Steering reaction flux by coupling product channels

TL;DR

The paper demonstrates a method to steer reaction flux between two product channels in an ultracold three-body recombination by magnetically tuning an avoided crossing between molecular exit channels $|U\rangle$ and $|L\rangle$ via an external field $\mathcal{B}$. By controlling the mixing angle $\alpha(\mathcal{B})$, the scheme behaves as a local beam splitter for the reaction pathway, directing flux according to the spin-content overlaps $|\ angle$ and enabling selective population of product channels. Experimental measurements on ultracold $^{87}$Rb show tunable production rates for the upper and lower branches, with flux redirected by up to a factor of about $19$ between channels, and these trends are captured qualitatively by two-body coupled-channel models and three-body simulations, albeit with quantitative discrepancies suggesting higher-order effects. The approach is general due to the ubiquity of energy-level crossings and could be combined with entrance-channel control methods (e.g., Feshbach schemes) to achieve more complex, interferometric control of chemical reactions across diverse species.

Abstract

We demonstrate a method for controlling the outcome of an ultracold chemical few-body reaction by redirecting a tunable fraction of reaction flux from one selected product channel to another one. In the reaction, three ultracold atoms collide to form a diatomic molecule. This product molecule can be produced in various internal states, characterizing the different product channels of the reaction. Our scheme relies on the coupling between two such product channels at an avoided molecular energy level crossing in the presence of an external magnetic field. The degree of coupling can be set by the magnetic field strength and allows for a widely tunable flux control between the two channels. This scheme is quite general and also holds great promise for a large variety of chemical processes with diverse species, since molecular energy level crossings are ubiquitous in molecular systems and are often easily accessible by standard laboratory equipment.

Figures (7)

• Figure 1: Schematic of a three-body recombination reaction, viewed in terms of coupled reaction channels. Three atoms on an entrance channel enter the reaction zone where they form a reaction complex. Coupling of channels allows for the reaction to propagate along various pathways. Some couplings can be externally tunable (e.g. the coupling between the channels labeled exit 1 and exit 2, as marked by the dashed ellipse). The particles leave the reaction zone on product/ exit channels, e.g., in terms of a diatomic molecule in a particular internal quantum state (as indicated by different colors) and a free atom. Exit channels denoted in parentheses are not connected to the entrance channel and therefore obtain no reaction flux.
• Figure 2: Schematics of the proposed reaction control scheme. (a) The two bare states $|B\uparrow \rangle$ and $|B\downarrow \rangle$ are coupled and form an avoided crossing as a function of the magnetic field. This results in a lower and an upper branch, $| L \rangle$ and $| U \rangle$, respectively. These two branches correspond to two exit channels of the three-body recombination reaction starting from the scattering state $|S\uparrow \rangle$. By tuning the external magnetic field, the reaction flux can be continuously steered between $| L \rangle$ and $| U \rangle$. The widths of the vertical arrows illustrate this behavior in a qualitative way. (b) Calculated spin contents $\left| \braket{ \uparrow | U} \right|^2$ and $\left| \braket{ \uparrow | L} \right|^2$ which correspond to the $| \uparrow \rangle$ components of $| U \rangle$ and $| L \rangle$.
• Figure 3: (a) Avoided crossing of the bare states $| B \uparrow \rangle$ and $| B \downarrow \rangle$, giving rise to an upper branch level $|U\rangle$ (red) and a lower branch level $|L\rangle$ (blue). The solid lines are calculated binding energies from a coupled-channel calculation. The data points are binding energies extracted from REMPI spectroscopy, where resonance positions were measured in small frequency steps with three repetitions of the experiment per frequency setting. Here, $h$ is Planck's constant. The error bars mainly reflect the typical uncertainty of the laser frequency and have been extracted from lorentzian fits of the resonance positions (95% confidence level). (b) REMPI spectra of the avoided crossing as a function of the laser frequency $\nu$ for four different magnetic fields $\mathcal{B}$. The REMPI spectra show the normalized atom number with a scale as indicated for the spectrum at the magnetic field of 85 G. Each data point represents the mean value of five repetitions of the experiment and the error bars correspond to one standard deviation. Four spectra corresponding to different magnetic fields are presented. The leftmost dip and the adjacent dip correspond to $|U\rangle$ and $|L\rangle$, respectively.The two dips on the right correspond to a reference level, $| R \uparrow \rangle$, detected via the intermediate levels $J'=3$ and $J'=5$Rescaling, respectively. The offset $\nu_0$ = 500.974420(10) THz is the photoassociation transition frequency towards the intermediate state $(2)^1\Sigma_u^+$, v$'$ = 36, $J'$ = 1 at zero magnetic field. The offset $\nu_Z$ is the Zeeman shift of the reference level which corresponds to the Zeeman shift of the atom pair $(f=1,m_f=-1)+(f=1,m_f=-1)$.
• Figure 4: (a) Measured ion production rates for the three product states $|U\rangle$, $|L\rangle$ and $|R \uparrow \rangle$. The reference state $|R \uparrow \rangle$ is detected via both the intermediate state $J'=3$ and $J'=5$Rescaling.The error bars are the standard deviations. The experiment was repeated 30 times for each data point. (b) Calculated molecular $| \uparrow \rangle$ content for the upper and lower molecular state, $\left| \braket{ \uparrow | U/L } \right|^2$, as in Eq. (\ref{['eq:1']}). For the calculation we used a two-body coupled channel Schrödinger equation with full molecular potentials.
• Figure S1: Calculated three-body recombination rate coefficients. The orange (blue) line corresponds to the upper (lower) state.