Vibrational Population Transfer Research Articles

Thermal modulation in Zeno and anti-Zeno effects on quantum measurement

ABSTRACTWe have proposed the mathematical formulations of quantum Zeno and anti-Zeno effects at non-zero temperature on vibrational population transfer and dissociation of a diatomic system. The proposed formulation has been tested for diatomic systems HBr+ and HI using time-dependent Fourier grid Hamiltonian method. The effect of temperature on the dynamics is incorporated through the population distribution at different vibrational states following Boltzmann distribution formula. It has been found that with increase in temperature Zeno effect increases and anti-Zeno effect decreases in case of survival probability on ground vibrational state. In case of dissociation, with increase in temperature Zeno effect increases while anti-Zeno effect remains almost same.

Theoretical study of Zeno and anti-Zeno effects on photodissociation dynamics: A model approach

Zeno and anti-Zeno effects in the evolution of the multi-photonic dissociation dynamics of the diatomic molecule HBr[Formula: see text] owing to repeated measurements demand if the system in the initial state have been studied. The effects have been calculated numerically for the case of vibrational population transfer and dissociation dynamics of HBr[Formula: see text] taking it as a model. We use time-dependent Fourier grid Hamiltonian (TDFGH) method as a mathematical tool in presence of intense radiation field as perturbation. The effects have been explored through a probable mechanism of population transfer from the ground vibrational state to the different upper vibrational states which ultimately go to the dissociation continuum. The results show significant differences in the mechanism of population transfer and the significant role of time interval of measurement ([Formula: see text] in Zeno and anti-Zeno effects. In case of survival probability of ground vibrational states, there is Zeno effect when the frequency of the laser to which the molecule is submitted is near the vibrational [Formula: see text] to [Formula: see text] resonance, while there is anti-Zeno effect if it is far from this resonance.

Fast-forward assisted STIRAP.

We consider combined stimulated Raman adiabatic passage (STIRAP) and fast-forward field (FFF) control of selective vibrational population transfer in a polyatomic molecule. The motivation for using this combination control scheme is 2-fold: (i) to overcome transfer inefficiency that occurs when the STIRAP fields and pulse durations must be restricted to avoid excitation of population transfers that compete with the targeted transfer and (ii) to overcome transfer inefficiency resulting from embedding of the actively driven subset of states in a large manifold of states. We show that, in a subset of states that is coupled to background states, a combination of STIRAP and FFFs that do not individually generate processes that are competitive with the desired population transfer can generate greater population transfer efficiency than can ordinary STIRAP with similar field strength and/or pulse duration.

Steering Vibrational Population Transfer via Double-∑-Type Laser Scheme

The vibrational state-selected population transfer from a highly vibrationally excited level to the ground level is of great importance in the preparation of ultra-cold molecules. By using the time-dependent quantum-wave-packet method, the population transfer dynamics is investigated theoretically for the HF molecule. A double-∑-type laser scheme is proposed to transfer the population from the ∣v=16〉 level to the ground vibrational level ∣v=0〉 on the ground electronic state. The scheme consists of two steps: The first step is to transfer the population from ∣v=16〉 to ∣v=7〉 via an intermediate level ∣v=11〉, and the second one is to transfer the population from ∣v=7〉 to ∣v=0〉 via ∣v=3〉. In each step, three vibrational levels form a ∑-type population transfer path under the action of two temporally overlapped laser pulses. The maximal population-transfer efficiency is obtained by optimizing the laser intensities, frequencies, and relative delays. Cases for the pulses in intuitive and counterintuitive sequences are both calculated and compared. It is found that for both cases the population can be efficiently (over 90%) transferred from the ∣v=16〉 level to the ∣v=0〉 level.

Selective Vibrational Population Transfer using Combined Stimulated Raman Adiabatic Passage and Counter-Diabatic Fields

We report studies of state-to-state vibrational energy transfer in an isolated polyatomic molecule driven by combined stimulated Raman adiabatic passage (STIRAP) and counter-diabatic fields (CDFs). The goal of these studies is development of a method for improving the efficiency of level-to-level population transfer under conditions that degrade the efficiency of conventional STIRAP-generated population transfer. The vehicles for our studies are selective population of one of a pair of near-degenerate states in nonrotating SCCl2 and enhancing the yield of nonrotating HNC in the HCN → HNC isomerization reaction. The efficiency of the population transfer within a subset of states embedded in a manifold of states is examined for the cases in which the transition dipole moments between the initial and target states are much smaller than and comparable to the transition dipole moments between background states and for the case in which the subset states have large transition dipole moments with the background ...

