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arXiv:2606.02988

Effective scatterings and universal clusters of heteronuclear ultracold mixtures in quasi-low dimensions

Tingting Shi, Xiaoling Cui

Published Jun 2, 2026• 0 citations
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Abstract

We study the effective s-wave scattering of two heteronuclear atoms harmonically confined in quasi-low dimensions, where the atoms have unequal masses and are subject to different confinement frequencies. The resulting effective scattering parameters in low dimensions, including scattering length and effective range, are derived as functions of three-dimensional scattering parameters and confinement strengths. Using realistic Li-K and Li-Cr mixtures as examples, we further compute the binding energies of universal $(1+N)$ clusters in quasi-low dimensions using the effective scattering parameters. Our findings suggest a promising pathway for practically observing universal clusters and their associated many-body phases in low-dimensional ultracold heteronuclear systems.

DOI
10.48550/arxiv.2606.02988

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We study the effective s-wave scattering of two heteronuclear atoms harmonically confined in quasi-low dimensions, where the atoms have unequal masses and are subject to different confinement frequencies. The resulting effective scattering parameters in low dimensions, including scattering length and effective range, are derived as functions of three-dimensional scattering parameters and confinement strengths. Using realistic Li-K and Li-Cr mixtures as examples, we further compute the binding energies of universal (1+N)(1+N)(1+N) clusters in quasi-low dimensions using the effective scattering parameters. Our findings suggest a promising pathway for practically observing universal clusters and their associated many-body phases in low-dimensional ultracold heteronuclear systems.
We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal (zzz-) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (CoM) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length a2Da_{\rm 2D}a2D​, the 2D effective range parameter R2DR_{\rm 2D}R2D​, and the bound-state energies, as functions of the sss-wave scattering length and effective range of the two atoms in free three-dimensional (3D) space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion. Around these resonances, a2Da_{\rm 2D}a2D​ varies rapidly with the 3D scattering parameters, while R2DR_{\rm 2D}R2D​ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by i.e., the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.
We study universal clusters in quasi-two-dimensions (q2D) that consist of a light (L) atom interacting with two or three heavy (H) identical fermions, forming the trimer or tetramer bound state. The axial confinement in q2D is shown to lift the threefold degeneracy of three-dimensional trimer (tetramer) in p -wave channel and uniquely select the ground state with magnetic angular momentum | m | = 1 ( m = 0 ). By varying the interaction or confinement strength, we explore the dimensional crossover of these clusters from 3D to 2D, characterized by a gradual change of critical H-L mass ratio for their emergence and momentum-space distribution. Importantly, we find that a finite effective range will not alter their critical mass ratios in the weak coupling regime. There, we establish an effective 2D model to quantitatively reproduce the properties of q2D clusters, and further identify the optimal interaction strengths for their detections in experiments. Our results suggest a promising prospect for observing universal clusters and associated high-order correlation effects in realistic q2D ultracold Fermi mixtures. Published by the American Physical Society 2024
We investigate the scattering and two-body bound states of two ultracold atoms in a quasi-two-dimensional (quasi-2D) confinement, with the confinement potential being an infinitely deep square well (box potential) in the transverse (zzz) direction, and the motion of the atoms in the $x\text{\ensuremath{-}}y$ plane being free. Specifically, we calculate the effective 2D scattering length and 2D effective range parameter of the low-energy scattering, as well as the energy and the transverse-excited-mode probability of the bound states. Comparing these results with those obtained under a harmonic transverse confinement potential, which has the same characteristic length as the box potential, we find that in most of the cases the 2D effective range parameter for the box confinement is approximately 0.28 of the one for the harmonic confinement. Moreover, the transverse-excited-mode probability of the bound states for the box confinement is also much lower than the one for the harmonic confinement. These results suggest that the transverse excitation in the box confinement is notably weaker than the one in the harmonic confinement with the same characteristic length. Therefore, achieving quasi-2D ultracold gases well described by pure-2D effective models, particularly those with 2D contact interaction, is more feasible through box confinement. Our results are helpful for the quantum simulation of 2D many-body physics with ultracold atoms, e.g., the suppression of 2D effective range parameter may lead to an enhancement of quantum anomaly in two-dimensional Fermi gases. Additionally, our calculation method is applicable to the two-body problems of ultracold atoms in other types of quasi-2D confinements.
In this dissertation, we study the few-body ultracold Bose-Fermi mixture and quasi-1D scattering at ultracold temperature. Degenerate quantum gases have attracted enormous attentions during the past two decades. They have opened new platforms of quantum simulation, precision measurement and quantum chemistry. The scattering properties of degenerate quantum gases are the first things to study in order to gain insight into various novel phenomena at ultracold temperatures.\nTo address the role of quantum statistics at ultracold temperature, we study the spectrum and dynamics of a few-body Bose-Fermi mixtures. In particular, we focus the dynamical evolution of a few-body Bose-Fermi mixture and concentrate on its universal behavior at large inter-particle scattering length. We predict the molecule formation efficiency in many-body Bose-Fermi mixtures by mapping this critical observable in few-body calculations. We also propose that a the quantum beat experiment could be used to measure the energy of the lowest Efimov trimer at unitarity.\nTo address the role of dimensionality, we study confinement induced resonances and similar phenomena in general transverse confining potentials. Well-separated energy scales in different dimensions allow the creation of reduced dimensional systems at ultracold temperatures. We develop a general framework to regularize the low-energy quasi-1D scattering phase shift associated with a zero range interaction.\nLastly, we discuss future prospects for the study of an ultracold Bose-Fermi mixture, and scattering in reduced dimensional systems of a more general topology.
When quantum particles are confined into lower dimensions, an effective three-body interaction inevitably arises and may cause significant consequences. Here we study bosons in one dimension with weak two-body and three-body interactions and predict the existence of two three-body bound states when both interactions are attractive. Their binding energies are universal functions of the two-body and three-body scattering lengths and have direct relevance to a broad range of quasi-one-dimensional systems realized with ultracold atoms.
The two-body scattering is greatly modified in reduced dimensions. With ultracold atoms, low dimensional configurations are routinely accessible thanks to the use of optical lattices which allow confinements sufficiently strong to freeze the motion along chosen directions. With two different atomic species, we use a species-selective optical potential, in the form of a standing wave, to confine only one species in 2D disks and study the scattering between particles existing in different dimensions, i.e., we realize a 2D-3D mix-dimensional configuration , reminiscent of a brane world. We review the scattering theory specific to this configuration and derive an effective scattering length α eff in terms of the free-space scattering length α and the confinement parameters. We detect experimentally the enhancement of inelastic collisions arising at particular values of α and relate these values to the divergences of α eff . Unlike the confinement-induced resonances predicted and observed for identical particles, our mixed-dimensional resonances occur in a series of several resonances, because the relative and centre-of-mass motion are coupled.