Physical Review A

Coherent control of vibrational population transfer in the Li2 molecule with femtosecond laser pulses in the presence of manifolds of rotational levels

Chitrakshya Sarkar, Santanu Bhattacharyya, Samir Saha

Published Aug 11, 2009• 3 citations

Abstract

We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level ${\text{Li}}_{2}$ molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels ${J}_{g}=0,2,\dots{},8$ associated with the initial vibrational level ${v}_{g}=0$ of the ground electronic state $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$, five rotational levels ${J}_{i}=1,3,\dots{},9$ associated with the vibrational level ${v}_{i}=1$ of the intermediate excited electronic state $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$, and five rotational levels ${J}_{f}=0,2,\dots{},8$ associated with the final target vibrational levels ${v}_{f}=1,2$ of the $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ state of the ${\text{Li}}_{2}$ 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 ${\text{Li}}_{2}$ 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.

DOI: 10.1103/physreva.80.023407

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Control of population transfer in a multilevel Li2 molecule by stimulated hyper-Raman nonadiabatic passage with chirped laser pulses

Chitrakshya Sarkar, Rangana Bhattacharya, Santanu Bhattacharyya +1 more

Physical Review AAug 14, 20087 citations

Communication: Transfer of more than half the population to a selected rovibrational state of H2 by Stark-induced adiabatic Raman passage

Nandini Mukherjee, Wenrui Dong, John A. Harrison +1 more

The Journal of Chemical PhysicsFeb 4, 201321 citations

Population transfer to excited vibrational levels of H2 molecule by stimulated hyper-Raman passage with chirped laser pulses

Chitrakshya Sarkar, Rangana Bhattacharya, Santanu Bhattacharyya +1 more

The Journal of Chemical PhysicsSep 12, 20071 citation

Selective excitation of LI2 by chirped laser pulses with all possible interstate radiative couplings

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The Journal of Chemical PhysicsOct 27, 20107 citations

Efficient coherent population transfer in NO molecules using pulsed lasers

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Physical Review LettersNov 29, 1993214 citations

Quantum Coherent Control and Propagation in Lambda System

Pooja Nadkarni Singh

May 1, 20160 citations

Physical Review A

Coherent control of vibrational population transfer in the Li2 molecule with femtosecond laser pulses in the presence of manifolds of rotational levels

Chitrakshya Sarkar, Santanu Bhattacharyya, Samir Saha

Published Aug 11, 2009• 3 citations

Publisher

Abstract

We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level

{\text{Li}}_{2}

molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels

{J}_{g}=0,2,\dots{},8

associated with the initial vibrational level

{v}_{g}=0

of the ground electronic state

X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}

, five rotational levels

{J}_{i}=1,3,\dots{},9

associated with the vibrational level

{v}_{i}=1

of the intermediate excited electronic state

A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}

, and five rotational levels

{J}_{f}=0,2,\dots{},8

associated with the final target vibrational levels

{v}_{f}=1,2

of the

X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}

state of the

{\text{Li}}_{2}

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

{\text{Li}}_{2}

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.

DOI: 10.1103/physreva.80.023407

Related papers

Control of population transfer in a multilevel Li2 molecule by stimulated hyper-Raman nonadiabatic passage with chirped laser pulses

