The Doppler-free optical-optical triple-resonance (DF-OOTR) spectroscopy and its line-shapes have been studied in detail theoretically and experimentally. The line center, linewidth and lineshape of an isolated DF-OOTR spectra compenent have been derived by using density matrix motion equation describing the interaction of a three-level system with three optical fields. The variations of the lineshape symmetry, the relative position and the strength of the Doppler-free Lorentzian dip to its background are comparable to the experimental traces varying with the relative intensities of the two mutual-saturating probe laser beams, as well as with the detuning of the first pumping laser from the intermediate level. The DF-OOTR technique shows a distinguished advantage especially in the labeling of the transitions and in the determination of absolute position of the upper level affected by perturbation shift, as these happened often in the dense molecular highly excited states.
The Doppler-free optical-optical triple-resonance (DF-OOTR) spectroscopy and its line-shapes have been studied in detail theoretically and experimentally. The line center, linewidth and lineshape of an isolated DF-OOTR spectra compenent have been derived by using density matrix motion equation describing the interaction of a three-level system with three optical fields. The variations of the lineshape symmetry, the relative position and the strength of the Doppler-free Lorentzian dip to its background are comparable to the experimental traces varying with the relative intensities of the two mutual-saturating probe laser beams, as well as with the detuning of the first pumping laser from the intermediate level. The DF-OOTR technique shows a distinguished advantage especially in the labeling of the transitions and in the determination of absolute position of the upper level affected by perturbation shift, as these happened often in the dense molecular highly excited states.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
This paper presents a theory of lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe fields using the steady-state solutions for the 3-level density matrix. When Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, each with an angular frequency half-width half maximum equal to the relaxation rates, which are assumed to be equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed to be much larger than the pump and probe Rabi frequencies and the probe frequency is higher than that of the pump, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit width that is proportional to the pump Rabi frequency, which is commonly known as power broadening. However, the width does not equal that Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.
This chapter shows that several non-linear features can be demonstrated and the line shape of sub-natural line width can be obtained by manipulation of the powers of the two interacting laser radiations. The interaction of the laser radiation can produce a coherent superposition of the atomic states such that atoms are trapped in one state so that the atomic system may be transparent even in the presence of radiation frequency that is on resonance. Saturation spectroscopy is more conveniently performed in three level atomic systems interacting with two laser radiations. One of the radiations, called pump beam, has higher intensity and frequency on resonance or close to resonance with the transition frequency across two levels of the atom. The second laser radiation, called probe beam, is weaker and interacts with two other energy levels, one of which is common to the pump transition. A few hyperfine transitions are within the envelope of one Doppler profile.
This paper describes a new class of techniques, called time-delayed laser saturation spectroscopy, which combine frequency- and time-domain methods of laser spectroscopy to provide a way of studying a molecular system as it evolves from an initially prepared stationary state to a second, final state. The specific example analyzed here is three-level free induction decay, in which the time-dependent gain of a Doppler-broadened molecular transition is probed after the sudden termination of an intense field resonating with a coupled transition. The theoretical calculation is based on the coupled density-matrix equations of motion in the slowly-varying envelope approximation. The time-delayed line shapes, which may be studied in either transmission or side fluorescence, exhibit linewidth asymmetries, line-shape deformations, Ramsey-type fringes, power broadening and dephasing, and dynamic Stark splittings and oscillatory decays. The technique provides a unique way of distinguishing the influence of Raman-type processes from that of population saturation and a means to separately measure the associated decay rates. The relationship of the present work to other studies is also discussed.
A theoretical study on double-resonance optical pumping for the transitions $5{S}_{1/2}\text{\ensuremath{-}}5{P}_{3/2}\text{\ensuremath{-}}4{D}_{3/2,5/2}$ of 87Rb atoms is presented. The full-density-matrix equations in the presence the probe and the coupling laser beams for all relevant magnetic sublevels of the hyperfine levels were solved numerically, and the absorption of a probe beam was calculated as a function of the detuning of the coupling beam. The calculated results were compared with experimental data, and they showed an excellent agreement. The results were also compared with the approximate results calculated when the coherence between the ground and the highest excited levels was neglected. We found that the dominant operating mechanism for double-resonance signals was the optical pumping rather than the two-photon coherence, although the latter affected the signals significantly.
Recent experiments have shown that optical pumping can produce line shapes with subnatural structure, and that this structure could prove to be useful for extracting oscillator strengths. A key question, however, regarding the optical-pumping technique's potential usefulness is how well it allows the determination of resonance line center. In the present paper we address this question theoretically by considering laser optical pumping and probing of an atomic beam. From the analysis (i) we find that depending on laser polarization the optical-pumping subnatural feature is either a dip or a signal enhancement, (ii) we derive the rigorously correct formula relating the dip width to the transition oscillator strength for an alkali-like atom exhibiting a homogeneous line shape, and (iii) we show that, compared to shot-noise-limited laser-induced fluorescence, the optical-pumping technique of signal enhancement is capable of a 15% improvement in the ability to find resonance line center.