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The Journal of Chemical Physics

Preparation of polarized molecules using coherent infrared multicolor ladder excitation

Nandini Mukherjee, Richard N. Zare

Published Apr 15, 2010• 19 citations
Publisher

Abstract

A density matrix treatment is presented for a general process of preparing polarized molecules through their coherent interaction with two or more infrared photons of different frequencies, each tuned to cause a transition between real levels. This process, which might be called infrared stimulated Raman adiabatic passage, allows complete population transfer to selected rotational-vibrational levels and controls the direction of the rotational angular momentum vector J of the molecule with the possibility of preparing higher moments of the J spatial distribution. HCl molecules in a supersonic molecular beam are considered as a candidate system. Theory predicts that under collision-free conditions two infrared laser pulses of microsecond duration and milliwatt power are able to achieve complete population transfer and alignment of HCl (v=2, J=2, and M=0) for mutually parallel excitation and HCl (v=2, J=2, and M=+/-1) for mutually perpendicular excitation. Orientation of the HCl (v=2, J=2, and M=+/-2) can also be achieved using two circularly polarized pulses of the same helicity. For simplicity, our treatment ignores nuclear spin depolarization, which would be the case for molecules such as (12)C(16)O and (12)C(16)OO(2). Polarized molecules in higher vibrational levels can be prepared using additional infrared pulses.

DOI
10.1063/1.3352553

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Population transfer, alignment and orientation by stimulated adiabatic passage

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We review and compare recent experiments and theoretical models demonstrating complete population transfer to selected states in atoms and molecules using (1) Stimulated Raman Adiabatic Rapid Passage (STIRAP) with temporally delayed but partially overlapping time dependent fundamental and Stokes fields and (2) Chirped Adiabatic Passage (CHIRAP) using frequency chirped field with the frequency swept through the resonance frequency of transitions. The transfer efficiency in these processes is unity when the adiabatic criteria are satisfied. Alignment and orientation of the initial and terminals levels of the transitions can be obtained using these methods. The dynamics involve the atomic or molecular internal angular momentum states because the Rabi frequencies for the transitions depend on the magnetic quantum numbers of the states. Full wavefunction and density matrix (necessary when spontaneous emission of the excited states plays a role) calculations are presented and adiabatic-following wavefunction and density matrix descriptions are advanced to explain unexpected experimental results.

