Delta-Kick Collimation of Heteronuclear Feshbach Molecules

TL;DR

This work extends delta-kick collimation to heteronuclear Feshbach molecules, showing that DKC can dramatically reduce expansion energies in both condensed and thermal regimes and that vibrational and translational motions remain largely decoupled during the kick. By employing a separable CM–relative motion framework and scaling dynamics across regimes, the study demonstrates robust collimation with final energies at the tens of picokelvin scale and provides guidance on parameter choices and time scales. The results have implications for long interrogation times in molecular interferometry and dual-species precision tests, including universality of free fall, and point toward future avenues such as space-based experiments and re-trapping with shallow optical potentials. Challenges remain in experimentally optimizing pre-expansion timing and trap parameters to push performance closer to theoretical limits.

Abstract

We present a theoretical study of delta-kick collimation (DKC) applied to heteronuclear Feshbach molecules, focusing on both condensed and thermal ensembles across various interaction and temperature regimes. We demonstrate that DKC enables significant reductions in molecular cloud expansion energies and beam divergence, achieving expansion energies in the picokelvin range, comparable to state-of-the-art results obtained experimentally with atoms. Furthermore, we show that vibrational and translational motions remain strongly decoupled throughout the process, ensuring molecular stability during the delta-kick. This work paves the way for advanced experimental sequences involving degenerate ground state molecules, light-pulse molecular interferometry, and applications of dual-species precision measurements, such as testing the universality of free fall.

Figures (3)

• Figure 1: Time evolution of the energies $E_\mathrm{R}(t)$ (red solid line and black dots in panel (a)), $E_\mathrm{r}(t)$ (blue dashed line in panel (b)), and $E_\mathrm{c}(t)$ (green dash-dotted line in panel (b)) during a typical DKC process. The solid red line represents results obtained including the coupling between the center-of-mass and vibrational motions, while the black dots correspond to calculations where this coupling is neglected.
• Figure 2: Expansion energy gain $\mathcal{G} = E_i/E_f$ as a function of the DKC duration for both the Thomas-Fermi regime (purple solid line) and the variational approach at different scattering lengths. While the gain does not depend on the scattering length in the Thomas-Fermi approach, the variational approach shows variations as the scattering length decreases from 500 a.u. (blue dotted line) to 250 a.u. (orange dashed line) and finally to 50 a.u. (red dash-dotted line). As expected, higher interaction strengths bring the gain of the variational method closer to that of the Thomas-Fermi regime.
• Figure 3: Expansion energy gain $\mathcal{G} = E_i/E_f$ as a function of the DKC duration for a molecular ensemble at finite temperature, with the molecule-molecule scattering length fixed at $a_\mathrm{dd} = 500$ a.u.. Different values of $\xi$ are investigated, corresponding to various thermal regimes. For $\xi = 0.9999$ (2 nK, purple dashed line), the system is in the condensed regime. For $\xi = 0.8958$ (30 nK, blue dotted line) and $\xi = 0.7056$ (50 nK, orange dash-dotted line) the system transitions to the hydrodynamic regime. Finally, $\xi = 0$ (red solid line) corresponds to a purely thermal ensemble. The maximum gains achieved in each case are as follows: 550 for the condensed regime $(\xi=0.9999)$, 282 for $\xi=0.8958$, 164 for $\xi=0.7056$, and 90 for the thermal regime $\xi=0$.