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

Vibration to Vibration: Product Energy Distribution of F + HD Crossed Molecular Beam Experiments

We investigated the F + HD(v = 1, j = 0) → HF + D reaction using the crossed molecular beam technique combined with the D atom Rydberg tagging time-of-flight spectroscopy. By detecting the products at various scattering angles for different collision energies in the range of 0.8-1.2 kcal/mol, we observed the forward-scattering products of HF(v' = 4) and determined the threshold energy for the opening of this reaction channel. Similar experiments were conducted for the F + HD(v = 0, j = 0) → HF + D reaction within the range of 1.1-1.6 kcal/mol, where forward-scattering products of HF(v' = 3) were observed, and the threshold energy for this reaction channel was determined as well. Furthermore, we measured the differential cross-sections for the F + HD → HF + D reaction in both the vibrational ground state and the excited state of HD and analyzed the vibrational quantum-state distribution of the HF products. It was found that the population of vibrational quantum states of the HF products increases synchronously with the excitation of the reactant HD vibrationally.

Enhanced Total Vibrational Excitation Yield in a Slow Narrow-Pulsed Hydrogen Molecular Beam

High-efficiency excitation of a molecular beam is critical for investigating state-selected chemistry. However, achieving vibrational excitation of the entire beam for Raman-active molecules such as H2 proves extremely challenging, primarily because laser pulses are much shorter than the molecular beam. In this study, we achieve a total excitation efficiency of over 20% by employing stimulated Raman pumping (SRP) in a slow, narrow-pulsed molecular beam. Through optimizing the intensity and spot shape of the SRP lasers, we attain saturated excitation within the laser crossing region. Furthermore, by reducing the beam velocity and narrowing the beam pulse using a cold valve and a fast chopper, we significantly enhance the total excitation yield. COMSOL simulation and a newly developed model reveal that a critical velocity allows the chopper to block unexcited molecules and reserve most of the excited ones from the beam, resulting in the highest overall excitation yield. This innovative setup opens new possibilities for state-selected experiments in surface science and ion-molecule reaction dynamics, particularly involving weak transitions and pulsed lasers.

Quantum-Controlled Collisions of H2 Molecules

The amount of information that can be obtained from a scattering experiment depends upon the precision with which the quantum states are defined in the incoming channel. By precisely defining the incoming states and measuring the outgoing states in a scattering experiment, we set up the boundary condition for experimentally solving the Schrödinger equation. In this Perspective we discuss cold inelastic scattering experiments using the most theoretically tractable H₂ and its isotopologues as the target. We prepare the target in a precisely defined rovibrational (v, j, m) quantum state using a special coherent optical technique called the Stark-induced adiabatic Raman passage (SARP). v and j represent the quantum numbers of the vibrational and rotational energy levels, and m refers to the projection of the rotational angular momentum vector j on a suitable quantization axis in the laboratory frame. Selection of the m quantum numbers defines the alignment of the molecular frame, which is necessary to probe the anisotropic interactions. For us to achieve the collision temperature in the range of a few degrees Kelvin, we co-expand the colliding partners in a mixed supersonic beam that is collimated to define a direction for the collision velocity. When the bond axis is aligned with respect to a well-defined collision velocity, SARP achieves stereodynamic control at the quantum scale. Through various examples of rotationally inelastic cold scattering experiments, we show how SARP coherently controls the dynamics of anisotropic interactions by preparing quantum superpositions of the orientational m states within a single rovibrational (v, j) energy state. A partial wave analysis, which has been developed for the cold scattering experiments, shows dominance of a resonant orbital that leaves its mark in the scattering angular distribution. These highly controlled cold collision experiments at the single partial wave limit allow the most direct comparison with the results of theoretical computations, necessary for accurate modeling of the molecular interaction potential.

