Mechanisms of anomalous three-body loss in a population-imbalanced three-component Fermi gas

TL;DR

This work develops a full three-body treatment for three distinguishable spin components in a $^6$Li Fermi gas using a hyperspherical adiabatic representation with van der Waals interactions and an eigenchannel $R$-matrix to obtain the $S$-matrix. At the field where the anomalous decay is observed, the three-body recombination rate scales as $K_3(E) \propto E^{-1}$ due to near-unitarity, and the thermally averaged rate $\langle K_3\rangle$ becomes sensitive to temperature and per-spin densities via $E_F^{(i)}\propto n_i^{2/3}$. Channel-resolved recombination and cross sections feed a Monte Carlo cascade that tracks secondary collisions and trap escape, revealing that most events remove fewer than three atoms and that energy retained in the gas drives evaporative loss, offering a plausible mechanism for the observed anomalous decay. The results connect microscopic few-body physics to macroscopic loss dynamics in a degenerate, three-component Fermi gas and highlight the role of secondary collisions and heating in shaping trap lifetimes near unitarity.

Abstract

Achieving precise control of ultracold atomic gases requires a detailed understanding of atom loss mechanisms. Motivated by the anomalous three-body decay in a three-component Fermi gas reported in Ref. [1], this work investigates mechanisms that possibly contribute to the observed loss. The three-body Schrödinger equation is solved in the hyperspherical adiabatic representation with pairwise van der Waals interactions, and the $S$-matrix is obtained via the eigenchannel $R$-matrix method to compute recombination rate coefficients $K_3$ and two-body cross sections. At the magnetic field strength where the anomalous decay occurs, $K_3$ is unitary limited, exhibiting the threshold energy scaling $K_3(E)\propto E^{-1}$. Consequently, the thermally averaged $\langle K_3 \rangle$ acquires a temperature dependence. Because the experiment is performed in the degenerate regime, $\langle K_3 \rangle$ also explicitly depends on the per-spin densities through the per-spin Fermi energies $E_{F}^{(i)}\propto n_i^{2/3}$. As the gas is diluted and degeneracy is reduced, $\langle K_3 \rangle$ approaches the non-degenerate value and becomes a function of temperature only. Channel-resolved branching ratios and cross sections are folded into a Monte Carlo cascade simulation of secondary collisions and trap escape. The analysis indicates that typical three-body recombination events remove fewer than three atoms on average, and that the atom losses are primarily due to the ejection of secondary collision products, rather than the initial three-body recombination products. Therefore, a significant fraction of the released binding energy remains in the trapped ensemble as kinetic energy. Retained energy drives evaporative loss, offering a plausible, partial explanation for the anomalous decay.

Figures (8)

• Figure 1: Scattering lengths $a(B)/r_{\rm vdW}$ for each spin pair as a function of magnetic field strength. The curves show the magnetic-field dependence of the two-body scattering lengths between the three lowest spin states of $^6$Li, expressed in units of the van der Waals length $r_{\rm vdW}$. Data adapted from Ref. Zurn2013.
• Figure 2: Effective three‐body hyperradial potentials $W_{\nu}(\rho)$ at $B = 690$ G. In the inset (zoomed-in region), the two deepest curves ($\nu=-2$ and $\nu=-1$) each asymptote at large $\rho$ to the negative binding energy of their respective Feshbach dimers, whereas the highest curve ($\nu=0$) merges into the three-atom continuum.
• Figure 3: Rescaled effective potentials $\xi^2_{\nu}(\rho)$ computed at $B = 690$ G. The dotted black line marks the Efimovian value $-s_0^2$ for three identical bosons, while the dashed black line indicates the universal coefficient $p_0^2 = 1$ associated with Efimov-like repulsion in a three-body system of distinguishable atoms. The two upper curves have been diabatized through a peak caused by an avoided crossing in the corresponding adiabatic potential energy curves.
• Figure 4: Rescaled effective potential $\xi_0^2(\rho)$ for the $\nu = 0$ channel at $B = 845$ G, where all pairwise scattering lengths are negative and large in magnitude. In the scale-free region $r_{\rm vdW} \ll \rho \ll |a_{ij}|$, the potential approximates the Efimovian form. At large $\rho$, it asymptotically approaches the free three-body continuum limit corresponding to $\lambda = 0$.
• Figure 5: Calculated binding energies of the first excited Efimov trimer and two-body dimer thresholds versus $B$, alongside experimental three-body radio-frequency association data from Lompe et al.Lompe2010b. Solid red and blue curves show the $(12)$ and $(23)$ dimer thresholds. The black, white, and gray solid curves with circular markers represent the calculated trimer binding energies obtained with the diagonal correction [\ref{['eq:3BP_dia']}], with three coupled channels [\ref{['eq:coupledequations']}], and without the diagonal correction. Black squares and red circles denote the experimental trimer binding energies extracted from Fig. 4 of Ref. Lompe2010b for the $\ket{1}$--$\ket{12}$ and $\ket{2}$--$\ket{23}$ initial mixtures.