The recent evolution toward resonant conditions of the two-color resonant four-wave-mixing (TC-RFWM) spectroscopy has been dictated by the high sensitivity required experimentally. While some models have been used in different contexts such as light pressure forces in strong polychromatic fields, magnetically assisted Sisyphus effect, or multiphoton resonances in \ensuremath{\Lambda} atoms, the existence in molecules of additional processes such as nonradiative transitions and rotational or vibrational dephasings requires the extension of previous models. For this reason, we give here a general description of the internal dynamics for a molecule undergoing two strong grating beams, acting either on two different transitions sharing a common level or on the same transition, and one weak probe beam to reproduce the ground-state grating and stimulated emission pumping configurations of TC-RFWM spectroscopy. By combining high spectral resolution and strong grating beams, we show that the TC-RFWM spectrum is very sensitive to the transition constants, dephasing constants, as well as to the transverse velocity of the molecules in the jet. The last case corresponding to a bichromatic field acting on a single transition is used to explain the origin of the line-shape asymmetry observed experimentally on jet-cooled molecules.
The recent evolution toward resonant conditions of the two-color resonant four-wave-mixing (TC-RFWM) spectroscopy has been dictated by the high sensitivity required experimentally. While some models have been used in different contexts such as light pressure forces in strong polychromatic fields, magnetically assisted Sisyphus effect, or multiphoton resonances in \ensuremath{\Lambda} atoms, the existence in molecules of additional processes such as nonradiative transitions and rotational or vibrational dephasings requires the extension of previous models. For this reason, we give here a general description of the internal dynamics for a molecule undergoing two strong grating beams, acting either on two different transitions sharing a common level or on the same transition, and one weak probe beam to reproduce the ground-state grating and stimulated emission pumping configurations of TC-RFWM spectroscopy. By combining high spectral resolution and strong grating beams, we show that the TC-RFWM spectrum is very sensitive to the transition constants, dephasing constants, as well as to the transverse velocity of the molecules in the jet. The last case corresponding to a bichromatic field acting on a single transition is used to explain the origin of the line-shape asymmetry observed experimentally on jet-cooled molecules.
Applying a recently developed ns Two-Colour Resonant Four-Wave Mixing (TC-RFWM) technique, a number of resonance lines forbidden by conventional three-level schemes are observed. A theoretical frequency-domain picture is developed with the help of exact (off-diagonal) relaxation matrices and general four-level schemes. The newly observed extra resonances are induced by collisional transfer of rotational energy. The role of the population, orientation and alignment gratings that are formed in both electronic states coupled by laser fields is elucidated. Relaxation models using the fast-collision approximation are elaborated for Hund's cases a and b giving quantitative arguments for the proposed interpretation. The potential of the TC-RFWM technique to study state-to-state transfer rates is emphasized.
We present a combined theoretical and experimental study of the effects of laser polarization on optical coherences produced in two-color, resonant four-wave mixing (TC-RFWM). A time-dependent model incorporating diagrammatic perturbation theory and spherical tensor formalism is used to interpret observations of quantum beats due to molecular hyperfine structure in time-resolved TC-RFWM in nitric oxide. Good agreement is found between the model and the observed time-resolved signals for two distinct excitation schemes and a variety of polarization configurations including both polarization and population gratings. Measured hyperfine energy intervals are reported for the $X{}^{2}{\ensuremath{\Pi}}_{1/2},$ v=0 ground state and the $A{}^{2}{\ensuremath{\Sigma}}^{+},$ v=0 excited state of NO. The experimental results demonstrate that TC-RFWM can be used to perform state-selective, quantum beat spectroscopy in three-level systems by suitably designing three experimental features: the excitation scheme for the matter-field interaction, the time ordering of the laser pulses, and the polarization of the incident laser beams.
In this paper we present theoretical calculations relating to pump-probe and four-wave mixing spectroscopy. In pump-probe spectroscopy, one measures the absorption profile for the situation when an arbitrary strong pump field drives a given transition and a probe (weak) field drives the same transition. We have studied the influence of level degeneracy and field polarization on pump-probe and four-wave mixing signals. Our results indicate that for some closed systems (no population loss to the reservoir) it is possible to observe resonances that are characterized by the ground state width. Previous calculations indicate that for a nondegenerate system this resonance can appear only for an open system, the so-called "pressure induced resonances.”1 Our result, which contradicts this conclusion, can be understood by noting the fact that there are in general three irreducible tensor2 (in general) contributions to the line shape (K = 0 population, K = 1 orientation, and K = 2 alignment). Thus, even if the system is closed for the population it may still remain open for orientation or alignment; this effect is responsible for the narrow resonance. Specific calculations are presented for J = 1/2 → 1/2 and J = 1→2 transitions.
