Research ArticleCHEMICAL PHYSICS

Scattering of adiabatically aligned molecules by nonresonant optical standing waves

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Science Advances  03 Apr 2020:
Vol. 6, no. 14, eaaz0682
DOI: 10.1126/sciadv.aaz0682
  • Fig. 1 State-dependent alignment-considering molecular polarizability αJ,M(I) and the corresponding molecular interaction potential for the given standing wave intensity variation.

    (A) Spatial intensity profile of an optical standing wave plotted as a function of x. The maximum intensity Imax of the standing wave is 13 × 1010 W/cm2. (B) The estimated alignment cosine <cos2θ>J,M (left) and the corresponding molecular polarizability αJ,M[I(x)] (right) shown for the spatially varying field intensity and for rotational states of J = 0 (black) and 2 (red, blue, and light orange). These two J states account for 88% of the CS2 population at Trot = 1 K. (C) Molecular interaction potentials UJ,M[I(x)] for αJ,M[I(x)] (solid lines) and αJ,M(0) (dotted lines) for the states marked in (B). The red solid curve is partially concealed by the light orange one.

  • Fig. 2 Schematic diagram of the experimental setup.

    A molecular beam of CS2 molecules is scattered by a pulsed optical standing wave. The rotationally cold molecular beam is produced by supersonic expansion from an Even-Lavie valve with stagnation pressure P0 and temperature T0. The standing wave is formed by focusing two counter-propagating laser beams (IR1 and IR2). Their wavelengths λ and waist radii w0 are 1064 nm and 22 μm, respectively. The velocity change due to the scattering is measured by the velocity map imaging technique. We ionize molecules passing through the center of the standing wave by a probe dye laser beam (Probe). An ion lens system consisting of three electrodes performs velocity map imaging. The ion signal is amplified and converted into a light signal by an MCP and a PS, respectively. The luminescence is recorded by an ICCD camera and a PMT.

  • Fig. 3 The measured (first panel) and simulated (second panel) transverse velocity distributions and their profiles (third panel) along the vx axis for eight I0 values for Trot = 1 K.

    (A to H) The number in each graph indicates I0 in the unit of 1010 W/cm2. The accumulation time for the measured images is 1200 s, which corresponds to 12,000 laser shots. The images are normalized to the total signal intensity of each image. Gray profiles with shading and solid black curves correspond to the profiles of the measured and simulated images, respectively. The profile in (A) represents the initial transverse velocity distribution, which is centered at vx ≈ 10 m/s. As I0 increases, the profile becomes asymmetric and its central peak position moves to vx ≈ −10 m/s. These asymmetries result from the phase-space rotation of the molecules during the laser pulse duration and the average initial velocity along the x axis, <v0x> ≈ 10 m/s (see Fig. 5, G and H, and Discussion for details). The degree of the rotation depends on UJ,M(I) ∝ αJ,M(I)I, which varies the asymmetries according to I0. For an initial velocity distribution of <v0x> = 0, the profiles would be symmetric.

  • Fig. 4 The same data as Fig. 3 for Trot = 35 K.

    (A to H) Compared with the data for Trot = 1 K in Fig. 3, a distinctive central peak around vx = –10 m/s appears at higher I0 for Trot = 35 K. This peak turns up in (F) at I0 = 3.9 × 1010 W/cm2, while it is clearly visible at I0 = 3.2 × 1010 W/cm2 for the lower rotational temperature (Fig. 3E). The shift of the peak arises from the half phase-space rotation of the initial distribution of the molecules. At Trot = 35 K, average values of <cos2θ>J,M and αJ,M(I) are smaller than at Trot = 1 K, as the molecules are less aligned at the higher temperature. Since the degree of the rotation increases with the product of αJ,M(I) and I, the half rotation requires higher I for Trot = 35 K.

  • Fig. 5 Comparison of the experimental measurements with two series of numerical simulation obtained with αJ,M(I) and αJ,M(0).

    (A) The measured velocity profile for I0 = 3.2 × 1010 W/cm2 (gray profile with shading) is plotted together with the corresponding simulated profiles obtained with (solid curve) and without (dashed curve) considering the molecular alignment. Two characteristic velocity widths, W0.1 and W0.5, are marked in the experimental profile (green and blue, respectively). (B and C) Velocity widths W0.1 and W0.5, determined from measured and simulated profiles, plotted against I0 for Trot = 1 K (B) and Trot = 35 K (C). Squares denote measured data, while solid and dotted curves represent simulation data with αJ,M(I) (considering alignment) and αJ,M(0) (ignoring alignment), respectively. (D) Horizontal error bars are estimated from the nominal energy stability of an IR laser beam (0.8%) and uncertainties in w0, τ, and pulse energy measurements (±0.1 mJ). Vertical error bars are calculated assuming ±10% errors in the profile peak determination. Calculated positions of molecules in the lowest rotational state (J = 0) are plotted as functions of time for 16 different trajectories, accounting for alignment effects [αJ,M(I), solid curves]. For two representative position functions A and B, we show comparison curves A′ and B′ calculated without alignment effects [αJ,M(0), dashed curves]. (E and F) The simulation results at t = 5 ns are plotted in phase-space diagrams for αJ,M(I) (E) and αJ,M(0) (F). The dotted curve indicates a separatrix at t = 0 ns, inside which the molecules are temporally trapped by the standing wave potential. Thick blue and green lines show two representative trajectories, corresponding to A and B in frame (D), from t = –5 to 5 ns [open circle at −5 ns, filled circle at 5 ns, compare to red shaded area in (D)]. The minimum W0.5 in (B) is associated with the half phase-space rotation of the molecules near the center of the diagram in (E). For αJ,M(0), those molecules cannot make a half rotation as illustrated by the three blue trajectories, resulting in a larger W0.5. The larger vx for B than for B′ originates from the wider vertical width of the separatrix for αJ,M(I) than for αJ,M(0) and leads to the larger W0.1.

Supplementary Materials

  • Supplementary Materials

    Scattering of adiabatically aligned molecules by nonresonant optical standing waves

    Lee Yeong Kim, Byung Gwun Jin, Tae Woo Kim, Ju Hyeon Lee, Bum Suk Zhao

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    This PDF file includes:

    • Phase space dynamics
    • Selection of molecules occupying the rotational ground state
    • Figs. S1 and S2

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