Collisions of ultracold 23Na87Rb molecules with controlled chemical reactivities

Abstract

The collision of molecules at ultracold temperatures is of great importance to understand the chemical interactions at the quantum regime. Although much theoretical work has been devoted to this, experimental data are only sparsely available, mainly because of the difficulty in producing ground-state molecules at ultracold temperatures. We report here the creation of optically trapped samples of ground-state bosonic sodium-rubidium molecules with precisely controlled internal states and, enabled by this, a detailed study on the inelastic loss with and without the NaRb + NaRb → Na₂ + Rb₂ chemical reaction. Contrary to intuitive expectations, we observed very similar loss and heating, regardless of the chemical reactivities. In addition, as evidenced by the reducing loss rate constants with increasing temperatures, we found that these collisions are already outside the Wigner region although the sample temperatures are sub-microkelvin. Our measurement agrees semiquantitatively with models based on long-range interactions but calls for a deeper understanding on the short-range physics for a more complete interpretation.

Fig. 1. Controlling the chemical reactivity of NaRb molecules by vibrational excitation.

The schematic reaction coordinates for the NaRb + NaRb → Na₂ + Rb₂ process are shown. (A) In the lowest rovibrational level (v = 0, J = 0), the reaction is endothermic by 47 cm⁻¹ and thus forbidden at ultracold temperatures. (B) In the first excited rovibrational level (v = 1, J = 0), the same reaction is already exothermic by 164 cm⁻¹ and thus allowed. Molecules can also relax from v = 1 to v = 0 following the collision, but experimentally, this cannot be distinguished from chemical reactions. The ground Na₂Rb₂ tetramer level, which has much lower energy than both the reactant and product molecule pairs, is also shown. Near the NaRb + NaRb collision threshold, the density of Na₂Rb₂* states is estimated to be too large to be resolved. As a result, the collision is in the highly resonant regime (12).

Fig. 2. High-resolution internal state control.

(A to C) Well-resolved hyperfine structures of (A) the rovibrational ground state (v = 0, J = 0), (B) the first excited rovibrational state (v = 1, J = 0), and (C) the rotationally excited state (v = 0, J = 2). The two M_F = 3 hyperfine levels marked by the open circles in (A) and (B) are used in this work. (C) Spectra obtained with different Raman laser polarization combinations to demonstrate M_F control. The color-coded vertical bars in (C) mark the predicted hyperfine line positions.

Fig. 3. Inelastic collisions with different chemical reactivities.

(A and B) Time evolutions of (A) molecule numbers and (B) temperatures for both nonreactive (v = 0, J = 0) (filled circles) and reactive (v = 1, J = 0) (filled squares) samples. The temperature measurement, which stops at 0.1 s because of reduced signal-to-noise ratio following the time-of-flight expansion, is obtained separately from the number evolution with samples of essentially identical conditions. Error bars represent 1 SD. The blue dashed and red solid curves are fitting results using Eq. 3 with temperature-dependent loss rate constants obtained from Fig. 4 (see text for details). The measured trap oscillation frequencies are [ω_x, ω_y, ω_z] = 2π × [217(3), 208(3), 38(2)] Hz for the (v = 0, J = 0) molecules and 2π × [219(3), 205(2), 40(2)] Hz for the (v = 1, J = 0) molecules. The calculated initial peak densities can reach 6 × 10¹¹ cm⁻³.

Fig. 4. Temperature dependence of β for different chemical reactivities.

Each β is obtained from a fit to Eq. 3 to a segment of one full loss and heating measurement. The solid lines are from fits of β to power-law functions of T. Theoretical results based on the CC calculation are also shown. The dashed vertical line marks the position of T_vdW. The error bars represent 1 SD.