Non-stationary two-photon absorption coherent spectroscopy free of Doppler broadening in an atomic gas has been considered in detail. Correct account has been taken of the level degeneracy and depolarizing collisions. This two-photon Doppler-free spectroscopy has been developed for determining the relaxation rates of the atomic multipole moments in gas. A criterion to test the adopted model of the depolarizing collisions has been developed. A possible method for the identification of the atomic transitions in the angular momentum has been formulated. A technique of precisely determining the separation between the energy levels of the two-photon transition has been proposed. The conditions under which the Stokes wave is conjugated with respect to the probe pulse in amplitude, phase and polarization have been determined for the atomic gas in the presence of depolarizing collisions.
Time-resolved coherent anti-Stokes Raman-scattering (CARS) measurements are carried out for iodine (I2) in solid krypton matrices. The dependence of vibrational dephasing time on temperature and vibrational quantum number v is studied. The v dependence is approximately quadratic, while the temperature dependence of both vibrational dephasing and spectral shift, although weak, fits the exponential form characteristic of dephasing by pseudolocal phonons. The analysis of the data indicates that the frequency of the pseudolocal phonons is approximately 30 cm(-1). The longest dephasing times are observed for v = 2 being approximately 300 ps and limited by inhomogeneous broadening. An increase in the dephasing rate of v = 2 as the temperature is lowered to T = 2.6 K is taken as a clear indication of lattice-strain-induced inhomogeneity of the ensemble coherence.
Saturation effects in coherent anti-Stokes Raman scattering (CARS) spectroscopy are discussed. The discussion is limited to Raman-resonant CARS (${\ensuremath{\omega}}_{l}\ensuremath{-}{\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{21}$, where ${\ensuremath{\omega}}_{l,s}$ are the frequencies of the pump fields with powers
Pl,s, and ${\ensuremath{\omega}}_{21}$ is the frequency of the Raman transition $|1〉\ensuremath{\rightarrow}|2〉$) with the possible addition of a one-photon resonance (${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ is the frequency of the electronic transition $|1〉\ensuremath{\rightarrow}|3〉$). For these cases we show that the CARS polarization
pCARS is proportional to the off-diagonal density-matrix element ${\ensuremath{\rho}}_{21}$. In order to determine ${\ensuremath{\rho}}_{21}$, we use Laplace transforms to solve the Bloch equations for the effective two-level system
∣1〉 and
∣2〉 when ${\ensuremath{\omega}}_{l}$ is far from resonance, or for the three-level system
∣1〉,∣2〉, and
∣3〉, when ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$. The steady-state expression for
pCARS in the former case gives ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}{P}_{s}^{\frac{1}{2}}$ at low powers and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{\ensuremath{-}1}{2}}$ at high powers. In the three-level system, we show that when the pressure is low and at least one field is weak, the slow time dependence of ${\ensuremath{\rho}}_{21}$ must be considered. When one field is strong and the other weak, the CARS spectrum is Stark split. When
Pl is high, for example, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{0}{P}_{s}^{\frac{1}{2}}$ for ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$ and ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{({P}_{l}{P}_{s})}^{\frac{1}{2}}$ when ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}\ifmmode\pm\else\textpm\fi{}{V}_{13}$ where
V13 is the one-photon Rabi frequency for the $|1〉\ensuremath{\rightarrow}|3〉$ transition. The Wilcox-Lamb approximation is used to reduce the three-level Bloch equations to rate equations containing one- and two-photon terms. When the fields are so weak that both one- and two-photon terms are small compared to the decay terms, the usual expression for
pCARS is reproduced. If only the direct two-photon processes are important, the effective-two-system results are reproduced. When both fields are intense and nearly resonant, the steady state is rapidly achieved. The results for the case where one field is much stronger than the other are essentially the same as those for one strong and one weak field. When the fields are of comparable strength, ${\mathcal{p}}_{\mathrm{CARS}}\ensuremath{\propto}{P}_{l}^{\frac{1}{2}}{P}_{s}^{0}$ for ${\ensuremath{\omega}}_{l}\ensuremath{\simeq}{\ensuremath{\omega}}_{31}$ and ${\ensuremath{\omega}}_{s}\ensuremath{\simeq}{\ensuremath{\omega}}_{32}$, and the CARS spectrum is split into five components.
A detailed analysis is made of transient coherent Doppler-free spectroscopy of two-photon absorption in an atomic gas. The hyperfine structure of the levels and elastic depolarizing collisions are allowed for. The analysis is used to develop a method for the determination of the time constant of relaxation of the multipole moments of atoms when such relaxation is due to radiative decay and collisions with a buffer gas. A way of determining the separation between the hyperfine structure components is demonstrated. It is shown that under conditions of excitation of the atoms the hyperfine structure of the levels can give rise to quantum beats of the density of a conjugate wave.
Phase-and-polarization coherent control is applied to control the nonlinear response of a quantum system. We use it to obtain high-resolution background-free single-pulse coherent anti-Stokes Raman spectra. The ability to control both the spectral phase and the spectral polarization enables measurement of a specific off-diagonal susceptibility tensor element while exploiting the different spectral response of the resonant Raman signal and the nonresonant background to achieve maximal background suppression.
A method of determining the relaxation constants of the multipole moments of gas atoms with non-zero nuclear spin has been proposed by using the polarisation properties and damping law of the non-stationary Raman scattering (NRS) of light. Correct account was taken of the depolarising atomic collisions and of the effect of the hyperfine structure (HFS) of the atomic levels. The NRS polarisation properties found have been assumed to be a basis method for the identification of optically forbidden transitions in both the electronic and total angular momenta. A possible method of determining the HFS constants through analysis of the NRS quantum beats has been established.