Controlling few-body reaction pathways using a Feshbach resonance

TL;DR

This work demonstrates coherent, spin-selective control of a three-body recombination pathway in ultracold $^{85}$Rb by magnetically admixing a specific spin state via a Feshbach resonance near $B\approx 155$ G. By tuning the admixture, the authors steer the reaction flux into particular spin channels, achieving large reallocation of the total three-body flux among product states, as observed with REMPI detection and supported by adiabatic hyperspherical calculations. The study reveals that an Efimov resonance globally enhances the total recombination rate $L_3$ without altering the relative channel flux, highlighting a distinction between global rate enhancement and pathway-specific control. The approach is general, coherent, and can be extended to other few-body reactions and interferometric control schemes, offering a versatile tool for state-selective chemistry at ultracold temperatures. The results establish a foundation for integrating Feshbach-based beam-splitting with other control methods to tailor final product spin-character and reaction pathways.$

Abstract

Gaining control over chemical reactions on the quantum level is a central goal of the modern field of cold and ultracold chemistry. Here, we demonstrate a novel method to coherently steer reaction flux of a three-body recombination process across different product spin channels. For this, we employ a magnetically-tunable Feshbach resonance to admix, in a controlled way, a specific spin state to the reacting collision complex. This allows for the control of the reaction flux into the admixed spin channel, which can be used to significantly change the reaction products. Furthermore, we also investigate the influence of an Efimov resonance on the reaction dynamics. We find that while the Efimov resonance can be used to globally enhance three-body recombination, the relative flux between the reaction channels remains unchanged. Our control scheme is general and can be extended to other reaction processes. It also provides new opportunities in combination with other control schemes, such as quantum interference of reaction paths.

Figures (6)

• Figure 1: Scheme for controlling the reaction flux into different spin channels using a two-body Feshbach resonance. (a) Atoms ($a,b,c$) undergo three-body recombination, where ($a,b$) form a molecule. During this process, atom $(c)$ is outside the ranges (cyan areas) for spin-exchange interaction with the other atoms. (b) Schematic representation of the Born-Oppenheimer potential energy curves for the atom pair ($a,b$). At close distance, the incoming scattering state (1) with spin $|\space\uparrow \rangle$ experiences admixing of the bound state (2) which has spin $|\space\downarrow \rangle$. Upon collision with the third atom ($c$) (not shown here) the scattering state can then relax into molecular bound states (3) or (4), with their respective spin states $|\space\downarrow \rangle$ and $|\space\uparrow \rangle$.
• Figure 1: Scattering length in the vicinity of the $s$-wave Feshbach resonance. The scattering length in units of Bohr radius is plotted as a function of magnetic field.
• Figure 2: Observation of $|\space\uparrow \rangle$ and $|\space\downarrow \rangle$ molecules. Shown are REMPI spectra as a function of the REMPI laser frequency $\nu$ for various magnetic fields $B$. Here, $\nu_0=497603.591\:\textrm{GHz}$. Each dip in a trace corresponds to a signal from a distinct molecular level. The REMPI signals are normalized, ranging from 0 to 1, as indicated by the vertical bar. The bar is valid for all data traces. The diamonds mark the theoretical positions of possible molecular signals and the colors indicate the spin state as well as the vibrational and rotational level ($\textrm{v}, L_R$). The faint color bands connecting the diamonds are guides to the eye. We note that the binding energy of the $|\space\uparrow \rangle$ level is smaller than that of the two $|\space\downarrow \rangle$ levels. In the shown spectra, however, the signal for $|\space\uparrow \rangle$ is at higher frequency $\nu$ since the intermediate rotational level for the REMPI is different, see also Methods.
• Figure 2: The three-body recombination rate constant $L_3$ for the $|\space\uparrow \rangle(-3,4)$ state at $80$ nK is compared to that at $860$ nK. The dashed line indicates the $L_3\propto a^4$ scaling.
• Figure 3: Opening up a product spin channel. (a) Molecule detection rates for three product states for which the quantum numbers $| \uparrow / \downarrow \rangle (\textrm{v}, L_R)$ are given in the legend. The gray dashed line marks the experimental detection limit and the light-green and purple shaded areas indicate the position of the Efimov and Feshbach resonance, respectively. The error bars in the plot indicate one standard deviation (1$\sigma$). (b) Calculated three-body recombination rate coefficients. The black dashed line is the total rate coefficient $L_{3,\mathrm{tot}}$. Solid colored lines correspond to partial rates for the states under discussion. Gray lines correspond to other molecular states. No calculations are shown for $152\:\textrm{G}\leq B \leq 157\:\textrm{G}$, see text. We expect theoretical errors up to a few tens of percent for the partial rate for vibrational levels down to v $= -4$, judging from when more vibrational states are included in our effective potentials Haze2023. (c) The normalized reaction rate coefficients $L_3/L_{3,\mathrm{tot}}$ do not exhibit a maximum at the Efimov resonance.