Asymmetric lineshapes of Efimov resonances in mass-imbalanced ultracold gases

TL;DR

This work addresses how mass-imbalanced three-body systems (HHL) exhibit asymmetric Efimov resonances in recombination into a shallow dimer, due to the coexistence of Efimov states with Stückelberg interference minima. By coupling an adiabatic hyperspherical framework with a semiclassical two-channel model and, separately, a simplified tail-based approach, they derive closed-form expressions for the recombination amplitude via $|S_{12}|^2$ and recast the resonant profiles into a Fano form with a tunable asymmetry parameter $q$ and width $ Gamma$. They demonstrate a $q$-reversal as the ratio $rac{|a_{HL}|}{a_{HH}}$ varies and show that as $|q| oty$, the Efimov resonances acquire zero width and effectively become bound states embedded in the three-body and atom-dimer continua. The results, illustrated with ${}^{6} m{Li}$-${}^{133} m{Cs}$-${}^{133} m{Cs}$ and ${}^{6} m{Li}$-${}^{87} m{Rb}$-${}^{87} m{Rb}$ systems, provide a practical fitting framework for experimental data and highlight novel phenomena unique to heteronuclear three-body collisions, such as q-reversal and bound-state-in-continuum behavior.

Abstract

The resonant profile of the rate coefficient for three-body recombination into a shallow dimer is investigated for mass-imbalanced systems. In the low-energy limit, three atoms collide with zero-range interactions, in a regime where the scattering lengths of the heavy-heavy and the heavy-light subsystems are positive and negative, respectively. For this physical system, the adiabatic hyperspherical representation is combined with a fully semi-classical method and we show that the shallow dimer recombination spectra display an asymmetric lineshape that originates from the coexistence of Efimov resonances with Stückelberg interference minima. These asymmetric lineshapes are quantified utilizing the Fano profile formula. In particular, a closed form expression is derived that describes the width of the corresponding Efimov resonances and the Fano lineshape asymmetry parameter $q$. The profile of Efimov resonances exhibits a $q-$reversal effect as the inter- and intra-species scattering lengths vary. In the case of a diverging asymmetry parameter, i.e. $|q|\to \infty$, we show that the Efimov resonances possess zero width and are fully decoupled from the three-body and atom-dimer continua, and the corresponding Efimov metastable states behave as bound levels.

Figures (8)

• Figure 1: (Color on line) An illustration of the lowest hyperspherical potential curves $U_\nu^{1/3}(R/a_{HH})$ with $a_{HH}>0$ and $a_{HL}<0$. The red (blue) line saturates at large hyperradii in the atom+dimer (three-body break-up) threshold. The quantities $\Phi^U_L$, and $\Phi^U_L$ indicate the JWKB phase accumulation in the upper potential curve. For the lower potential the corresponding phase is denoted by $\Phi^L_L$. The vertical dashed line represents the hyperradius where the non-adiabatic coupling $P-$matrix element $P_{12}$ maximizes. The horizontal dotted line refers to the three-body collisional energy $\bar{E}$ in units of $\frac{\hbar^2}{m_H a_{HH}^2}$, and the three-body parameter, $\frac{r_{3b}}{a_{HH}}$ depicted by the blue region.
• Figure 2: (Color on line) The Stokes correction phase as a function of the non-adiabatic probability $p$.
• Figure 3: (Color on line) The degree of diabaticity $p$ as a function of the scattering length ratio $a_{HH}/|a_{HL}|$ for different mass ratios $m_H/m_L$ covering the regime of strong-to-weak mass-imbalanced three-body systems.
• Figure 4: (Color on line) The scaled $\frac{|S_{12}|^2}{(k a_{HL})^4}$ matrix element versus the ratios $\frac{|a_{HL}|}{a_{HH}}$ and $\frac{r_{3b}}{a_{HH}}$ for the $^6\rm{Li}-^{87}\rm{Rb}-^{87}\rm{Rb}$ system at low-energy $E=\frac{\hbar^2 k^2}{2\mu}$. (a) semi-classical approach and (b) R-matrix numerical calculations.
• Figure 5: (Color online) An illustration of the approximate hyperspherical potential curves shown in \ref{['fig:fig1']} where $s_0$ and $s_0^*$ are the universal Efimov scaling coefficients. These piecewise curves are used in \ref{['eq:eq10a', 'eq:eq10b', 'eq:eq11']}.