Confined Few-Particle Systems Beyond Mean-Field Theory Adopt Gaussian-Type Orbitals and Morse Interactions

The ability to precisely control and manipulate individual atoms and molecules presents a significant challenge to theoretical physics, demanding new approaches to understanding their interactions. Matee ur Rehman, Paul Winter, and Fabio Revuelta, alongside Alejandro Saenz, from Humboldt-Universit ät zu Berlin and Universidad Polit écnica de Madrid, address this challenge by developing a theoretical framework for accurately modelling the behaviour of multiple confined particles. Their work moves beyond simplified, average-based calculations to provide a full-dimensional treatment of particle interactions, crucial for interpreting experiments using advanced optical trapping techniques. By employing a sophisticated mathematical approach using Gaussian functions and a realistic model of atomic interactions, the team achieves a level of accuracy and efficiency that promises to advance the understanding of complex many-body systems and facilitate the design of future experiments in this rapidly evolving field.

Few-Body Physics with Ultracold Atomic Gases

Scientists are advancing our understanding of how multiple atoms interact at extremely low temperatures, crucial for exploring fundamental physics and developing new quantum technologies. This research focuses on solving the complex equations governing these systems, employing sophisticated computational methods to accurately model interactions between a small number of atoms. These ultracold atomic gases serve as ideal testbeds for exploring quantum phenomena and validating theoretical models. The team utilizes variational methods, making educated guesses about the system’s behavior and refining them to minimize calculated energy.

They represent atomic wavefunctions using Gaussian-type orbitals, a mathematically convenient approach widely used in quantum chemistry. The accuracy of these methods is rigorously tested by comparing results with highly accurate solutions obtained through more computationally intensive techniques, carefully considering realistic interactions between atoms using potential energy surfaces like the Morse potential. This work demonstrates the accuracy and reliability of the chosen computational methods and Gaussian-type orbital basis sets, observing avoided crossings in energy levels as system parameters vary, indicating significant changes in the system’s behavior. These findings contribute to our fundamental understanding of quantum systems and provide a foundation for exploring more complex phenomena.

Realistic Six-Dimensional Integrals for Ultracold Atoms

Scientists have developed a new computational technique to accurately model interacting ultracold atoms trapped in complex arrangements. This advancement addresses limitations in existing methods when trap size becomes comparable to atomic interaction range and atoms are distributed in non-symmetric arrays. Researchers implemented a method using Cartesian Gaussians to represent atomic wavefunctions, enabling calculations for systems with multiple confined particles in complex spatial configurations. To validate their approach, the team calculated six-dimensional integrals arising from a realistic atom-atom interaction described by the Morse potential, employing full configuration-interaction calculations for direct comparison with highly accurate reference results for two atoms within an isotropic harmonic trap. A key innovation lies in the direct calculation of the interatomic interaction, bypassing simplified approximations often used in computational modeling. This approach, while computationally demanding, provides a foundation for accurately modeling complex many-body systems.

Gaussian Basis Functions Model Atomic Tweezer Arrays

Scientists have developed a novel computational approach for accurately describing the behavior of ultracold atoms trapped in arbitrary tweezer arrays, a significant advancement for quantum simulation and computation. This work addresses the challenge of modeling systems where atoms are confined by multiple, irregularly spaced traps, implementing a quantum-chemistry inspired technique utilizing Cartesian Gaussians as basis functions to represent atomic wavefunctions. A key achievement was the efficient formulation and implementation of algorithms to evaluate two-particle integrals involving Gaussian basis functions, specifically for the realistic Morse potential describing interatomic interactions. These calculations are essential for determining energy levels and spatial distribution of atoms within the traps, rigorously tested by comparing full configuration-interaction calculations for two atoms in an isotropic harmonic trap with established reference results. The researchers demonstrated the method’s effectiveness in regimes where interatomic interaction length becomes comparable to trap length.

Accurate Many-Body Calculations with Cartesian Gaussians

Scientists have demonstrated a new computational approach to accurately model interacting neutral atoms confined within optical traps. Researchers successfully implemented a method utilizing Cartesian Gaussians as basis functions to solve the complex many-body problem, implementing a Morse model potential to describe atom-atom interactions and assessing performance through comparisons with established calculations for two atoms in a harmonic trap. The results indicate that accurate energy spectra can be obtained with relatively modest computational effort, and that the approach properly implements the necessary calculations. Detailed analysis of the eigenfunctions reveals strong agreement with reference calculations, even for excited states with complex nodal structures. The accuracy of the calculations is dependent on the size of the basis set and its optimization for a given interaction potential, with future work potentially focusing on refining basis set parameters and extending the method to systems with a larger number of interacting atoms.