Vibrational overtone excitation of D2 in a molecular beam with a high-energy, narrow-bandwidth, nanosecond optical parametric oscillator/amplifier

We have built a high-energy, narrow-bandwidth, nanosecond light source for efficient preparation of vibrationally excited molecules in a molecular beam. It consists of an injection-seeded optical parametric oscillator and two optical parametric amplifiers. Pumped by the second harmonic of a commercial injection-seeded Nd:YAG laser, it can generate pulse energies up to 377 mJ at 655 nm with a bandwidth smaller than 200 MHz. Its stability is excellent, with a standard deviation of pulse energy of 5.2 mJ and a wavelength stability of 0.001 cm^-1. We demonstrated this light source in a crossed-molecular-beam experiment of the H + D₂ (v = 2, j = 0) → HD + D reaction, in which it was used for overtone excitation of D₂ molecules from (v = 0, j = 0) to (v = 2, j = 0) with an overall excitation efficiency of 2.5%.

Stark-induced adiabatic Raman passage examined through the preparation of D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0)

We study the conditions that must be met for successful preparation of a large ensemble in a specific target quantum state using Stark-induced adiabatic Raman passage (SARP). In particular, we show that the threshold condition depends on the relative magnitudes of the Raman polarizability (r_0v) and the difference of the optical polarizabilities (Δα_00→vj) of the initial (v = 0, j = 0) and the target (v, j) rovibrational levels. Here, v and j are the vibrational and rotational quantum numbers, respectively. To illustrate how the operation of SARP is controlled by these two parameters, we experimentally prepared D₂ (v = 2, j = 0) and D₂ (v = 2, j = 2, m = 0) in a beam of D₂ (v = 0, j = 0) molecules using a sequence of partially overlapping pump and Stokes laser pulses. By comparing theory and experiment, we were able to determine the Raman polarizability r₀₂ ≈ 0.3 × 10^-41 Cm/(V/m) and the difference polarizabilities Δα_00→20 ≈ 1.4 × 10^-41 Cm/(V/m) and Δα_00→22 ≈ 3.4 × 10^-41 Cm/(V/m) for the two Raman transitions. Our experimental data and theoretical calculations show that because the ratio r/Δα is larger for the (0,0) → (2,0) transition than the (0,0) → (2,2) transition, much less optical power is required to transfer a large population to the (v = 2, j = 0) level. Nonetheless, our experiment demonstrates that substantial population transfer to both the D₂ (v = 2, j = 0) and D₂ (v = 2, j = 2, m = 0) is achieved using appropriate laser fluences. Our derived threshold condition demonstrates that with increasing vibrational quantum number, it becomes more difficult to achieve large amounts of population transfer.

A review of dynamical resonances in A + BC chemical reactions

The concept of the transition state has played an important role in the field of chemical kinetics and reaction dynamics. Reactive resonances in the transition-state region can dramatically enhance the reaction probability; thus investigation of the reactive resonances has attracted great attention from chemical physicists for many decades. In this review, we mainly focus on the recent progress made in probing the elusive resonance phenomenon in the simple A  +  BC reaction and understanding its nature, especially in the benchmark F/Cl  +  H₂ and their isotopic variants. The signatures of reactive resonances in the integral cross section, differential cross section (DCS), forward- and backward-scattered DCS, and anion photodetachment spectroscopy are comprehensively presented in individual prototype reactions. The dynamical origins of reactive resonances are also discussed in this review, based on information on the wave function in the transition-state region obtained by time-dependent quantum wave-packet calculations.

Imaging rotations and vibrations in polyatomic molecules with X-ray scattering

An approach for calculating elastic X-ray scattering from polyatomic molecules in specific electronic, vibrational, and rotational states is presented, and is used to consider the characterization of specific states in polyatomic molecules using elastic X-ray scattering.

Elastic X-ray scattering from state-selected molecules

The characterization of electronic, vibrational, and rotational states using elastic (coherent) X-ray scattering is considered. The scattering is calculated directly from complete active space self-consistent field level ab initio wavefunctions for H₂ molecules in the ground-state X¹Σ_g⁺ and first-excited EF¹Σ_g⁺ electronic states. The calculated scattering is compared to recent experimental measurements [Y.-W. Liu et al., Phys. Rev. A 89, 014502 (2014)], and the influence of vibrational and rotational states on the observed signal is examined. The scaling of the scattering calculations with basis set is quantified, and it is found that energy convergence of the ab initio calculations is a good indicator of the quality of the scattering calculations.

