Direct observation of bimolecular reactions of ultracold KRb molecules

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Science  29 Nov 2019:
Vol. 366, Issue 6469, pp. 1111-1115
DOI: 10.1126/science.aay9531

Glimpsing an exchange of partners

When two diatomic molecules collide, they can sometimes swap partners. For instance, two potassium-rubidium (KRb) molecules can produce K2 and Rb2. The four-atom intermediate formed upon collision is typically too scarce and short-lived to spot, even using ultrafast techniques. Hu et al. circumvented this problem by studying the reaction at temperatures approaching 0 kelvin. Using a combination of mass spectrometry and velocity-map imaging, the authors directly characterized the ionized K2Rb2 complex as well as the reactant and product populations.

Science, this issue p. 1111


Femtochemistry techniques have been instrumental in accessing the short time scales necessary to probe transient intermediates in chemical reactions. In this study, we took the contrasting approach of prolonging the lifetime of an intermediate by preparing reactant molecules in their lowest rovibronic quantum state at ultralow temperatures, thereby markedly reducing the number of exit channels accessible upon their mutual collision. Using ionization spectroscopy and velocity-map imaging of a trapped gas of potassium-rubidium (KRb) molecules at a temperature of 500 nanokelvin, we directly observed reactants, intermediates, and products of the reaction 40K87Rb + 40K87Rb → K2Rb2* → K2 + Rb2. Beyond observation of a long-lived, energy-rich intermediate complex, this technique opens the door to further studies of quantum-state–resolved reaction dynamics in the ultracold regime.

The creation of ensembles of molecules at ultralow temperatures enables a variety of high-resolution spectroscopic studies, allows broader exploration of reaction phase space, and promises quantum-state control over the outcome of chemical reactions. Already, investigations of single partial-wave collisions have provided detailed benchmarks of short-range molecular potentials (1, 2), exotic conditions at low temperatures have facilitated the synthesis of new chemical species (3), and highly sensitive and precise methods of detection have traced state-to-state reactions between atoms and weakly bound Feshbach molecules (4). Further, chemical reaction rates for barrierless reactions can be altered (5, 6), in some case by orders of magnitude, merely by changing the nuclear spins of the reactants and entering quantum degeneracy (7). These studies all rely on the substantial control attainable over the quantum states of the ultracold molecules.

Despite recent advances in ultracold molecule studies, a key capability has been missing: namely, characterization of transient reaction intermediates and final products. Previous experiments have shown evidence of ultracold reactions between bialkali molecules through the quantum-state–specific detection of loss of reactants (5), similar to that shown in the inset to Fig. 1, providing insights into how long-range forces determine the kinetic collision rates of the reactants. These reactions have been observed to occur with a high probability after just a single collision, approaching unity in certain cases (5, 8, 9). Despite tour-de-force levels of control over the precise rovibrational quantum state of the reactants to open up additional energetically allowed reaction channels, no substantial differences based on the reactant species or initial quantum state have yet been observed (8, 9), and the nature of the molecular loss is still a matter of debate (10).

Fig. 1 Energetics of the bimolecular reactions of ultracold KRb molecules.

The ground-state energies are obtained from spectroscopic data for KRb (28), K2 (38), and Rb2 (39) and from calculation for KRb2, K2Rb, and K2Rb2 at the equilibrium configuration (40). Here, we define the incident energy of two free KRb molecules as zero energy. Because the energies of the triatomic reaction channels are much higher than those of the reactants, these channels are energetically forbidden. In comparison, the tetratomic reaction channel KRb + KRb → K2Rb2* → K2 + Rb2 is exothermic and therefore energetically allowed. K2Rb2* denotes the transient intermediate complex. ρc(E) is the density of states of K2Rb2* near the incident energy E. Two isomers of K2Rb2 with D2h and Cs symmetries connect to the KRb + KRb and K2 + Rb2 dissociation limits, respectively. No is the number of exit channels that consist of all combinations of quantum states of K2 and Rb2 that have a total energy below E. The inset (at top left) shows the number decay of KRb molecules measured by ionization detection. Each data point is accumulated over 300 experimental cycles. The error bars denote shot noise. The black curve is a weighted fit to the two-body decay model used in (5), with a root mean square error (RMSE) of 1.37.

