Asymmetric Lineshapes of Efimov Resonances in Mass-Imbalanced Ultracold Gases

Panagiotis Giannakeas,Chris H Greene

doi:10.3390/atoms9040110

Panagiotis Giannakeas, Chris H Greene

Open Access

https://doi.org/10.3390/atoms9040110

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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|→∞, 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.

Highlights

Heavy dimer possesses a unique property that only mass-imbalanced systems exhibit, namely the co-existence of Efimov resonances with Stückelberg suppression effects in the same range of scattering lengths. We further study this particular attribute of HHL systems and demonstrate that the corresponding Efimov resonances in the recombination rate coefficient plotted versus scattering length can display an asymmetric profile, which can be quantified by the Fano profile formula
Relaxation and recombination processes into deep dimer channels are neglected, and we focus on the physics that arises due to energies near the break-up threshold, i.e., the zero-energy limit
We focus on the two lowest potential curves of HHL systems, which suffice to describe three-body recombination processes into shallow dimers, as was shown in Ref. [36], permitting the derivation of closed-form expressions for the S-matrix

Summary

Introduction

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Efimov to occur for three equal-mass particles that interact via zero-range potentials, with trimer binding energies that scale geometrically [5] The existence of these exotic trimer states was experimentally confirmed by Kraemer et al in an ultracold gas of Cs atoms [6]. Three-body collisions of ultracold atoms with unequal masses offer more favorable experimental conditions that enable observation of multiple successive trimer states and measurement of their geometrical energy scaling, i.e., the smoking gun of Efimov physics [26,27,28].

General Considerations and Methods

The Adiabatic Hyperspherical Representation and the Semi-Classical Approach

A Simplified Semi-Classical Model

Asymmetric Lineshapes in Three-Body Recombination Coefficients

Summary