Preparation of a selected high vibrational energy level of isolated molecules

Stark induced adiabatic Raman passage (SARP) allows us to prepare an appreciable concentration of isolated molecules in a specific, high-lying vibrational level. The process has general applicability, and, as a demonstration, we transfer nearly 100 percent of the HD (v = 0, J = 0) in a supersonically expanded molecular beam of HD molecules to HD (v = 4, J = 0). This is achieved with a sequence of partially overlapping nanosecond pump (355 nm) and Stokes (680 nm) single-mode laser pulses of unequal intensities. By comparing our experimental data with our theoretical calculations, we are able to draw two important conclusions: (1) using SARP a large population (>10¹⁰ molecules per laser pulse) is prepared in the (v = 4, J = 0) level of HD and (2) the polarizability α_00,40 (≅0.6 × 10^-41 C m² V^-1) for the (v = 0, J = 0) to (v = 4, J = 0) Raman overtone transition is only about five times smaller than α_00,10 for the (v = 0, J = 0) to (v = 1, J = 0) fundamental Raman transition. Moreover, the SARP process selects a specific rotational level in the vibrational manifold and can prepare one or a phased linear combination of magnetic sublevels (M states) within the selected vibrational-rotational level. This capability of preparing selected, highly excited vibrational levels of molecules under collision-free conditions opens new opportunities for fundamental scattering experiments.

Extremely short-lived reaction resonances in Cl + HD (v = 1) → DCl + H due to chemical bond softening

The Cl + H2 reaction is an important benchmark system in the study of chemical reaction dynamics that has always appeared to proceed via a direct abstraction mechanism, with no clear signature of reaction resonances. Here we report a high-resolution crossed–molecular beam study on the Cl + HD (v = 1, j = 0) → DCl + H reaction (where v is the vibrational quantum number and j is the rotational quantum number). Very few forward scattered products were observed. However, two distinctive peaks at collision energies of 2.4 and 4.3 kilocalories per mole for the DCl (v′ = 1) product were detected in the backward scattering direction. Detailed quantum dynamics calculations on a highly accurate potential energy surface suggested that these features originate from two very short-lived dynamical resonances trapped in the peculiar H-DCl (v′ = 2) vibrational adiabatic potential wells that result from chemical bond softening. We anticipate that dynamical resonances trapped in such wells exist in many reactions involving vibrationally excited molecules.

A new perspective: imaging the stereochemistry of molecular collisions

The concept of the steric effect plays a central role in chemistry. This Perspective describes how the polarization of reactant molecules in space can be used to probe directly the steric effect, and highlights some of the new measurements that are made possible by coupling reactant orientation and alignment with ion imaging techniques.

Coherent superposition of M-states in a single rovibrational level of H2 by Stark-induced adiabatic Raman passage

We prepare an ensemble of isolated rovibrationally excited (v = 1, J = 2) H2 molecules in a phase-locked superposition of magnetic sublevels M using Stark-induced adiabatic Raman passage with linearly polarized single-mode pump (at 532 nm, ∼6 ns pulse duration, 200 mJ/pulse) and Stokes (699 nm, ∼4 ns pulse duration, 20 mJ/pulse) laser excitation. A biaxial superposition state, given by [line]ψ(t)⟩ = 1/√(2)[[line]ν = 1, J = 2, M = -2⟩ - [line]ν = 1, J = 2, M = +2⟩], is prepared with linearly but cross-polarized pump and Stokes laser pulses copropagating along the quantization z-axis. The degree of phase coherence is measured by using the O(2) line of the H2 E,F-X (0,1) band via 2 + 1 resonance enhanced multiphoton ionization (REMPI) at 210.8 nm by recording interference fringes in the REMPI signal in a time-of-flight mass spectrometer as the direction of the UV laser polarization is rotated using a half-wave plate. Nearly 60% population transfer from H2 (v = 0, J = 0) ground state to the superposition state in H2 (v = 1, J = 2) is measured from the depletion of the Q(0) line of the E,F-X (0,0) band as the Stokes frequency is tuned across the (v = 0, J = 0) → (v = 1, J = 2) Raman resonance.