Vibrational population transfer of the HF molecule: One-photon and two-photon transitions

The population transfer process between the vibrational levels of the HF molecule is investigated by solving the time-dependent Schrödinger equation. The two vibrational levels of υ = 0 and 2 are set to be the initial and target states (an overtone transition). The transition processes under the one- and two-photon resonance conditions are considered, respectively. The influences of the laser intensity, frequency and pulse duration on population transfer are explored. It is found that the one-photon transition process is adiabatic, while the two-photon transition process is diabatic. Other vibrational levels, such as υ = 1 and 3, may participate into the two-photon transition process. Compared to the one-photon transition, a much longer pulse duration is required for the two-photon transition to achieve a high population-transfer efficiency, and the two-photon transition is more sensitive to the laser intensity. Almost a complete population transfer can be achieved for the two-photon resonance case, when the intensity is over 0.0091 a.u. with the appropriate duration (1180 fs) and frequency (0.017674 a.u.).

Steering the optimization pathway in the control landscape using constraints

We show how additional constraints, restricting the spectrum of the optimized pulse or confining the system dynamics, can be used to steer optimization in quantum control towards distinct solutions. Our examples are multi-photon excitation in atoms and vibrational population transfer in molecules. We show that a spectral constraint is most effective in enforcing non-resonant two-photon absorption pathways in atoms and avoiding unnecessarily broad spectra in Raman transitions in molecules. While a constraint restricting the system to stay in an allowed subspace is also capable of identifying non-resonant excitation pathways, it does not avoid spurious peaks in the pulse spectrum. Both constraints are compatible with monotonic convergence but imply different additional numerical costs.

Determining Equilibrium Fluctuations Using Temperature-Dependent 2D-IR

We demonstrate the capability of temperature-dependent 2D-IR to characterize sources of vibrational population transfer. In a model system of iron diene tricarbonyl "piano stool" complexes, this approach reveals symmetry breaking associated with equilibrium fluctuations and differentiates these from fluxional rearrangement. Tricarbonyl(1,3-butadiene)iron and tricarbonyl(1,5-cyclooctadiene)iron are shown to undergo intramolecular vibrational redistribution (IVR) coupled to the wagging motion of their carbonyl ligands. In the case of both molecules, these equilibrium fluctuations are distinguished from chemical exchange behaviors by their temperature dependence and arguments of molecular symmetry.

Experimental and Theoretical Study of Multi-Quantum Vibrational Excitation: NO(v = 0→1,2,3) in Collisions with Au(111)

We measured absolute probabilities for vibrational excitation of NO(v = 0) molecules in collisions with a Au(111) surface at an incidence energy of translation of 0.4 eV and surface temperatures between 300 and 1100 K. In addition to previously reported excitation to v = 1 and v = 2, we observed excitation to v = 3. The excitation probabilities exhibit an Arrhenius dependence on surface temperature, indicating that the dominant excitation mechanism is nonadiabatic coupling to electron-hole pairs. The experimental data are analyzed in terms of a recently introduced kinetic model, which was extended to include four vibrational states. We describe a subpopulation decomposition of the kinetic model, which allows us to examine vibrational population transfer pathways. The analysis indicates that sequential pathways (v = 0 → 1 → 2 and v = 0 → 1 → 2 → 3) alone cannot adequately describe production of v = 2 or 3. In addition, we performed first-principles molecular dynamics calculations that incorporate electronically nonadiabatic dynamics via an independent electron surface hopping (IESH) algorithm, which requires as input an ab initio potential energy hypersurface (PES) and nonadiabatic coupling matrix elements, both obtained from density functional theory (DFT). While the IESH-based simulations reproduce the v = 1 data well, they slightly underestimate the excitation probabilities for v = 2, and they significantly underestimate those for v = 3. Furthermore, this implementation of IESH appears to overestimate the importance of sequential energy transfer pathways. We make several suggestions concerning ways to improve this IESH-based model.

