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arXiv:2307.06028 · Communications in Theoretical Physics

Disassociation of a one-dimensional cold molecule via quantum scattering

Wenliang Li, Hai-Jing Song, Tieling Song, D. L. Zhou

Published Nov 24, 2023• 0 citations
arXivHTMLPDF

Abstract

Abstract Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum. We expect that our model can be realized in experiments in the near future.

DOI
10.1088/1572-9494/ad0f8d

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Abstract Motivated by the recent experimental developments in ultracold molecules and atoms, we propose a simple theoretical model to address the disassociation, reflection, and transmission probability of a one-dimensional cold molecule via quantum scattering. First, we show the Born approximation results in the weak interaction regime. Then, by employing the Lippmann–Schwinger equation, we give the numerical solution and investigate the disassociation’s dependence on the injection momentum and the interaction strengths. We find that the maximum disassociation rate has a limit when increasing the interaction strengths and injection momentum. We expect that our model can be realized in experiments in the near future.
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We theoretically investigate the quantum states of a Hamiltonian model for quasi-one-dimensional ultracold trapped gases. From the ansatz given by the numerical solution of the Schrödinger equation of the system, we develop a scattering potential functional form and an approximate solution for the analytical approach of the model. We obtain the set of approximate eigenstates and eigenenergies that can be used in future improvements on the study of atomic scattering in low dimensional ultracold gases. We also show that there is a parity inversion of the ground state of the model as the interaction strength increases.
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Kapitza-Dirac scattering, the diffraction of matter waves from a standing light field, is widely utilized in ultracold gases, but its behavior in the strongly interacting regime is an open question. Here we develop a numerically-exact two-body description of Kapitza-Dirac scattering for two contact-interacting atoms in a one-dimensional harmonic trap subjected to a pulsed optical lattice, enabling us to obtain the numerically exact dynamics. We map how interaction strength, lattice depth, lattice wavenumber, and pulse duration reshape the diffraction pattern, leading to an interaction-dependent population redistribution in real and momentum-space. By comparing the exact dynamics to an impulsive sudden-approximation description, we delineate the parameter regimes where it remains accurate and those, notably at strong attraction and small lattice wavenumber, where it fails. Our results provide a controlled few-body benchmark for interacting Kapitza-Dirac scattering and quantitative guidance for Kapitza-Dirac-based probes of ultracold atomic systems.
In this work, a system including two neutral atoms confined to an external one-dimensional Morse potential was modelled. The problem can be relevant to cold atom physics, where neutral atoms may be effectively confined in radially tight tubes formed by optical lattices. The atom-atom interaction was considered as a nonlocal separable potential. Analytical expressions for wave-function as well as transition matrix were derived. The contributions of bound states and resonances in the complex energy plane were calculated. For numerical computations, the bound states in a system of argon gas confined in graphite were considered. Since the most important quantity in the low energy quantum scattering problems is “scattering length,” considering various values of Morse parameters, the behavior of this parameter was described versus the reduced energy.