When two molecules approach one another, they initially form an energy-rich intermediate collision complex, the dynamics of which could hold the key for understanding the details of the ensuing ultracold, barrierless, bimolecular reactions. In higher-temperature reactions, this transient complex persists for only one or two vibrational periods and, at most, on the order of a rotational period (~1 ps) (11, 12). Studying the dynamics or kinetics of such complexes in the gas phase has typically required ultrafast (1317) or stabilizing collisional (1820) techniques. Structural investigations of these complexes have been previously obtained by photodetachment (21, 22), photoabsorption (23), or photodissociation (24). On the basis of the Rice-Ramsperger-Kassel-Marcus (RRKM) theory, the lifetime of an intermediate complex is given by τc=2πρc/No, where ρc(E) denotes the density of states of the intermediate complex near the incident energy E, and No is the number of energetically allowed exit channels (Fig. 1). Preparing reactant KRb molecules in the pure rovibronic ground state in the ultralow-temperature regime tightly constrains the number of energetically allowed exit channels, greatly extending the lifetime of the intermediate complex. For reactions between bialkali molecules, depending on the species, τc has been estimated to be on the order of hundreds of nanoseconds to microseconds (25, 26), which makes direct observation of the complex a possible goal. However, no such observations have been made because all previous work has been based on the observation of loss of reactants. Direct multispecies detection methods are necessary to fully describe the details of these ultracold reactions (27).

Here, we report the direct detection of a predicted intermediate as well as products in the ultracold chemical metathesis reaction 40K87Rb + 40K87Rb → K2Rb2* → K2 + Rb2 (Fig. 1) (25, 26). In our study, we combined precise quantum-state preparation of the ultracold reactants with an ionization-based detection method that allows for direct and simultaneous detection of reactants (KRb), intermediates (K2Rb2*), and final products (K2 and Rb2).

We began by implementing an established protocol (28) to create an optically trapped gas of v = 0, N = 0, X1Σ+ ground-state KRb molecules. Here, v and N are the vibrational and rotational quantum number of the molecules, respectively. In brief, ultracold K and Rb atoms are first converted to weakly bound molecules with 20% efficiency by a magnetic field sweep (1.4 ms) through a Feshbach resonance at 546.62 G (29). Then a pair of Raman beams is applied in a stimulated Raman adiabatic passage (STIRAP) (30) pulse sequence (4 μs) to coherently transfer the weakly bound molecules into a single hyperfine state of the rovibronic ground state with 85% efficiency. Residual Rb and K atoms are removed 8 μs after the STIRAP pulse sequence. The atom-to-molecule transfer is mostly coherent and, therefore, can be reversed with high efficiency. To detect the ground-state KRb molecules, a reversed STIRAP sequence is applied, followed by absorption imaging on an atomic transition (Fig. 2A). Typically, 5 × 103 KRb molecules are created at 500 nK, with a peak density of 1012 cm−3, and trapped by a crossed optical dipole trap (ODT) at a laser wavelength of 1064 nm.

Fig. 2 Schematic of our ultracold chemistry apparatus.

Ground-state KRb molecules at 500 nK are trapped by a crossed optical dipole trap. (A) Absorption image of KRb molecules. The colorbar indicates the optical depth of the KRb cloud. CCD, charge-coupled device. (B) The trapped molecules are surrounded by VMI ion optics (31), which consist of a series of disk-shaped electrodes. We use a pulsed UV laser to photoionize the molecules. B, magnetic field. (C) Example TOF spectrum, which can be converted to a mass spectrum using the following relation: mass = 0.16248(u/μs2) × TOF2 (where u is the unified atomic mass unit). (D) For each species identified in the mass spectrum, we also obtain a VM image from which the momentum distribution can be inferred.