Ultrafast Vibrational Population Transfer Dynamics in 2-Acetylcyclopentanone Studied by 2D IR Spectroscopy

2-Acetylcyclopentanone (2-ACP), which is a β-dicarbonyl compound, undergoes keto-enol isomerization, and its enol tautomers are stabilized by a cyclic intramolecular hydrogen bond. 2-ACP (keto form) has symmetric and asymmetric vibrational modes of the two carbonyl groups at 1748 and 1715 cm(-1) , respectively, which are well separated from the carbonyl modes of its enol tautomers in the FTIR spectrum. We have investigated 2-ACP dissolved in carbon tetrachloride by 2D IR spectroscopy and IR pump-probe spectroscopy. Vibrational population transfer dynamics between the two carbonyl modes were observed by 2D IR spectroscopy. To extract the population exchange dynamics (i.e., the down- and uphill population transfer rate constants), we used the normalized volumes of the cross-peaks with respect to the diagonal peaks at the same emission frequency and the survival and conditional probability functions. As expected, the downhill population transfer time constant (3.2 ps) was measured to be smaller than the uphill population transfer time constant (3.8 ps). In addition, the vibrational population relaxation dynamics of the two carbonyl modes were observed to be the same within the experimental error and were found to be much slower than vibrational population transfer between two carbonyl modes.

Vibrational cooling of cesium molecules using noncoherent broadband light

We demonstrate selective vibrational population transfer in cold cesium dimers using a simple approach based on the use of a shaped incoherent broadband diode laser near threshold. Optical pumping into a single vibrational level is accomplished with an incoherent light source by eliminating transitions from the targeted vibrational level. The broadband spectrum of the laser is wide enough to electronically excite several vibrational states of the molecule simultaneously. This method is relatively inexpensive, simple, and flexible to allow for development of new applications, in particular, the preparation of optically closed molecular system, opening the way to direct laser cooling of molecules.

Coherent control of vibrational population transfer in theLi2molecule with femtosecond laser pulses in the presence of manifolds of rotational levels

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.

Waiting Time Dynamics in Two-Dimensional Infrared Spectroscopy

We review recent work on the waiting time dynamics of coherent two-dimensional infrared (2DIR) spectroscopy. This dynamics can reveal chemical and physical processes that take place on the femto- and picosecond time scale, which is faster than the time scale that may be probed by, for example, nuclear magnetic resonance spectroscopy. A large number of chemically relevant processes take place on this time scale. Such processes range from forming and breaking hydrogen bonds and proton transfer to solvent exchange and vibrational population transfer. In typical 2DIR spectra, multiple processes contribute to the waiting time dynamics and the spectra are often congested. This makes the spectra challenging to interpret, and the aid of theoretical models and simulations is often needed. To be useful, such models need to account for all dynamical processes in the sample simultaneously. The numerical integration of the Schrodinger equation (NISE) method has proven to allow for a very general treatment of the dynamical processes. It accounts for both the motional narrowing resulting from solvent-induced frequency fluctuations and population transfer between coupled vibrations. At the same time, frequency shifts arising from chemical-exchange reactions and changes of the transition dipoles because of either non-Condon effects or molecular reorientation are included in the treatment. This method therefore allows for the disentanglement of all of these processes. The NISE method has thus far been successfully applied to study chemical-exchange processes. It was demonstrated that 2DIR is not only sensitive to reaction kinetics but also to the more detailed reaction dynamics. NISE has also been applied to the study of population transfer within the amide I band (CO stretch) and between the amide I and amide II bands (CN stretch and NH bend) in polypeptides. From the amide I studies, it was found that the population transfer can be used to enhance cross-peaks that act as structural markers for beta-sheet structure in proteins. From the amide I/II investigation, it was found that the amide II band and the hydrogen-bond stretch vibration are important parts of the relaxation pathway for the amide I vibration. With the development of simple approximations, it becomes possible to apply the NISE method even to very big systems, such as the OH stretch of bulk water, which can only be described well when large numbers of coupled vibrations are taken into account.

OPTIMALLY CONTROLLED VIBRATIONAL POPULATION TRANSFER IN A DIATOMIC QUANTUM SYSTEM

A time-dependent formulation of quantum control is employed to investigate optimally controlled vibrational population transfer in a diatomic quantum system. The problem of finding the optimal laser field needed to achieve a specific quantum transition from an initial state to the desired target goal is formulated using an iterative method and the conjugate gradient method (CGM). The time-dependent Schrödinger equation is solved with interaction of laser radiation with matter included within a dipole approximation in the Hamiltonian. Appropriate boundary conditions are chosen for the evolution problem. The control objective is chosen as the value of transition probability from an initial state to a target state. A comparison is made between the results obtained using the iterative method and the CGM for optimization. Finally, quantum bits are encoded using the vibrational states of the diatomic in the regime of low-vibrational excitation.

