Nonadiabatic interaction effects on population transfer inH2by stimulated Raman transition with partially overlapping laser pulses

Abstract

We have theoretically investigated the population transfer in a four-level ${\mathrm{H}}_{2}$ system by stimulated Raman transition from the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}({\ensuremath{\nu}}_{g}{=0,J}_{g}=0)$ level to higher rovibrational levels $({\ensuremath{\nu}}_{f}{,J}_{f})$ of the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state via the excited intermediate $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}({\ensuremath{\nu}}_{i}{=14,J}_{i}=1)$ and $C{}^{1}{\ensuremath{\Pi}}_{u}^{+}({\ensuremath{\nu}}_{i}{=3,J}_{i}=1)$ levels coupled with each other by nonadiabatic interaction, using time-dependent overlapping pump and Stokes laser fields. The density-matrix treatment, which permits the convenient inclusion of the spontaneous emissions from the intermediate levels, has been employed to describe the dynamics of the two-photon Raman resonance process. The present study performs the calculations of final populations (after both the pulses are over) of the ground and terminal levels for Q-branch ${(J}_{f}=0)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ and first overtone $({\ensuremath{\nu}}_{f}=2)$ transitions and the S-branch ${(J}_{f}=2)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ transition as a function of time delay between the two pulses for the cases of on-resonance as well as off-resonance excitations in a wide range $(2\ifmmode\times\else\texttimes\fi{}{10}^{5}--2\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ of peak intensities ${I}_{P}^{0}$ ${(I}_{S}^{0})$ of the pump (Stokes) fields. Both fields are assumed to have the same temporal shape, duration, peak intensities, and linear parallel polarizations. The accurate values of spontaneous radiative relaxation rates of the intermediate levels to the initial and final levels, taking into account their J and M dependence, are explicitly included in our calculations. The pulse width (full width at half maximum) ${\ensuremath{\tau}}_{p}$ is taken as 170 ns so that total spontaneous decay can occur during the pulse duration. The transfer efficiency is found to be very sensitive to the peak intensities of the laser pulses in each case of transition considered. Special attention is paid to the effects of the nonadiabatic (NA) interaction between $B(14,1)$ and $C(3,1)$ levels on population transfer efficiency. Calculations are also done in some particular cases using the adiabatic Born-Oppenheimer (ABO) approximation. The results with ABO approximation are found to differ remarkably from those obtained including NA interaction. Our calculations for the four-level ${\mathrm{H}}_{2}$ system reveal that almost complete population is transferred in counterintuitive pulse order for both on-resonance and off-resonance excitations with intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$ For intuitive pulse sequence also a large population transfer is achieved for on-resonance excitation at intermediate values of ${I}_{P}^{0}$ ${(I}_{S}^{0})$ and for off-resonance excitation at intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$