Abstract We study the effects of coupling between molecular vibrational modes attendant the excitation of Raman transitions. Raman active vibrational modes are described by two two‐level systems (TLSs) with nondegenerate ground states. The population inversion is investigated under the condition of zero relative phase between initially populated states. We use two ultrafast laser pulses for the pump and the Stokes fields that have chirps the same in the magnitude and opposite in the sign. Within this model, the coupling induces nonadiabatic effects leading to a diverse population distribution. By introducing the time delay between the Stokes and the pump pulse, we realized a complete population transfer in both coupled TLSs. We demonstrated the population inversion in a more generic case of the averaged initial relative phase. © 2012 Wiley Periodicals, Inc.
We propose a method to control population transfer and coherence in a multimode system using a transform-limited pump and a linearly chirped Stokes pulse in stimulated Raman scattering. Simultaneously applied pump and Stokes pulse are shown to induce the ac Stark shifts that result in nonadiabatic coupling of the dressed states, through which the pulse chirp governs population distribution. The method may be applied to selectively excite Raman transitions having the frequency difference less than the bandwidth of a transform-limited pulse.
Coherent anti-Stokes Raman scattering (CARS) microscopy has been a major tool of investigation of biological structures as it contains the vibrational signature of molecules. A quantum control method based on chirped pulse adiabatic passage was recently proposed for selective excitation of a predetermined vibrational mode in CARS microscopy [Malinovskaya and Malinovsky, Opt. Lett. 32, 707 (2007)]. The method utilizes the chirp sign variation at the peak pulse amplitude and gives a robust adiabatic excitation of the desired vibrational mode. Using this method, we investigate the impact of coupling between vibrational modes in molecules on controllability of excitation of the CARS signal. We analyze two models of two coupled two-level systems (TLSs) having slightly different transitional frequencies. The first model, featuring degenerate ground states of the TLSs, gives robust adiabatic excitation and maximum coherence in the resonant TLS for positive value of the chirp. In the second model, implying nondegenerate ground states in the TLSs, a population distribution is observed in both TLSs, resulting in a lack of selectivity of excitation and low coherence. It is shown that the relative phase and coupling between the TLSs play an important role in optimizing coherence in the desired vibrational mode and suppressing unwanted transitions in CARS microscopy.
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 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.
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.