omega }}_{\mathit{k}}$>Γ. If ${\mathrm{\omega }}_{\mathit{k}}$<Γ, one of the doublets can be resolved provided that ${\mathrm{\omega }}_{\mathit{k}}$>${\mathrm{\Gamma }}_{\mathit{A}}$, where ${\mathrm{\Gamma }}_{\mathit{A}}$ is some effective atomic ground state width in the problem. The positions, widths, and relative weights of all the components are readily predicted using a dressed-atom theory in which quantization of the center-of-mass momentum is included. An analytical expression for the probe field spectrum is obtained for a simple case in which spontaneous decay to the lower level is neglected. Validity criteria for the results are discussed.