Quantum Controlled Cold Scattering Challenges Theory.

Our previous rotationally inelastic cold scattering experiments between state prepared D2 (v = 2, j = 2, m = 0) and He disagreed with theory, raising serious concerns about either our understanding of the anisotropic potential or the accuracy of the measurement. To further interrogate interactions between molecular hydrogen and atomic helium, we study the Δj = 1and Δj = 2 rotational relaxation of HD (v = 2, j = 2, m = 0) by collision with He. The two rotational transitions probe different anisotropic components of the van der Waals potential. Our state resolved scattering study shows that these two transitions are mediated by two different shape resonances l = 1 for Δj = 1 and l = 2 for Δj = 2. The strong l = 1 resonance dominates the Δj = 1 scattering, agreeing with theory. However, the dominance of the weaker l = 2 resonance in the Δj = 2 transition, which matches our earlier D2-He result, contradicts theoretical calculations. The continued contradiction, when we expect one-to-one correspondence between our stereodynamically controlled scattering experiment and theoretical calculations, makes us question the accuracy of the weaker anisotropic part of the H2-He interaction potential.

Resonant cold scattering of highly vibrationally excited D2 with Ne.

To accurately map weak D2-Ne long-range interactions, we have studied rotationally inelastic cold scattering of D2 prepared in the vibrationally excited (v = 4) and rotationally aligned (j = 2, m) quantum state within the moving frame of a supersonically expanded mixed molecular beam. In contrast to earlier high energy D2-Ne collision experiments, the (j = 2 → j' = 0) cold scattering produced highly symmetric angular distributions that strongly suggest a resonant quasi-bound collision complex that lives long enough to make a few rotations. Our partial wave analysis indicates that the scattering dynamics is dominated by a single resonant l = 2 orbital, even in the presence of a broad temperature (0-5 K) distribution that allows incoming orbitals up to l = 5. The dominance of a single orbital suggests that the resonant complex stabilizes through the coupling of the internal (j = 2) and orbital (l = 2) angular momentum to produce a total angular momentum of J = 0 for the D2-Ne complex.

Coherent Preparation of Highly Vibrating and Rotating D2 Molecules.

Highly vibrationally and rotationally excited hydrogen molecules are of immense interest for understanding and modeling the physics and chemistry of the cold interstellar medium. Using a sequence of two Stark-induced adiabatic Raman passages, we demonstrate the preparation of rotationally excited D2 molecules in the fourth excited vibrational level within its ground electronic state. The nearly complete population transfer to the target state is confirmed by observing both the threshold behavior as a function of the laser power and the depletion of the intermediate level. The vibrational excitation reported here opens new possibilities in the study of the much debated four-center reaction between a pair of hydrogen molecules. Additionally, these rovibrationally excited molecules could be potentially used to generate the high-intensity D- ion beams considered essential for D-T thermonuclear fusion by enhancing the cross section for dissociative electron attachment by 5 orders of magnitude compared to that of the ground state.

Anisotropic dynamics of resonant scattering between a pair of cold aligned diatoms.

The collision dynamics between a pair of aligned molecules in the presence of a partial-wave resonance provide the most sensitive probe of the long-range anisotropic forces important to chemical reactions. Here we control the collision temperature and geometry to probe the dynamics of cold (1-3 K) rotationally inelastic scattering of a pair of optically state-prepared D2 molecules. The collision temperature is manipulated by combining the gating action of laser state preparation and detection with the velocity dispersion of the molecular beam. When the bond axes of both molecules are aligned parallel to the collision velocity, the scattering rate drops by a factor of 3.5 as collision energies >2.1 K are removed, suggesting a geometry-dependent resonance. Partial-wave analysis of the measured angular distribution supports a shape resonance within the centrifugal barrier of the l = 2 incoming orbital. Our experiment illustrates the strong anisotropy of the quadrupole-quadrupole interaction that controls the dynamics of resonant scattering.

Quantum mechanical double slit for molecular scattering.

Interference observed in a double-slit experiment most conclusively demonstrates the wave properties of particles. We construct a quantum mechanical double-slit interferometer by rovibrationally exciting molecular deuterium (D2) in a biaxial (v = 2, j = 2) state using Stark-induced adiabatic Raman passage, where v and j represent the vibrational and rotational quantum numbers, respectively. In D2 (v = 2, j = 2) → D2 (v = 2, j' = 0) rotational relaxation via a cold collision with ground state helium, the two coherently coupled bond axis orientations in the biaxial state act as two slits that generate two indistinguishable quantum mechanical pathways connecting initial and final states of the colliding system. The interference disappears when we decouple the two orientations of the bond axis by separately constructing the uniaxial states of D2, unequivocally establishing the double-slit action of the biaxial state. This double slit opens new possibilities in the coherent control of molecular collisions.