Simulation of vibrational energy transfer in two-dimensional infrared spectroscopy of amide I and amide II modes in solution

Population transfer between vibrational eigenstates is important for many phenomena in chemistry. In solution, this transfer is induced by fluctuations in molecular conformation as well as in the surrounding solvent. We develop a joint electrostatic density functional theory map that allows us to connect the mixing of and thereby the relaxation between the amide I and amide II modes of the peptide building block N-methyl acetamide. This map enables us to extract a fluctuating vibrational Hamiltonian from molecular dynamics trajectories. The linear absorption spectrum, population transfer, and two-dimensional infrared spectra are then obtained from this Hamiltonian by numerical integration of the Schrodinger equation. We show that the amide I/amide II cross peaks in two-dimensional infrared spectra in principle allow one to follow the vibrational population transfer between these two modes. Our simulations of N-methyl acetamide in heavy water predict an efficient relaxation between the two modes with a time scale of 790 fs. This accounts for most of the relaxation of the amide I band in peptides, which has been observed to take place on a time scale of 450 fs in N-methyl acetamide. We therefore conclude that in polypeptides, energy transfer to the amide II mode offers the main relaxation channel for the amide I vibration.

Control of excited-state population and vibrational coherence with shaped-resonant and near-resonant excitation

We investigated numerically and experimentally the enhancement of vibrational coherence and population transfer in solution using tailored pulses. The general control mechanism is based on the precise control of the absorption after excitation with multipulses. Transient absorption was used as an experimental method to quantify the enhancement after the excitation with a shaped pump pulse in the low-pulse energy regime. A density-matrix approach was used to investigate the effect of the shaped excitation of a four-level system (two ground-state vibrational levels + two excited-state vibrational levels). Density-matrix simulation results suggest similar wavelength dependence as observed in the transient absorption experiment. The results show that enhancement of population transfer and vibrational coherence depends crucially on the overlap between the excitation pulse spectrum and the molecular absorption band.

Selective and efficient excitation of diatomic molecules by an ultrashort pulse train

In this paper, I discuss the selective and efficient vibrational population transfer between electronic states of diatomic molecules by a weak, ultrashort pulse train. The spectrum of each individual pulse in the train is wide enough to simultaneously excite several vibrational levels of the molecule. However, selectivity is achieved by mismatching the frequency comb, associated with the pulse train, to the excited vibrational levels. Efficiency results from the coherent accumulation of population from one pulse in the train to the next.

Two-Dimensional Infrared Population Transfer Spectroscopy for Enhancing Structural Markers of Proteins

We propose the possibility of using vibrational population transfer to enhance the structural markers for protein motifs that occur in two-dimensional infrared spectroscopy. We demonstrate the potential of this method by calculating the spectrum of the trpzip2 β-hairpin peptide, a system that is small enough to allow accurate simulation of its two-dimensional infrared spectra, including vibrational population transfer induced by a fluctuating solvent. The results show that under selected experimental conditions, in particular by using perpendicular polarization and finite waiting times, the cross peaks that constitute the well-known Z-shape marker for β-sheet structure in two-dimensional spectra are strongly enhanced. This enhancement is shown to result from vibrational population transfer. It should be possible to use the same technique for enhancing cross peaks in other structures and generally improve structure determination by two-dimensional infrared spectroscopy. The simulated population transfer times are in good agreement with those observed in experiments on typical proteins.

Rotation–torsion–vibration term-value mapping for CH 3OH: Torsion-mediated doorways and corridors for intermode population transfer

Fourier transform infrared spectra of CH 3OH from 930–1650 cm −1 have been analyzed to reveal details of the rotation–torsion–vibration energy manifold of the CO-stretching, CH 3-rocking, OH-bending and CH 3-deformation modes and their torsional combination states. Mapping of the upper-state term values as a function of the rotational quantum number J has shown the locations of numerous substate crossing resonances that give rise to J-localized spectral perturbations and substate mixing and thereby create “doorways” for collision-induced population transfer among the different modes. Other near-degenerate substates are more globally mixed over a wide range of J, corresponding to “corridors” of doorways. Where both partner substates in a doorway resonance have been identified, the perturbations have been analyzed to find estimates of the interaction matrix elements and the degree of mixing between the coupled states. Many of the resonances are between substates of differing torsional quantum number, highlighting the importance of torsion in generating the doorway channels and enhancing intermode vibrational population transfer.

Selective vibrational population transfer between electronic states of the Na 2 molecule with ultrashort laser pulses

The laser induced selective excitation for a three-state model of the Na 2 molecule is theoretically investigated by using the time-dependent wavepacket method. Employing a pair of ultrashort laser pulses of varying intensities, the vibrational population can be selectively transferred between different electronic states. The selective excitation can also be achieved by controlling the delay time between the pump and probe pulses. The dynamics processes of the selective excitation are qualitatively described via the concept of light-induced potentials.