Chitrakshya Sarkar, Rangana Bhattacharya, Santanu Bhattacharyya +1 more

We have theoretically studied the population transfer in a five-level ${\mathrm{Li}}_{2}$ dimer by $(2+2)$ -photon stimulated hyper-Raman nonadiabatic passage (STIHRNAP) from the initial ground level ${v}_{g}=0$ , ${J}_{g}=0$ to the final rovibrational levels ${v}_{f}=1$ (2), ${J}_{f}=0,2$ , of the ground electronic state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ via the resonant intermediate levels ${v}_{i}=1$ , ${J}_{i}=0,2$ , 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 $992--1028\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ 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 $35--275\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for maximum population inversion. We have controlled rotational branching in population transfer to the final rotational levels ${J}_{f}=0$ ( $Q$ branch) and ${J}_{f}=2$ ( $S$ branch) of the fundamental $({v}_{f}=1)$ and first overtone $({v}_{f}=2)$ transitions by judicious choice of laser parameters. We have applied a $(2+2)$ -photon STIHRNAP process to a model multilevel molecular system $({\mathrm{Li}}_{2})$ and achieved almost complete population transfer from the initial ground to the final target rovibrational levels with chirped ir laser pulses.We have theoretically studied the population transfer in a five-level ${\mathrm{Li}}_{2}$ dimer by $(2+2)$-photon stimulated hyper-Raman nonadiabatic passage (STIHRNAP) from the initial ground level ${v}_{g}=0$, ${J}_{g}=0$ to the final rovibrational levels ${v}_{f}=1$ (2), ${J}_{f}=0,2$, of the ground electronic state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ via the resonant intermediate levels ${v}_{i}=1$, ${J}_{i}=0,2$, 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 $992--1028\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ 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 $35--275\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ for maximum population inversion. We have controlled rotational branching in population transfer to the final rotational levels ${J}_{f}=0$ ($Q$ branch) and ${J}_{f}=2$ ($S$ branch) of the fundamental $({v}_{f}=1)$ and first overtone $({v}_{f}=2)$ transitions by judicious choice of laser parameters. We have applied a $(2+2)$-photon STIHRNAP process to a model multilevel molecular system $({\mathrm{Li}}_{2})$ and achieved almost complete population transfer from the initial ground to the final target rovibrational levels with chirped ir laser pulses.

Physical Review AAug 14, 20087 citations

Communication: Transfer of more than half the population to a selected rovibrational state of H2 by Stark-induced adiabatic Raman passage

Nandini Mukherjee, Wenrui Dong, John A. Harrison +1 more

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.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.

The Journal of Chemical PhysicsFeb 4, 201321 citations

Population transfer to excited vibrational levels of H2 molecule by stimulated hyper-Raman passage with chirped laser pulses

Chitrakshya Sarkar, Rangana Bhattacharya, Santanu Bhattacharyya +1 more

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.

The Journal of Chemical PhysicsSep 12, 20071 citation

Selective excitation of LI2 by chirped laser pulses with all possible interstate radiative couplings

Souvik Chatterjee, S. S. Bhattacharyya

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.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.

The Journal of Chemical PhysicsOct 27, 20107 citations

Efficient coherent population transfer in NO molecules using pulsed lasers

S. Schiemann, Axel Kuhn, S. Steuerwald +1 more

Highly efficient and selective population transfer in NO molecules in the electronic ground state ( ${\mathit{X}}^{2}$ ${\mathrm{\ensuremath{\Pi}}}_{1/2}$) from the vibrational level v''=0 to the level v''=6 is demonstrated. It shows, for the first time with pulsed lasers, that a rather generally applicable scheme for complete control over the level population in atoms and molecules is now available. The efficiency relies on a counterintuitive interaction sequence of two lasers with the molecule in a process of stimulated Raman scattering involving adiabatic passage.Highly efficient and selective population transfer in NO molecules in the electronic ground state (${\mathit{X}}^{2}$${\mathrm{\ensuremath{\Pi}}}_{1/2}$) from the vibrational level v''=0 to the level v''=6 is demonstrated. It shows, for the first time with pulsed lasers, that a rather generally applicable scheme for complete control over the level population in atoms and molecules is now available. The efficiency relies on a counterintuitive interaction sequence of two lasers with the molecule in a process of stimulated Raman scattering involving adiabatic passage.

