The line shape of a pair of Doppler-broadened closely spaced transitions sharing a common lower level and under the effect of a standing-wave monochromatic radiation field is studied. The eight steady-state optical Bloch equations are solved analytically to obtain the polarization by retaining terms up to the third power in the electric-field amplitude. The absorption coefficient derived for the standing-wave case consists of two Lamb dips for the two allowed transitions at ${\mathrm{\ensuremath{\omega}}}_{1}$ and ${\mathrm{\ensuremath{\omega}}}_{2}$ and a crossover resonance dip at the intermediate frequency ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$=(${\mathrm{\ensuremath{\omega}}}_{1}$+${\mathrm{\ensuremath{\omega}}}_{2}$)/2. The Lamp-dip peak frequencies show intensity-dependent shifts. Numerical computations are presented for different values of Rabi frequencies and relaxation linewidth parameters, which are small compared to the frequency difference \ensuremath{\Delta}=${\mathrm{\ensuremath{\omega}}}_{2}$-${\mathrm{\ensuremath{\omega}}}_{1}$. The computed line shape and frequency shift are compared with the observed results in the Balmer ${\mathrm{H}}_{\mathrm{\ensuremath{\alpha}}}$ line of hydrogen and the infrared Zeeman spectra of methane.
The
5S1/2→6P3/2 transition of rubidium at
420 nm is a promising candidate for a portable warm-vapor all-optical atomic clock. Despite recent precision spectroscopy studies at
420 nm in Rb, an experimental determination of the saturation intensity of this transition has not yet been reported. The saturation intensity is a fundamental parameter that influences the identification of a potential clock transition frequency in terms of optimizing various intensity-dependent parameters and connected systematics. In this work, we report the first experimental measurement of the saturation intensity of the
420 nm transition in Rb, obtaining
(23.18±0.28) mW/cm
2 for the
87Rb
F=2→F′=3 transition and
(25.56±0.37) mW/cm
2 for the
85Rb
F=3→F′=4 transition, in excellent agreement with theoretical predictions. We further investigate the temperature dependence of the Doppler-free Lamb-dip amplitude and linewidth over
59.03 ± 0.37 -
91.20 ± 0.90∘C in a
100 mm commercial vapor cell, identifying around
82.02 ± 0.73∘C as the optimal operating temperature, where the signal-to-noise ratio of the Lamb-dip amplitude with temperature reaches a maximum and the observed Lamb-dip linewidth exhibits a minimum. We also present precise measurements of the magnetic-dipole (
A) and electric-quadrupole (
B) hyperfine constants of the
6P3/2 state for both isotopes, with the measured values being consistent with previously reported values for the hyperfine constants.
We propose a new simple approximate solution to the two-state rate equation model for analyzing decay signals of saturation cavity ring-down spectrometry in the adiabatic and low-saturation regime. It helps obtain baseline-immune Doppler-free spectra for hyperfine transitions and linear absorption coefficients of a gas in the saturation regime. To demonstrate it, a baseline-immune Lamb dip spectrum of the R1A2 transitions in the 2v2 + v3 band of methane was recorded. The line position was determined to be 6 076.108 457 7(11) cm-1, the relative uncertainty being 1.8 × 10-10.