Three-wave mixing spectroscopy of chiral molecules, which exist in left-handed and right-handed conformations, allows for enantio-selective population transfer despite random orientation of the molecules. This is based on constructive interference of the three-photon pathways for one enantiomer and destructive one for the other. We prove here that three mutually orthogonal polarization directions are required to this end. Two different dynamical regimes exist to realize enantioselective population transfer, and we show that they correspond to different phase conditions in the three-wave mixing. We find the excitation scheme used in current rotational three-wave mixing experiments of chiral molecules with C 1 symmetry to be close to optimal and discuss prospects for ro-vibrational three-wave mixing experiments of axially chiral molecules. Our comprehensive study allows us to clarify earlier misconceptions in the literature. arXiv:1904.02208v2 [quant-ph] 8 Jul 2019 , (6) (a) (b) (c) J J J J J+1 J+1 J J J+1 |1⟩ |2⟩ |3⟩ 12 23 13 FIG. 1. Scheme for cyclic population transfer between three rotational states. The possible combinations of J-states for such three-level cycles are denoted by (a), (b), and (c).2. Proof that enantio-selective cyclic electric dipole excitation of rotational states requires three mutually orthogonal polarization directionsWe consider the transition matrix elements between two rotational states of an asymmetric top, J , τ , M |H int |J , τ , M =
New extensive millimeter-wave measurements of the 12 C 16 O dimer have been made, and more than 300 new spectral transitions have been observed in the frequency range 81-135 GHz. A joint analysis of these and previous millimeter-wave data yielded the precise location of 33 new energy levels of A + symmetry and 20 levels of A -symmetry. These energy levels are located at 8-18 cm -1 above the zero-point level. Some of them belong to already known stacks, and others make up 9 new stacks of the dimer. Newly determined stacks have K ) 0, 1, and, for the first time, 2, where K is the projection of the total angular momentum on the intermolecular axis. The energy levels from accompanying rovibrational calculations with the use of a recently developed hybrid CCSD(T)/DFT-SAPT potential are in very good agreement with experiment. Analysis of the calculated wave functions revealed that two new stacks of A + symmetry with K ) 2 correspond to overall rotation of the dimer while the other newly observed stacks belong to the geared bend overtone modes. The ground vibrational states of the two "isomers" found are more or less localized at the two minima in the potential surface, whereas all the geared bend excited states show a considerable amount of delocalization.
We report the detection of absorption lines by the reactive ions OH + , H 2 O + and H 3 O + along the line of sight to the submillimeter continuum source G10.6−0.4 (W31C). We used the Herschel HIFI instrument in dual beam switch mode to observe the ground state rotational transitions of OH + at 971 GHz, H 2 O + at 1115 and 607 GHz, and H 3 O + at 984 GHz. The resultant spectra show deep absorption over a broad velocity range that originates in the interstellar matter along the line of sight to G10.6−0.4 as well as in the molecular gas directly associated with that source. The OH + spectrum reaches saturation over most velocities corresponding to the foreground gas, while the opacity of the H 2 O + lines remains lower than 1 in the same velocity range, and the H 3 O + line shows only weak absorption. For LSR velocities between 7 and 50 km s −1 we estimate total column densities of N(OH + ) ≥ 2.5 × 10 14 cm −2 , N(H 2 O + ) ∼6 × 10 13 cm −2 and N(H 3 O + ) ∼4.0 × 10 13 cm −2 . These detections confirm the role of O + and OH + in initiating the oxygen chemistry in diffuse molecular gas and strengthen our understanding of the gas phase production of water. The high ratio of the OH + by the H 2 O + column density implies that these species predominantly trace low-density gas with a small fraction of hydrogen in molecular form.
We report the detection of absorption by interstellar hydroxyl cations and water cations, along the sight-line to the bright continuum source W49N. We have used Herschel's HIFI instrument, in dual beam switch mode, to observe the 972 GHz N = 1-0 transition of OH + and the 1115 GHz 1 11 −0 00 transition of ortho-H 2 O + . The resultant spectra show absorption by ortho-H 2 O + , and strong absorption by OH + , in foreground material at velocities in the range 0 to 70 km s −1 with respect to the local standard of rest. The inferred OH + /H 2 O + abundance ratio ranges from ∼3 to ∼15, implying that the observed OH + arises in clouds of small molecular fraction, in the 2−8% range. This conclusion is confirmed by the distribution of OH + and H 2 O + in Doppler velocity space, which is similar to that of atomic hydrogen, as observed by means of 21 cm absorption measurements, and dissimilar from that typical of other molecular tracers. The observed OH + /H abundance ratio of a few ×10 −8 suggests a cosmic ray ionization rate for atomic hydrogen of 0.6−2.4 × 10 −16 s −1 , in good agreement with estimates inferred previously for diffuse clouds in the Galactic disk from observations of interstellar H + 3 and other species.
We report the detection of strong absorption by interstellar hydrogen fluoride along the sight-line to the submillimeter continuum source G10.6-0.4 (W31C). We have used Herschel's HIFI instrument, in dual beam switch mode, to observe the 1232.4763 GHz J = 1−0 HF transition in the upper sideband of the Band 5a receiver. The resultant spectrum shows weak HF emission from G10.6-0.4 at LSR velocities in the range -10 to -3 km s −1 , accompanied by strong absorption by foreground material at LSR velocities in the range 15 to 50 km s −1 . The spectrum is similar to that of the 1113.3430 GHz 1 11 −0 00 transition of para-water, although at some frequencies the HF (hydrogen fluoride) optical depth clearly exceeds that of para-H 2 O. The optically-thick HF absorption that we have observed places a conservative lower limit of 1.6 × 10 14 cm −2 on the HF column density along the sight-line to G10.6-0.4. Our lower limit on the HF abundance, 6 × 10 −9 relative to hydrogen nuclei, implies that hydrogen fluoride accounts for between ∼30% and 100% of the fluorine nuclei in the gas phase along this sight-line. This observation corroborates theoretical predictions that -because the unique thermochemistry of fluorine permits the exothermic reaction of F atoms with molecular hydrogen -HF will be the dominant reservoir of interstellar fluorine under a wide range of conditions.
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