Observation of a Halo Trimer in an Ultracold Bose-Fermi Mixture

TL;DR

This work reports the direct observation of a heteronuclear halo trimer composed of two light Na bosons bound to a heavy K impurity in an ultracold Na-K mixture. Using rf association spectroscopy near a broad Na-K Feshbach resonance, the authors measure the NaK dimer and Na2K trimer binding energies, finding the trimer energy to track the dimer energy across an order-of-magnitude range in interaction strength, consistent with a weakly bound three-body state. The trimer is interpreted as a dimer with a loosely attached third Na, with its structure and line shapes analyzed using adiabatic hyperspherical theory and realistic Na-K potentials; the energies agree with theory within a few kilohertz, and the study reveals universal aspects of halo trimers in heteronuclear mixtures. The results impact our understanding of few-body universality, many-body physics in ultracold mixtures, and molecule-association protocols, while outlining paths to improved lifetimes and more stringent tests of theory.

Abstract

The quantum mechanics of three interacting particles gives rise to interesting universal phenomena, such as the staircase of Efimov trimers predicted in the context of nuclear physics and observed in ultracold gases. Here, we observe a novel type of halo trimer using radiofrequency spectroscopy in an ultracold mixture of $^{23}$Na and $^{40}$K atoms. The trimers consist of two light bosons and one heavy fermion, and have the structure of a Feshbach dimer weakly bound to one additional boson. We find that the trimer peak closely follows the dimer resonance over the entire range of explored interaction strengths across an order of magnitude variation of the dimer energy, as reproduced by our theoretical analysis. The presence of this halo trimer is of direct relevance for many-body physics in ultracold mixtures and the association of ultracold molecules.

Figures (8)

• Figure 1: Detection of halo trimers using radiofrequency spectroscopy. (a) Schematic representation of free-to-bound transitions into Na-K dimer and Na$_2$-K trimer states with binding energies $E_d, E_t$, respectively, red-detuned from the bare atomic hyperfine transition. (b-c) Depletion spectra taken at 101.8 G, where losses due to resonant coupling to the dimer state and trimer state are present in (b) Na and (c) K. The underlying dimer and trimer fitted lineshapes are shown as blue and red shaded regions, respectively, with solid lines marking the binding energies and solid curves showing the summed lineshape.
• Figure 2: Rf-association of dimers and trimers. Depletion spectra of Na (K), shown as the upper (lower) trace within each panel with square (circle) markers, taken at B-fields between 100.5 and 103 G, in proximity to the Feshbach resonance at 110 G. The trimer feature (red shaded) closely tracks the dimer (blue shaded) at each field. The initially prepared K : Na ratios prior to the rf pulse vary between datasets from $0.3-0.65$.
• Figure 3: (a) The ratio between the fitted trimer and dimer feature heights, in the K spectra. (b) The intraspecies ratio of the fitted trimer (red triangles) and dimer (blue circles) peak depletions vs applied magnetic field. The trimer data clusters around $2:1$ Na-K loss ratio, whereas the dimer data lies between $1:1$ and $2:1$. The solid lines (shaded regions) show the weighted mean and standard deviation of the estimated ratios, across magnetic fields.
• Figure 4: (a-b) Depletion spectra taken with a 30 ms Blackman-envelope rf pulse, at $B=105$ G ($a\approx 1633 a_0$). The loss in Na population on the dimer feature is strongly suppressed here. (c) A spectrum taken by applying a shorter 3 ms square pulse, with pulse parameters chosen to observe the arriving dimer and trimer populations in the final state $\ket{\downarrow}_\mathrm{K}$. There is only one spectral feature here, with the trimer arrivals being noticeably absent, due to their short intrinsic lifetime relative to the rf pulse duration.
• Figure 5: (a) The measured binding energies of the dimer (blue) and trimer (red) vs applied magnetic field. Error bars showing 68% confidence intervals are found by bootstrapping and are within the markers. (b) Difference in measured binding energies of the dimer and trimer (green circles) along with the theoretical prediction (solid line). The shaded region shows the FWHM of the Lorentzian convolution kernel used to fit the lineshapes, setting a frequency scale for systematic error of the fit model.