The purpose of this research is to study the dynamic behavior of a resonant system using four-wave-mixing spectroscopy (FWM). From this study, we have obtained rich information about the FWM spectral response of systems which have different state-specific reservoir couplings. Atomic sodium (Na) is used as our model system. It is shown that the FWM spectral response depends strongly on how each level couples to the vacuum radiation field (through spontaneous emission). This effect is illustrated in the line shape obtained from a nearly degenerate FWM (NDFWM) experiment for a simple two-level system in Na. A narrow spike on top of a wide resonance is observed at zero pump-probe detuning (δ = 0) when the upper-state decay rate $\gamma\sb2$ to the reservoir is larger than the lower-state decay rate $\gamma\sb1$. The width of the spike is 2$\gamma\sb1$ and the width of the wide resonance is determined by the total upper-level decay rate (2$\gamma\sbsp{2}{\rm t}$). From the NDFWM spectrum, all the decay rates characterizing a two-level system may be measured directly. If magnetic substate degeneracy is included, the NDFWM line shape has contributions arising from orientation and alignment gratings, as well as from population gratings. For a two-level system closed with respect to population, the orientation or alignment gratings may contribute a narrow resonance at δ = 0 in the NDFWM response. These features are demonstrated for the first time by using NDFWM. Reservoir coupling can also occur through collisions with externally added gas. Collisions can cause a closed two-level system to become open, resulting in NDFWM spectra that show a narrow resonance at δ = 0 with a width below the residual Doppler width (Dicke narrowing). This is also the first time that Dicke narrowing has been observed in population terms. Finally, we present a calculation of the NDFWM response for strong degenerate pump fields and a weak probe field. We compare the differences between NDFWM spectra of closed two- and three-level systems in the presence of strong pumps.
In this article, we analyse a new sensitive spectroscopic technique in which a sample cell is irradiated by a two-frequency pump beam (ω + Δ ± δ/2) and a counter-propagating probe beam (ω). The phase-conjugate fields re-emitted at frequencies ω ± δ, via four-wave mixing processes, are detected through their heterodyne beating with the probe field. The properties of the heterodyne beat signal are studied by means of a perturbation calculation of the nonlinear response of the medium, carried out to the third order in the incident fields. In resonant gas media, the emission lineshape exhibits a Doppler-free doublet structure [frequency splitting 3 δ/2 for single-photon resonances, and δ/2 for two-photon transitions]. By using a phase-sensitive detection of the beat signal, one can separately analyse real (dispersion) or imaginary parts (absorption) of the nonlinear susceptibility. For single-photon transitions, the signal phase shift is related to the atomic levels lifetime and allows one to study the relaxation dynamics in gas phase (like quenching collisions, velocity diffusion, etc...). This is particularly interesting for cross-over resonances, in which only the common level contributes. In three-level systems, one also predicts a selective resonant enhancement of the phase-conjugate emission through Raman-type two-photon processes. Most of these predictions have been experimentally verified.
Degenerate (one-color) and two-color variants of the resonant four-wave mixing (RFWM) have developed into a sensitive and nonintrusive spectroscopic tool to study molecules in different gaseous environments. Yet, the fully non-degenerate (four-color, 4C) RFWM was scrutinized and implemented only for the Coherent AntiStokes Raman Scattering (CARS) excitation schemefootnote{B. Attal-Tr'{e}tout, P. Berlemont, and J. P. Taran, Mol. Phys. textbf{70}, 1 (1990).},footnote{J.P. Kuehner, S.V. Naik, W.D. Kulatilaka, N. Chai, N.M. Laurendeau, R.P. Lucht, M.O. Scully, S. Roy, A.K. Patnaik, and J.R. Gord, J. Chem. Phys. textbf{128}, 174308 (2008).} . Here, by using the line-space approachfootnote{A. Kouzov and P. Radi, J. Chem. Phys. textbf{140}, 194302 (2014).}, we analyze other 4C-RFWM schemes potentially interesting for the efficient up- and down-frequency conversion as well as for studies of molecular states. Decoupled expressions of the 4C-RFWM amplitudes are derived which allows to predict their polarization dependence.