We have theoretically investigated the population transfer from the initial ground rovibrational level v(g)=0, J(g)=0 to the final rovibrational levels v(f)=1,2, J(f)=0 of the ground electronic state X (1)Sigma(g) (+) via the resonant intermediate level v(i)=6, J(i)=0 of the excited electronic state EF (1)Sigma(g) (+) of H(2) molecule by (2+2)-photon stimulated hyper-Raman passage (STIHRP). The density matrix technique has been employed to evaluate the population transfer to the final target levels using linearly chirped pump and Stokes laser pulses with different chirp rates. Both the pulses are considered to have the same temporal shape, pulse width, and linear parallel polarizations. We have studied in detail the dependence of the population transfer on the set of laser parameters for pulse (peak) intensities in the ranges of 1.5 x 10(11)-1.0 x 10(12) and 1.0 x 10(12)-7.0 x 10(12) W/cm(2). The corresponding pulse widths (full width at half maximum) are of the order of 115-200 and 15-30 ps. We have found that the chirp rate parameters can be optimized to achieve almost complete population transfer from the ground (g) to the final (f) target levels. This, to our knowledge, is the first application of a (2+2)-photon STIHRP process with chirpings to a model molecular system (H(2)). The study demonstrates the suitability of the chirped (2+2)-photon STIHRP technique for selective and almost total inversion of vibrational population in a diatomic molecule.
We have theoretically investigated the population transfer from the initial ground rovibrational level v(g)=0, J(g)=0 to the final rovibrational levels v(f)=1,2, J(f)=0 of the ground electronic state X (1)Sigma(g) (+) via the resonant intermediate level v(i)=6, J(i)=0 of the excited electronic state EF (1)Sigma(g) (+) of H(2) molecule by (2+2)-photon stimulated hyper-Raman passage (STIHRP). The density matrix technique has been employed to evaluate the population transfer to the final target levels using linearly chirped pump and Stokes laser pulses with different chirp rates. Both the pulses are considered to have the same temporal shape, pulse width, and linear parallel polarizations. We have studied in detail the dependence of the population transfer on the set of laser parameters for pulse (peak) intensities in the ranges of 1.5 x 10(11)-1.0 x 10(12) and 1.0 x 10(12)-7.0 x 10(12) W/cm(2). The corresponding pulse widths (full width at half maximum) are of the order of 115-200 and 15-30 ps. We have found that the chirp rate parameters can be optimized to achieve almost complete population transfer from the ground (g) to the final (f) target levels. This, to our knowledge, is the first application of a (2+2)-photon STIHRP process with chirpings to a model molecular system (H(2)). The study demonstrates the suitability of the chirped (2+2)-photon STIHRP technique for selective and almost total inversion of vibrational population in a diatomic molecule.
We have theoretically studied the population transfer in a five-level Li2 dimer by (2+2)-photon stimulated hyper-Raman nonadiabatic passage (STIHRNAP) from the initial ground level vg=0, Jg=0 to the final rovibrational levels vf=1 (2), Jf=0,2, of the ground electronic state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ via the resonant intermediate levels vi=1, Ji=0,2, of the excited electronic state $2\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$. Linearly chirped pump and Stokes laser pulses with different chirp rates and without any initial detuning are applied simultaneously. Both the pulses are taken to have the same temporal shape, pulse width, and linear parallel polarizations. The density matrix method has been used to compute the populations of the levels. We have investigated in detail the population transfer for laser wavelengths (at time t=0) in the range of 992−−1028nm and (peak) intensities in the range of $1.5\ifmmode\times\else\texttimes\fi{}{10}^{10}--3.0\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$. The required pulse widths are of the order of 35−−275ps for maximum population inversion. We have controlled rotational branching in population transfer to the final rotational levels Jf=0 (Q branch) and Jf=2 (S branch) of the fundamental (vf=1) and first overtone (vf=2) transitions by judicious choice of laser parameters. We have applied a (2+2)-photon STIHRNAP process to a model multilevel molecular system (Li2) and achieved almost complete population transfer from the initial ground to the final target rovibrational levels with chirped ir laser pulses.
