Hanle fluorescence spectra of an atom with aJg=0⇆Je=1 transition

Abstract

We have investigated the two basic types of Hanle fluorescence spectra, distinguished by the direction of observation, from a V-type atom with a ${\mathrm{J}}_{\mathrm{g}}$ =0\ensuremath{\leftrightarrows}${\mathrm{J}}_{\mathrm{e}}$ =1 transition excited by a linearly polarized laser. In the absence of a magnetic field to lift the Zeeman degeneracy of the sublevels, the incoherent fluorescence spectrum ${\mathrm{G}}_{\mathrm{X}}^{\mathrm{inc}}$(\ensuremath{\omega}) is dark for all Rabi frequencies, while the incoherent fluorescence spectrum ${\mathrm{G}}_{\mathrm{Y}}^{\mathrm{inc}}$(\ensuremath{\omega}) exhibits a single peak for small Rabi frequencies and a Mollow-like triplet for large Rabi frequencies. However, if a magnetic field is applied, the incoherent spectra are composed, in general, of five peaks. When ${\mathrm{\ensuremath{\omega}}}_{\mathrm{B}}$ \ensuremath{\ll}\ensuremath{\Omega}, the incoherent spectrum ${\mathrm{G}}_{\mathrm{X}}^{\mathrm{inc}}$(\ensuremath{\omega}) has four peaks, while ${\mathrm{G}}_{\mathrm{Y}}^{\mathrm{inc}}$(\ensuremath{\omega}) has a Mollow-like triplet, and the integrated area (i.e., the fluorescence intensity) under the spectrum ${\mathrm{G}}_{\mathrm{X}}^{\mathrm{inc}}$(\ensuremath{\omega}) is much less than that of ${\mathrm{G}}_{\mathrm{Y}}^{\mathrm{inc}}$(\ensuremath{\omega}). When ${\mathrm{\ensuremath{\omega}}}_{\mathrm{B}}$ \ensuremath{\gg}:\ensuremath{\Omega}, both incoherent spectra have a two-peak structure similar to that of a two-level atom far off resonance, but the integrated area under the spectrum ${\mathrm{G}}_{\mathrm{X}}^{\mathrm{inc}}$(\ensuremath{\omega}) is much greater than that of ${\mathrm{G}}_{\mathrm{Y}}^{\mathrm{inc}}$(\ensuremath{\omega}). When ${\mathrm{\ensuremath{\omega}}}_{\mathrm{B}}$ =\ensuremath{\Omega}\ensuremath{\gg}:\ensuremath{\gamma}, both spectra have a similar five-peak structure, and the same integrated area. The results obtained are interpreted in the dressed atomic state representation. In the strong-field limit, the secular approximation is invoked, and analytical expressions of the resonance fluorescence spectra are derived which demonstrate the dependence of the peak heights and widths of the resonance fluorescence spectra on the intensities of the magnetic and linear polarized laser fields in a more transparent way.