Shape resonance determined from angular distribution in D2 (v = 2, j = 2) + He → D2 (v = 2, j = 0) + He cold scattering.

We find an l = 2 shape resonance fingerprinted in the angular distribution of the cold (∼1 K) Δj = 2 rotationally inelastic collision of D2 with He in a single supersonic expansion. The Stark-induced adiabatic Raman passage is used to prepare D2 in the (v = 2, j = 2) rovibrational level with control of the spatial distribution of the bond axis of the molecule by magnetic sublevel selection. We show that the rate of Δj = 2 D2-D2 relaxation is nearly two orders of magnitude weaker than that of D2-He. This suggests that the strong D2-He scattering is caused by an orbiting resonance that is highly sensitive to the shape of the long-range potential.

Harnessing the Power of Adiabatic Curve Crossing to Populate the Highly Vibrationally Excited H_{2} (v=7, j=0) Level.

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.

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 (r0v) and the difference of the optical polarizabilities (Δα00→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 Δα00→20 ≈ 1.4 × 10-41 Cm/(V/m) and Δα00→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.

HD (v = 1, j = 2, m) orientation controls HD-He rotationally inelastic scattering near 1 K.

To investigate how molecular orientations affect low energy scattering, we have studied the rotational relaxation of HD (v = 1, j = 2, m) → (v' = 1, j' = 0) by collision with ground-state He, where v, j, and m designate the vibrational, rotational, and magnetic quantum numbers, respectively. We experimentally probed different collision geometries by preparing three specific m sublevels, including an m entangled sublevel, belonging to a single rovibrational (v = 1, j = 2) energy level within the ground electronic state of HD using Stark-induced adiabatic Raman passage. Low collision energies (0-5 K) were achieved by coexpanding a 1:19 HD:He mixture in a highly collimated supersonic beam, which has defined the direction of the collision velocity and restricted the incoming orbital angular momentum states, defined by the quantum number l, to l ≤ 2. Partial wave analysis of experimental data shows that a single l = 2 input orbital dominates the scattered angular distribution, implying the presence of a collisional resonance. The differential scattering angular distribution exhibits a greater than fourfold stereodynamic preference for the m = 0 input state vs m = ±2, when the quantization axis is oriented parallel to the collision velocity.

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation.

Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H2 and D2 using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0-5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H2/HD and D2/HD scattering suggest the presence of anisotropically sensitive resonances.

Quantum control of molecular collisions at 1 kelvin.

Measurement of vector correlations in molecular scattering is an indispensable tool for mapping out interaction potentials. In a coexpanded supersonic beam, we have studied the rotationally inelastic process wherein deuterium hydride (HD) (v = 1, j = 2) collides with molecular deuterium (D2) to form HD (v = 1, j = 1), where v and j are the vibrational and rotational quantum numbers, respectively. HD (v = 1, j = 2) was prepared by Stark-induced adiabatic Raman passage, with its bond axis aligned preferentially parallel or perpendicular to the lab-fixed relative velocity. The coexpansion brought the collision temperature down to 1 kelvin, restricting scattering to s and p partial waves. Scattering angular distributions showed a dramatic stereodynamic preference (~3:1) for perpendicular versus parallel alignment. The four-vector correlation measured between the initial and final velocities and the initial and final rotational angular momentum vectors of HD provides insight into the strong anisotropic forces present in the collision process.

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 α00,40 (≅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 α00,10 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.

Angular and internal state distributions of H2 (+) generated by (2 + 1) resonance enhanced multiphoton ionization of H2 using time-of-flight mass spectrometry.

We report direct measurement of the anisotropy parameter ß for the angular distribution of the photoelectron and photoion in (2 + 1) resonance enhanced multiphoton ionization process of H2 X (1)Σg (+) (v = 0, J = 0) molecules through the intermediate H2 E,F (1)Σg (+) (v' = 0, J' = 0) level (λ = 201.684 nm) using a time-of-flight mass spectrometer. The time-of-flight spectra were recorded as the direction of polarization of the ionizing laser was varied with respect to the flight axis of the H2 molecular beam and were fitted to an angular distribution in an appropriately rotated coordinate system with the z-axis oriented along the time-of-flight axis. The anisotropy parameter ß was found to be 1.72 ± 0.13 by fitting the time-of-flight spectra and agreed with previous measurements. Using secondary ionization with a delayed laser pulse of different wavelength, we also determined the vibrational energy distribution of the ions, showing that 98% ± 4% of the ions are generated in their ground vibrational state, in agreement with the calculated Franck-Condon factors between the H2 E,F (1)Σg (+) (v' = 0) and H2 (+) X (1)Σg (+) (v″) vibrational levels.