Because the absorption imaging detection is tied directly to the quantum-state–specific STIRAP transfer, it is sensitive to only the KRb molecules in the STIRAP populated quantum state. To probe chemical reaction products and the intermediate complex, we chose a more general detection method that entailed photoionization of neutral reaction species into bound molecular ions, acceleration of the ions in an electric field, and measurement of their arrival time and position on a multichannel plate (MCP) (Fig. 2C). By combining mass spectrometry and velocity-map imaging (VMI) (31) in our ultracold molecule apparatus, we could thereby identify reacting species and study reaction dynamics.

We performed three separate experiments to probe the reactants, intermediate complex, and products of the ultracold reaction. The detection procedure worked as follows: After KRb creation but before the ionization pulse, we ramped the magnetic field down to 30 G within 15 ms to reduce subsequent Lorentz forces that might deflect ions away from the detector, housed 1 m downstream. We then applied an ultraviolet (UV) ionization pulse while simultaneously triggering the MCP to record ion signals. For the detection of reactants and products, we chose a photoionization wavelength of 285 nm, which is above the ionization threshold of KRb, K, Rb, and any species composed of combinations of multiple K and Rb atoms (table S1). For the detection of the intermediate complex, the wavelength was varied over a range of 285 to 356 nm. To avoid space-charge effects, the laser power was kept low enough to ensure that, at most, one ion was generated per UV pulse. The ODT was switched off for a variable time period during and before the ionization pulse to preclude its influence on the chemical reaction, the lifetime of the intermediate collisional complex, and the photoionization process. We repeated this detection procedure at 1 kHz for the reactant and product detection (see timing diagram in fig. S1) and at 7 kHz for the intermediate complex detection. The mass, and thereby elemental composition, of each detected ion could be inferred from its time of flight (TOF), whereas the momentum of the ion was mapped through its location on the VM image (32).

To demonstrate the ionization detection capability in our ultracold molecular apparatus and to gain information beyond absorption imaging, we first probed the trapped KRb molecules in the ODT (Fig. 2, C and D). As expected, the dominant signal results from KRb+. The VM image for the KRb+ signal has a width limited by the detector resolution, consistent with the negligible translational energy in the ultracold regime. Measurable amounts of Rb+ and K+ were also detected. The VM images for K+ and Rb+ both show two distinct components: an isotropic central peak and an anisotropic ring. The ions forming the central peak originate from residual ultracold atoms from the molecule-creation process after the cleanup pulses. On the basis of the known ionization cross sections and estimated ion detection efficiencies (table S1), we put an upper bound of 250 atoms of each species in the trap. These populations are small compared with the KRb population, ensuring that the dominant reaction in the subsequent study is the desired bimolecular reaction. The sensitivity of ionization detection allowed us to quantify the small number of residual atoms in the ODT, which are not detected through absorption imaging. To analyze the Rb+ ions that form the ring pattern, we extracted the translational energy release (TER) from the diameter of the ring to obtain a TER of 8.3 × 103 cm−1. By comparing this TER to the calculated molecular potentials of KRb and KRb+ (33), we identified a two-photon dissociative ionization pathway that contributes to this atomic ion signal. The same analysis also applies to the ring pattern of the K+ ions (fig. S3).

After KRb molecules are created, the bimolecular reaction occurs continuously with a measured decay rate coefficient of 7.6(3) × 10−12 cm3/s until the reactants are depleted (Fig. 1, inset), consistent with previous studies (5). To probe the products of the bimolecular reaction while reducing the perturbation to the reactants during ionization, we shaped our ionization beam into a “hollow bottle” (Fig. 3B) with the laser intensity concentrated in a ring outside of the ODT to keep the reactants in the dark; the measured intensity contrast between the peak and center of the beam was 500 (32). To further reduce the hollow volume for higher-efficiency ionization, we crossed two hollow-bottle beams at a 40° angle centered on the ODT (32). To observe the bimolecular reaction without the possible influence of the ODT light, we shut off the ODT for 170 μs before each ionization pulse, thereby precluding any role of the ODT in the formation of all but those products with translational energy <0.0127 cm−1 (34).

