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State-to-state chemistry for three-body recombination in an ultracold rubidium gas

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Science  17 Nov 2017:
Vol. 358, Issue 6365, pp. 921-924
DOI: 10.1126/science.aan8721
  • Fig. 1 REMPI scheme and overview of relevant molecular states.

    (A) A two-color (1, 2) REMPI scheme detects weakly bound molecules close to the 5s + 5s dissociation threshold. The probe laser drives a resonant transition toward the Embedded Image, v′ = 66 vibrational level, which exhibits a simple rotational substructure (see inset). J′ is the total angular momentum quantum number excluding nuclear spins. Afterward, two photons from the ionization laser ionize the molecule. a0 is the Bohr radius. (B) Calculated energy levels of selected, weakly bound molecular states with the quantum numbers v and R for vibration and mechanical rotation, respectively. Only levels with total positive parity and angular momentum F = 2 that correlate to the fa = fb = 1 atomic asymptote are shown. This asymptote marks the zero energy reference level. The vibrational quantum number v is counted downwards starting at v = –1 for the most weakly bound vibrational state.

  • Fig. 2 Photoassociation and REMPI spectra.

    Shown is the remaining atom fraction N/N0 as a function of the probe laser frequency ν, where N0 is the number of remaining atoms for a far off-resonant probe laser. Orange data correspond to the photoassociation spectrum, with a single line at ν = ν0 ≡ 281,445.045 GHz. For better visibility the record is shifted up by 0.05 units. The blue and green data are REMPI spectra. For the blue data, the ionization laser frequency is 281,629.15 GHz, whereas for the green data, the laser was red-shifted by 150 MHz. Each REMPI data point is the average of 10 repetitions, with the error bars representing the statistical standard deviation. For better visibility, the green spectrum is vertically shifted by –0.25 units, which cuts off part of its photoassociation line. The vertical lines mark assigned resonant transitions of the first REMPI step (v and R are vibrational and rotational quantum numbers). For black arrows, see text.

  • Fig. 3 Discrimination of hyperfine levels.

    The REMPI spectrum shows two transition lines to J′ = 1, starting from the vibrational and rotational quantum numbers v = –3, R = 0 (peak on the right) and v = –3, R = 2 (peak on the left), respectively (see also, Fig. 2). Γion is the ion production rate. The vertical lines show calculated positions of possible product signals with hyperfine quantum numbers F = 0 and 2. The data reveal that only F = 2 states are substantially populated. Each data point is the average of 43 repetitions, and error bars indicate the statistical standard deviation. The red solid line is a Lorentzian fit of the two transition lines. The fit was not weighted to the error bars and has a reduced chi-square value of χ2 = 0.96. As before, ν = 281,445.045 GHz.

  • Fig. 4 Population distribution of molecular product states following three-body recombination.

    The plot shows the loss rate constants L3 (v, R) due to three-body recombination into various molecular product channels, as specified by the quantum numbers v (vibration) and R (rotation) and the respective binding energy Eb. R is indicated next to the data points. All product channels belong to the fa = 1, fb = 1 atomic asymptote and have F = 2. Circles are measurements. Crosses are calculations, rescaled as described in (26). Error bars in the gray region indicate upper limits derived from the experimental noise level. Two circles for the same product channel correspond to REMPI transitions to two different excited levels, J′ = R ± 1. The inset presents the branching ratio into the five vibrational levels, calculated by summing over all respective rotational contributions and by normalizing with the total loss rate constant L3. The dashed dotted lines (figure and inset) are proportional to Embedded Image. The error bars correspond to the statistical standard deviation.

Supplementary Materials

  • State-to-state chemistry for three-body recombination in an ultracold rubidium gas

    Joschka Wolf, Markus Deiß, Artjom Krükow, Eberhard Tiemann, Brandon P. Ruzic, Yujun Wang, José P. D'Incao, Paul S. Julienne, Johannes Hecker Denschlag

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    • Materials and Methods
    • Figs. S1 to S7
    • Captions for Data S1 to S5
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    Data S5
    Measured and calculated data shown in Fig.4.

    Additional Data

    Data S1
    Data S2
    Data S3a
    Data S3b
    Data S3c
    Data S4

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