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Physical Review X

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

Alexander Y. Chuang, Huan Q. Bui, Arthur Christianen, Yiming Zhang, Yiqi Ni, Denise Ahmed-Braun, Carsten Robens, Martin W. Zwierlein

Published May 12, 2025• 6 citations
Publisher

Abstract

The quantum mechanics of three interacting particles gives rise to fundamental and 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 radio-frequency spectroscopy in an ultracold mixture of Na 23 and K 40 atoms. The trimers consist of two light bosons and one heavy fermion, and they 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 and 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.

DOI
10.1103/flty-9d72

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The quantum mechanics of three interacting particles gives rise to fundamental and 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 radio-frequency spectroscopy in an ultracold mixture of Na 23 and K 40 atoms. The trimers consist of two light bosons and one heavy fermion, and they 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 and 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.
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^{23}23Na and 40^{40}40K 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.
This thesis reports on experiments studying the few-body physics of three distinguishable fermionic atoms with large scattering lengths. The experiments were performed with ultracold gases of fermionic 6Li atoms in three different hyperfine states. By tuning the strength of the interactions between the atoms with Feshbach resonances and measuring the rate constants for inelastic three-atom and atom-dimer collisions the intersections of two universal trimer states with the three-atom and atom-dimer continuum could be located. Subsequently, one of these Efimov states was directly observed with RF-association spectroscopy. Using this technique the binding energy of this Efimov state was measured as a function of the strength of the interparticle interactions. The experiments presented in this thesis provide a nearly complete understanding of the universal few-body physics of three-component Fermi gases of 6Li atoms. This understanding will be the foundation for future studies of the many-body physics of three-component Fermi gases.
Few-Body Problem Seemingly simple, quantum mechanical few-body systems are notoriously difficult to describe. Efimov trimers, three-body bound states with interactions tuned to be in close vicinity of the formation of two-body bound states, are the most tractable of these systems, with relevance, for example, in nuclear physics. Observed recently in ultracold atomic gases through their signatures in the rate of inelastic three-body collisions, Efimov trimers are predicted to appear at interaction strengths whose ratios are universally specified. By measuring binding energy as a function of interaction strength, Lompe et al. (p. 940 ) directly observed the association of three distinguishable atoms into a bound state. This technique may enable more precise studies of the trimer state, potentially revealing the nature of nonuniversal corrections suggested by prior experiments.
Ultracold atomic gases with tunable interactions offer an ideal platform for studying interacting quantum matter. While the few- and many-body physics are generally complex and intractable, the problem can be greatly simplified in an atomic gas by a controlled separation of relevant length and energy scales. Precise control of experimental parameters, via Feshbach resonances, optical potentials and radio-frequency radiation, enables deterministic measurements of few-body physics, including universal physics and the Efimov effect. In this thesis, I present our recent studies on precisely measuring two- and three-body physics in an ultracold Bose gas. I begin by describing our new apparatus used for generating and studying ultracold 39K gas samples. Then, I focus on our precision spectroscopy of Feshbach dimer binding energies, spanning three orders of magnitude and with sub-kilohertz resolution. These measurements enable us to locate a Feshbach resonance and determine scattering length values with unprecedented accuracy. Finally, I present our precise measurements locating an exotic three-body state, specifically the Efimov ground state. We find that the trimer state location significantly deviates from the value predicted by van der Waals universality. Due to small experimental and systematic uncertainties, our measurement is the strongest evidence of departure from the universal value and is the first observed deviation near a Feshbach resonance of intermediate strength.
We present a theoretical analysis of rf association of Efimov trimers in a two-component Bose gas with short-range interactions. Using the adiabatic hyperspherical formalism to solve the quantum three-body problem, we obtain universal expressions for three-body rf association rates as a function of the sss-wave scattering length a>0a>0a>0. We find that the association rates scale as ${a}^{\ensuremath{-}2}$ in the limit of large aaa, and diverge as a3aad3{a}^{3}{a}_{ad}^{3}a3aad3​ whenever an Efimov state crosses the atom-dimer threshold (where aad{a}_{ad}aad​ stands for the atom-dimer scattering length). Our calculations show that trimer formation rates as large as $\ensuremath{\sim}101010{}^{\ensuremath{-}21}$ cm6{}^{6}6/s can be achieved with rf Rabi frequencies on the order of 1 MHz, suggesting that direct rf association is a powerful tool for making and probing few-body quantum states in ultracold atomic gases.
Three interacting particles form a system which is well known for its complex physical behavior. A landmark theoretical result in few-body quantum physics is Efimov's prediction of a universal set of weakly bound trimer states appearing for three identical bosons with a resonant two-body interaction. Surprisingly, these states even exist in the absence of a corresponding two-body bound state and their precise nature is largely independent of the particular type of the two-body interaction potential. Efimov's scenario has attracted great interest in many areas of physics; an experimental test however has not been achieved. We report the observation of an Efimov resonance in an ultracold thermal gas of cesium atoms. The resonance occurs in the range of large negative two-body scattering lengths and arises from the coupling of three free atoms to an Efimov trimer. We observe its signature as a giant three-body recombination loss when the strength of the two-body interaction is varied near a Feshbach resonance. This resonance develops into a continuum resonance at non-zero collision energies, and we observe a shift of the resonance position as a function of temperature. We also report on a minimum in the recombination loss for positive scattering lengths, indicating destructive interference of decay pathways. Our results confirm central theoretical predictions of Efimov physics and represent a starting point from which to explore the universal properties of resonantly interacting few-body systems.