Fig. 3 Identification of the reaction products.

(A) Mass spectrum of the reaction products ionized by 285-nm UV laser pulses. Color-coded ion signals correspond to species associated with the reaction of two KRb molecules compared with the ionization background (the green trace). Noise ions that show up in both the signal and the background spectra have no appreciable effect on the ion signals of interest (section S6). m/z, mass/charge ratio. (B) Geometries of the relevant beams with schematic representations of the reactants and products superimposed. The Gaussian beam spot in the center is the ODT and the ring surrounding it is the ionization beam. (C to E) TOF data for the KRb+, K2+, and Rb2+ ions, respectively. The red curve in (C) is a time resolution–limited Gaussian to describe TOF line shape for the ions generated in the center, whereas the curves in (D) and (E) are simulated TOF line shapes for the ions generated in the ring. For the simulation, we use physical parameters of our system such as the diameter of the hollow-bottle beams (0.45 mm), the intersection angle of the two hollow beams (40°), and the VMI electric field (section S3). The only fitting parameter in this model is the overall amplitude of the signal. (F to H) Momentum distributions of the KRb+, K2+, and Rb2+ ions, respectively. White solid circles represent the active area of the detector; yellow dashed circles represent the momenta corresponding to 10.4 cm−1 of translational energy.

The dominant peaks in the mass spectrum (Fig. 3A) are again K+, Rb+, and KRb+, primarily from photoionization of trapped KRb molecules by the residual intensity at the centers of the hollow-bottle beams. Aside from these dominant peaks, we can clearly identify ions corresponding to the masses of K2+ and Rb2+. All peaks aside from these five species appear with comparable intensities in a background spectrum (green trace) taken in the absence of ultracold atoms and molecules.

We postulate that K2+ and Rb2+ come from direct ionization of the reaction products K2 and Rb2 (Fig. 1). To support such an assignment, we draw evidence from the TOF line shapes and the VM images. The TOF line shapes characterize the spatial origin of the ions in the ionization beam. The KRb+ line shape (Fig. 3C) is sharp and described well by the time resolution–limited Gaussian for ions that originate from the central part of the hollow ionization beams, which coincides with the position of the ODT. K2+ and Rb2+ share similar TOF line shapes, as shown in Fig. 3, D and E, which are much wider than that of KRb+. The simulated line shape (with only total amplitude as a free parameter; see section S3 in the supplementary materials) based on the beam geometry for particles ionized by the ring portion of the hollow ionization beams matches well to the data, which supports the assignment that these signals are from reaction products escaping the central KRb cloud. The presence of a center peak in Fig. 3E that is not captured by the simulated curve is likely due to the product ionization at the center of the hollow beams, where the beams are not perfectly dark. We also rule out the role of ion-neutral reactions, owing to their negligible estimated rates (section S4).

In addition to the mass spectrometry of the K2+ and Rb2+ ions, we simultaneously recorded the momentum distribution of the K2+ and Rb2+ ions with VMI (Fig. 3, G and H). To characterize the radius of the distribution, we performed Bayesian fits (section S5) to the images, assuming a circular Gaussian density on a flat background with uninformative priors. The radius of K2+ (or Rb2+) corresponds to a translational energy of 0.59 cm−1 (0.29 cm−1), well above the MCP resolution of 0.02 cm−1. The ionization process of K2 (Rb2) would impart to the resulting ion a photon recoil energy of 0.0159 cm−1 (0.0112 cm−1), too small to substantially affect the momentum distribution of the ions. Therefore, the measured K2+ and Rb2+ translational energies closely resemble those of their parent neutrals. The sum of measured translational energies is smaller than the exothermicity, 10.4 cm−1, of the bimolecular KRb reaction (Fig. 1). Further, their translational energy ratio, 0.49 ± 0.06, is consistent with the expected ratio, 0.46, originating from two different mass products flying apart with zero center-of-mass momentum. This finding provides further evidence to support the identification of K2+ and Rb2+ ions as arising from ionization of the products of the KRb + KRb chemical reaction.