Bulletin of the American Physical Society•May 1, 1993•0 citations
A density matrix treatment is presented for a general process of preparing polarized molecules through their coherent interaction with two or more infrared photons of different frequencies, each tuned to cause a transition between real levels. This process, which might be called infrared stimulated Raman adiabatic passage, allows complete population transfer to selected rotational-vibrational levels and controls the direction of the rotational angular momentum vector J of the molecule with the possibility of preparing higher moments of the J spatial distribution. HCl molecules in a supersonic molecular beam are considered as a candidate system. Theory predicts that under collision-free conditions two infrared laser pulses of microsecond duration and milliwatt power are able to achieve complete population transfer and alignment of HCl (v=2, J=2, and M=0) for mutually parallel excitation and HCl (v=2, J=2, and M=+/-1) for mutually perpendicular excitation. Orientation of the HCl (v=2, J=2, and M=+/-2) can also be achieved using two circularly polarized pulses of the same helicity. For simplicity, our treatment ignores nuclear spin depolarization, which would be the case for molecules such as (12)C(16)O and (12)C(16)OO(2). Polarized molecules in higher vibrational levels can be prepared using additional infrared pulses.
We suggest that infrared stimulated Raman adiabatic passage, a coherent multiple excitation process, can be used to create a superposition of (2J+1) highly correlated M-state sublevels of a rigid rotor molecule with vibrational level v and rotational level J. This method employs the (v=0,J-2) to (v=2,J) S-branch transition, which is carried out in a counterintuitive manner in which the v=1 to v=2 transition is pumped prior to the v=0 to v=1 transition, causing nearly complete population transfer to the v=2 final level. We use perpendicular and parallel linearly polarized infrared excitation (biaxial excitation). Specifically, the perpendicular polarization connects the v=1 intermediate level to the final vibrational level v=2, and the parallel polarization connects the initial level v=0 to the intermediate level v=1. By this means we break the cylindrical symmetry for an ensemble of vibrationally excited molecules in a rovibrational eigenstate (v=2,J). The angular momentum polarization is determined by the relative phases rather than by the populations of the magnetic M-sublevels. For the phase correlated ensemble, the angular momentum polarization can be considered as a purely quantum mechanical effect. Using a fully general density matrix treatment, we illustrate this approach by considering a beam of carbon monoxide (CO) molecules. We find that significant polarization for J=2, 5, and 10 can be achieved with a cw infrared laser source having modest power (∼100 mW/mm(2)). We believe that this technique is a general one and may offer an experimentally accessible new platform for different applications, from scattering studies with M-state entangled ensembles of molecules to logic gate operations of a quantum computer.
A large ensemble of ∼10^{9} H_{2} (v=7, j=0) molecules is prepared in the collision-free environment of a supersonic beam by transferring nearly the entire H_{2} (v=0, j=0) ground-state population, where v and j are the vibrational and rotational quantum numbers, respectively. This is accomplished by controlling the crossing of the optically dressed adiabatic states using a pair of phase coherent laser pulses. The preparation of highly vibrationally excited H_{2} molecules opens new opportunities to test fundamental physical principles using two loosely bound yet entangled H atoms.
We have theoretically investigated the vibrational population transfer in the presence of manifolds of rotational levels in a model 15-level Li2{\text{Li}}_{2}Li2​ molecular system by stimulated Raman adiabatic passage with intense unchirped femtosecond laser pulses. We have considered five rotational levels Jg=0,2,…,8{J}_{g}=0,2,\dots{},8Jg​=0,2,…,8 associated with the initial vibrational level vg=0{v}_{g}=0vg​=0 of the ground electronic state $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$, five rotational levels Ji=1,3,…,9{J}_{i}=1,3,\dots{},9Ji​=1,3,…,9 associated with the vibrational level vi=1{v}_{i}=1vi​=1 of the intermediate excited electronic state $A\text{ }{^{1}\ensuremath{\Sigma}}_{u}^{+}$, and five rotational levels Jf=0,2,…,8{J}_{f}=0,2,\dots{},8Jf​=0,2,…,8 associated with the final target vibrational levels vf=1,2{v}_{f}=1,2vf​=1,2 of the $X\text{ }{^{1}\ensuremath{\Sigma}}_{g}^{+}$ state of the Li2{\text{Li}}_{2}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{\text{Li}}_{2}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 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.
Abstract We present a multi-color ladder excitation scheme that exploits Stark-induced adiabatic Raman passage to selectively populate a highly excited vibrational level of a molecule. We suggest that this multi-color coherent ladder excitation provides a practical way of accessing levels near the vibrational dissociation limit as well as the dissociative continuum, which would allow the generation of an entangled pair of fragments with near-zero relative kinetic energy. Specifically, we consider four- and six-photon coherent excitation of molecular hydrogen to high vibrational levels via intermediate vibrational levels, which are pairwise coupled by two-photon resonant interaction. Using a sequence of three partially overlapping, single-mode, nanosecond laser pulses we show that the sixth vibrational level of H 2 , which is too weakly coupled to be easily accessed by direct two-photon Raman excitation from the ground vibrational level, can be efficiently populated without leaving any population stranded in the intermediate level. Furthermore, we show that the fourteenth vibrational level of H 2 , which is the highest vibrational level in the ground electronic state with a binding energy of 22 meV, can be efficiently and selectively populated using a sequence of four pulses. The present technique offers the unique possibility of preparing entangled quantum states of H atoms without resorting to an ultracold system.
We review and compare recent experiments and theoretical models demonstrating complete population transfer to selected states in atoms and molecules using (1) Stimulated Raman Adiabatic Rapid Passage (STIRAP) with temporally delayed but partially overlapping time dependent fundamental and Stokes fields and (2) Chirped Adiabatic Passage (CHIRAP) using frequency chirped field with the frequency swept through the resonance frequency of transitions. The transfer efficiency in these processes is unity when the adiabatic criteria are satisfied. Alignment and orientation of the initial and terminals levels of the transitions can be obtained using these methods. The dynamics involve the atomic or molecular internal angular momentum states because the Rabi frequencies for the transitions depend on the magnetic quantum numbers of the states. Full wavefunction and density matrix (necessary when spontaneous emission of the excited states plays a role) calculations are presented and adiabatic-following wavefunction and density matrix descriptions are advanced to explain unexpected experimental results.