The optical Hanle effect (light-shift-induced zero-field level crossing) has been investigated theoretically and experimentally. In the case of a $J=0\ensuremath{\rightarrow}1\ensuremath{\rightarrow}0$ three-level system and of a $J=0\ensuremath{\rightarrow}1$ two-level system, the resonance line shape has been obtained using a nonlinear-response-function method. Approximate expressions, valid under the conditions for the observation of light shifts, are obtained and compared with exact calculations as well as with the corresponding expression for the magnetic Hanle effect. As concerns the weak laser beam which produces the coherent excitation of atomic substates, we have calculated the linear response in the limiting case of monochromatic and of broad-band excitation. The experimental investigation has been performed for the Ba resonance line using two cw dye lasers at $\ensuremath{\lambda}=5535$ \AA{} and an atomic beam. The absorption- and dispersion-shaped level crossing resonances have been observed, for narrow- and broad-band excitation, by varying the power of the strong nonresonant laser beam. We have checked that the line shapes are only dependent upon the reduced variable $\frac{{P}_{L}}{\ensuremath{\delta}}$ (
PL; beam power; $\ensuremath{\delta}$: frequency detuning). Using the theoretical expressions, we have tried to fit the experimental curves. Provided that the Gaussian distribution of the beams is taken into account, we have obtained a good agreement between theory and experiment for the whole set of experimental data.
We have investigated the two basic types of Hanle fluorescence spectra, distinguished by the direction of observation, from a V-type atom with a
Jg =0\ensuremath{\leftrightarrows}
Je =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
GXinc(\ensuremath{\omega}) is dark for all Rabi frequencies, while the incoherent fluorescence spectrum
GYinc(\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
GXinc(\ensuremath{\omega}) has four peaks, while
GYinc(\ensuremath{\omega}) has a Mollow-like triplet, and the integrated area (i.e., the fluorescence intensity) under the spectrum
GXinc(\ensuremath{\omega}) is much less than that of
GYinc(\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
GXinc(\ensuremath{\omega}) is much greater than that of
GYinc(\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.
Abstract The development with time of the excitation of a transition between two atomic or molecular energy levels under the influence of monochromatic laser radiation is examined under conditions of strictly homogeneous line-broadening. The ratio of the number of atoms or molecules, N2, in an excited state to the total number, N, is calculated for various ratios of the intensity parameter β ═ E0μ/ħ to the half line-width γ. E0 is the amplitude of the electric field in the incident radiation and the dipole moment matrix element for the transition. Exact expressions for N2/N as a function of time are given for the situation when the frequency ω/2π of the radiation is exactly equal to that of the transition ω0/2π. Numerical calculations are made for the situation when the ‘detuning’ δ ═ ω — ω0 is not equal to zero. Approximate expressions are also derived in terms of δ for use in a later paper which deals with mixed homogeneous and inhomogeneous line-broadening.