Next, we focused on the transient intermediate collision complex, K2Rb2*. To observe the complexes that by conservation of momentum should exist only in the vicinity of the reactants, we shaped the UV ionization beam into a Gaussian beam profile. After data accumulation, we observed signals consistent with the masses of K2Rb+ and KRb2+ (fig. S2). On the basis of their VM images, which show large translational energies (Fig. 4A, inset), we hypothesize that these ions are from dissociative ionization of K2Rb2*. To substantiate this idea, we varied the wavelength of the ionization beam to determine the relationship between the translational energy of the triatomic ions and the energy of the photon. We found that the characteristic translational energy associated with the KRb2+ ion decreases as the ionization energy decreases. The ionization energy where the translational energy becomes zero (at 345 ± 4 nm) agrees with our theoretical predictions (346 ± 2 nm) of the dissociative ionization threshold for the transient intermediate, K2Rb2* + hν → KRb2+ + K(4s) + e (h, Planck’s constant; ν, photon frequency; e, electron).

Fig. 4 Direct detection of the intermediate complex K2Rb2*.

(A) (Inset) VM image of detected KRb2+ ions (using an ionization laser wavelength of 285 nm). For each wavelength, R2 is extracted from such an image, where R is the Gaussian width of the ion spatial distribution and R2 is proportional to the TER. The measured TER of the KRb2+ ions is plotted versus the ionization photon energy. Error bars denote the standard deviation of the mean (standard error). Fits are described in section S5. The solid line is an unweighted linear fit to the data above 2.9 × 104 cm−1, with a RMSE of 1.44, from which an experimental dissociative ionization threshold wavelength of 345 ± 4 nm is determined. (B) Calculated threshold wavelengths of the direct photoionization and dissociative ionization of the intermediate complex. The energies for the dissociative ionization thresholds are those corresponding to the equilibrium geometry of the ionic complex (table S1) and are therefore lower bounds on the ionization energy. (C) TOF mass spectrum produced using an ionization laser wavelength of 356 nm. (Inset) Corresponding VM image of the detected K2Rb2+ ions. The yellow dashed circle corresponds to 10.4 cm−1. We do not observe any species larger than K2Rb2, up to m/z = 1500. (D) K2Rb2+ counts are plotted against toff, where toff denotes the length of ODT off-time before UV photoionization. Error bars include shot noise and 10% molecule number fluctuations. A weighted linear fit (blue line) with a RMSE of 1.17 determines a slope of −0.2 ± 0.2, consistent with a zero value.

These theoretical calculations of ionization threshold energies of diatomic, triatomic, and tetratomic K- and Rb-containing molecules (Fig. 4B) are based on the same methodology used in (35) and references therein. Briefly, each alkali-metal atom was modeled as a one-electron system in the field of an ionic core (K+ or Rb+). We used a semiempirical effective core potential plus a core polarization potential to represent the correlation between the valence electron and the core electrons (32). The K2Rb+ and KRb2+ triatomic ions were modeled as two–valence electron systems and the K2Rb2+ ion as a three–valence electron molecule. In the framework of such a simplification, the ground-state potential energy surface can be obtained with good accuracy via the diagonalization of the full electronic Hamiltonian (i.e., full configuration interaction) expressed on a large Gaussian basis set. For all molecular and atomic species, the energies were computed with respect to the same origin—namely, the energy of the four cores (K+ + K+ + Rb+ + Rb+). This allowed for the determination of transition energies between different species.