By using Stark-induced adiabatic Raman passage (SARP) with partially overlapping nanosecond pump (532 nm) and Stokes (683 nm) laser pulses, 73% ± 6% of the initial ground vibrational state population of H(2) (v = 0, J = 0) is transferred to the single vibrationally excited eigenstate (v = 1, J = 0). In contrast to other Stark chirped Raman adiabatic passage techniques, SARP transfers population from the initial ground state to a vibrationally excited target state of the ground electronic surface without using an intermediate vibronic resonance within an upper electronic state. Parallel linearly polarized, co-propagating pump and Stokes laser pulses of respective durations 6 ns and 4.5 ns, are combined with a relative delay of ~4 ns before orthogonally intersecting the molecular beam of H(2). The pump and Stokes laser pulses have fluences of ~10 J/mm(2) and ~1 J/mm(2), respectively. The intense pump pulse generates the necessary sweeping of the Raman resonance frequency by ac (second-order) Stark shifting the rovibrational levels. As the frequency of the v = 0 → v = 1 Raman transition is swept through resonance in the presence of the strong pump and the weaker delayed Stokes pulses, the population of (v = 0, J = 0) is coherently transferred via an adiabatic passage to (v = 1, J = 0). A quantitative measure of the population transferred to the target state is obtained from the depletion of the ground-state population using 2 + 1 resonance enhanced multiphoton ionization (REMPI) in a time-of-flight mass spectrometer. The depletion is measured by comparing the REMPI signal of (v = 0, J = 0) at Raman resonance with that obtained when the Stokes pulse is detuned from the Stark-shifted Raman resonance. No depletion is observed with either the pump or the Stokes pulses alone, confirming that the measured depletion is indeed caused by the SARP-induced population transfer from the ground to the target state and not by the loss of molecules from photoionization or photodissociation. The two-photon resonant UV pulse used for REMPI detection is delayed by 20 ns with respect to the pump pulse to avoid the ac Stark shift originating from the pump and Stokes laser pulses. This experiment demonstrates the feasibility of preparing a large ensemble of isolated molecules in a preselected single quantum state without requiring an intermediate vibronic resonance.
We have theoretically investigated the population transfer in a four-level H2 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 (Jf=0) fundamental $({\ensuremath{\nu}}_{f}=1)$ and first overtone $({\ensuremath{\nu}}_{f}=2)$ transitions and the S-branch (Jf=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 IP0(IS0) 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 H2 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 IP0(IS0). For intuitive pulse sequence also a large population transfer is achieved for on-resonance excitation at intermediate values of IP0(IS0) and for off-resonance excitation at intermediate and high values of IP0(IS0).
We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level Li2 molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels Jg=0,2,…,8 associated with the initial vibrational level vg=0 of the ground electronic state $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$, five rotational levels Ji=1,3,…,9 associated with the vibrational level vi=1 of the intermediate excited electronic state $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$, and five rotational levels Jf=0,2,…,8 associated with the final target vibrational levels vf=1,2 of the $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ state of the Li2 alkali dimer. The pump and Stokes laser pulses are taken to have the same temporal (Gaussian) shapes, pulse widths, and linear parallel polarizations. The laser wavelengths are in the (visible) range of 700--740 nm. The (peak) intensities of the pulses are of the order of $1\ifmmode\times\else\texttimes\fi{}{10}^{12}--2.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{W}/{\text{cm}}^{2}$ and the pulse widths are of the order of 20--50 fs. We have solved the 15 coupled time-dependent Schr\"odinger equations to study the population transfer to the target-excited vibrational levels. We have observed that, even with ``mushrooming'' of closely spaced rotational levels, efficient and selective population transfer to excited vibrational levels in Li2 alkali dimer can be achieved for counterintuitive pulse sequence by controlling the pump and Stokes laser parameters. We have endeavored to explain the results within the framework of adiabatic picture.
We have numerically explored the feasibility and the mechanism of population transfer to the excited E (1)Σ(g) electronic state of Li(2) from the v=0 level of the ground electronic state X (1)Σ(g) using the A (1)Σ(u) state as an intermediate. In this system, the use of transform limited pulses with a frequency difference greater than the maximum Rabi frequency does not produce population transfer when all possible radiative couplings are taken into account. We have employed two synchronous pulses far detuned from the allowed transition frequencies, mainly with the lower frequency pulse positively chirped, and both pulses coupling the successive pair of states, X-A and A-E. The adiabaticity of the process has been investigated by a generalized Floquet calculation in the basis of 12 field dressed molecular states, and the results have been compared with those obtained from the full solution of time dependent Schrödinger equation. The conventional representation of the process in terms of three (or four) adiabatic potentials is not valid. It has been found that for cases of almost complete population transfer in full calculations with the conservation of the vibrational quantum number, adiabatic passage is attained with the 12 state Floquet model but not with the six state model. The agreement between the full calculations and the 12 state Floquet calculations is generally good when the transfer is adiabatic. Another characteristic feature of this work is the gaining of control over the vibrational state preparation in the final electronic state by careful tuning of the laser parameters as well as the chirp rate sign. This causes time dependent changes in the adiabatic potentials and nonadiabatic transfers can be made to occur between them.
Abstract We have theoretically investigated the population transfer and the selective excitation of vibrational states of the target state in a three-state Na 2 molecule using the chirped adiabatic passage. The population transfer among electronic states is studied. Compared with the single negative chirped pulse, complete population transfer can be achieved by using a positive chirped pulse. The effects of laser parameters on vibrational population distribution are discussed, and the selective excitation of vibrational states can be achieved by adjusting the central frequency. Finally, we give the method of selective excitation of specific vibrational states.