Physical Review LettersNov 29, 1993214 citations

Quantum Coherent Control and Propagation in Lambda System

Pooja Nadkarni Singh

Strong coherence in quasi-resonant laser driven system interferes with effective relaxations, resulting in behaviors like, coherent population trapping and Electromagnetically induced transparency. The Raman system can optimize this utilizing excited coherence in the lambda system when exposed to counter- intuitive pump-stokes pulses. The phenomenon can result in complete population transfer between vibrational levels called Stimulated Raman adiabatic passage(STIRAP). STIRAP and CHIRAP have been studied with Gaussian and chirped pulses. The optical propagation effects in dense medium for these phenomenon is studied to calculate the limitations and induced coherences. Further, the effect of rotational levels has been investigated. The molecular vibrational coherence strongly depends on the effect of rotational levels. The change in coherence interaction for ro-vibrational levels are reported and explained. We have considered the effects on the phase of radiation related to rotational mechanical motion of quantum system by taking advantages in ultra strong dispersion medium provided by quantum coherence in lambda system. The enhanced Fizeau effect on a single atom is observed.Strong coherence in quasi-resonant laser driven system interferes with effective relaxations, resulting in behaviors like, coherent population trapping and Electromagnetically induced transparency. The Raman system can optimize this utilizing excited coherence in the lambda system when exposed to counter- intuitive pump-stokes pulses. The phenomenon can result in complete population transfer between vibrational levels called Stimulated Raman adiabatic passage(STIRAP). STIRAP and CHIRAP have been studied with Gaussian and chirped pulses. The optical propagation effects in dense medium for these phenomenon is studied to calculate the limitations and induced coherences. Further, the effect of rotational levels has been investigated. The molecular vibrational coherence strongly depends on the effect of rotational levels. The change in coherence interaction for ro-vibrational levels are reported and explained. We have considered the effects on the phase of radiation related to rotational mechanical motion of quantum system by taking advantages in ultra strong dispersion medium provided by quantum coherence in lambda system. The enhanced Fizeau effect on a single atom is observed.

May 1, 20160 citations

We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level

{\text{Li}}_{2}

molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels

{J}_{g}=0,2,\dots{},8

associated with the initial vibrational level

{v}_{g}=0

of the ground electronic state

X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}

, five rotational levels

{J}_{i}=1,3,\dots{},9

associated with the vibrational level

{v}_{i}=1

of the intermediate excited electronic state

A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}

, and five rotational levels

{J}_{f}=0,2,\dots{},8

associated with the final target vibrational levels

{v}_{f}=1,2

of the

X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}

state of the

{\text{Li}}_{2}

1\ifmmode\times\else\texttimes\fi{}{10}^{12}--2.5\ifmmode\times\else\texttimes\fi{}{10}^{13}\text{ }\text{W}/{\text{cm}}^{2}

{\text{Li}}_{2}

We have theoretically studied the population transfer in a five-level

{\mathrm{Li}}_{2}

dimer by

(2+2)

-photon stimulated hyper-Raman nonadiabatic passage (STIHRNAP) from the initial ground level

{v}_{g}=0

{J}_{g}=0

to the final rovibrational levels

{v}_{f}=1

(2),

{J}_{f}=0,2

, of the ground electronic state $X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ via the resonant intermediate levels

{v}_{i}=1

{J}_{i}=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--1028\phantom{\rule{0.3em}{0ex}}\mathrm{nm}

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--275\phantom{\rule{0.3em}{0ex}}\mathrm{ps}

for maximum population inversion. We have controlled rotational branching in population transfer to the final rotational levels

{J}_{f}=0

(

Q

branch) and

{J}_{f}=2

(

S

branch) of the fundamental

({v}_{f}=1)

and first overtone

({v}_{f}=2)

transitions by judicious choice of laser parameters. We have applied a

(2+2)

-photon STIHRNAP process to a model multilevel molecular system

({\mathrm{Li}}_{2})

and achieved almost complete population transfer from the initial ground to the final target rovibrational levels with chirped ir laser pulses.

Highly efficient and selective population transfer in NO molecules in the electronic ground state (

{\mathit{X}}^{2}

${\mathrm{\ensuremath{\Pi}}}_{1/2}$) from the vibrational level v''=0 to the level v''=6 is demonstrated. It shows, for the first time with pulsed lasers, that a rather generally applicable scheme for complete control over the level population in atoms and molecules is now available. The efficiency relies on a counterintuitive interaction sequence of two lasers with the molecule in a process of stimulated Raman scattering involving adiabatic passage.