To directly observe the transient intermediate complex K2Rb2*, we tuned the wavelength of our ionization laser to 356 nm, with energy well below the lowest dissociative ionization channel. Figure 4C displays a mass spectrum obtained with ionization at 356 nm, and a strong signal of K2Rb2+ is evident. Notably, the ionization process transforms the transient intermediate into a bound molecular ion that has no energetically allowed dissociation channel (Fig. 4B) and can therefore survive its flight to the MCP. Although we have not yet directly measured the lifetime of the complex, owing to the technical challenges of precisely establishing a zero of time, the signal strength of our direct observation enables an estimated lifetime of 350 ns (or 3 μs), assuming the ionization cross section of the K2Rb2 intermediate complex is 10 Mb (or 1 Mb). This cross section has not been reported in the literature.

The origin of the observed intermediate complex has been the subject of previous debate (10, 25). The long-lived transient complex could potentially collide with another KRb, causing the prior’s decay into a deeply bound K2Rb2 molecule and leading to the conversion of its internal energy into a large, observable TER (25, 26). In contrast, we observe a detector resolution–limited small momentum distribution of the K2Rb2+ ions (Fig. 4C, inset), consistent with the zero-momentum transient intermediate.

Moreover, because the reactants are trapped in the ODT, a light-assisted process could be a competing, confounding factor, as suggested by Christianen et al. (10). To examine the role of the ODT on the detected intermediate complex, we varied the time that the ODT was switched off before ionization from 1 to 70 μs (see inset of Fig. 4D). If the ODT contributed to the formation of deeply bound K2Rb2 molecules, which have no radiative decay pathway and only potentially leave the probed volume on a millisecond time scale if untrapped, K2Rb2 would steadily build up in concentration in the presence of the ODT. As a result, the concentration of K2Rb2 should decrease monotonically as the ODT off-duration increases. Instead, we find that the yield of K2Rb2+ ions has no monotonic trend with the ODT off-duration (Fig. 4D). This result is evidence that the intermediates we observe are formed upon collision of two KRb molecules, with no notable effect from the ODT.

The direct observation of 2KRb → K2Rb2* → K2 + Rb2 opens numerous possibilities of exploring the detailed role of quantum mechanics in ultracold chemical reaction dynamics by measuring the lifetime of the intermediate complex (25, 26), testing the transition from quantum to semiclassical reactions (36), and resolving the quantum states of the reaction products (37) and the intermediate.

Supplementary Materials

Supplementary Text

Figs. S1 to S4

Tables S1 to S2

References (4252)

References and Notes

  1. See details in the supplementary materials.
  2. It would take 170 μs for a Rb2 molecule with translational energy of 0.0127 cm−1 to travel from the center of the KRb cloud to the ionization ring with a diameter of 0.45 mm.
Acknowledgments: We thank D. Herschbach, L. Zhu, T. Karman, and J. Ye for discussion; K. Liu for introducing us to the VMI techniques; T. Pfau, E. Narevicius, and M. Greiner for discussions on apparatus design; J. Doyle for loaning laser equipment; and W. Stwalley, P. Gould, and the late E. Eyler for sharing KRb spectroscopy literature. The 40K isotope used in this research was supplied by the U.S. Department of Energy (DOE), Office of Science, by the Isotope Program in the Office of Nuclear Physics. Funding: This work is supported by the DOE Young Investigator Program, the David and Lucile Packard Foundation, and the NSF through the Harvard-MIT CUA. Author contributions: The experimental work and data analysis were carried out by M.-G.H., Y.L., D.D.G., Y.-W.L., A.H.G., T.R., and K.-K.N. Theoretical calculations were done by R.V., N.B.-M., and O.D. All authors contributed to interpreting the results and writing the manuscript. Competing interests: The authors declare no competing interests. Data and materials availability: Data from the main text and supplementary materials are available through the Harvard Dataverse (41).
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