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arXiv:2504.07893 · The European Physical Journal Plus

Molecular excited state in the interaction quench dynamics of two different atoms in a two-dimensional anisotropic trap

I. S. Ishmukhamedov, Altay Ishmukhamedov, Zh. E. Jalankuzov, Д. В. Исмаилов

Published Jan 16, 2024• 1 citation
arXivHTMLPDF
DOI
10.1140/epjp/s13360-024-04864-2

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We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the dependence of the energy gaps on the anisotropy parameter. The relation between the two- and one-dimensional scattering lengths as well as the Tan contacts is established. The contact, capturing the two-body short-range correlations, shows an increasing tendency for a larger anisotropy. Subsequently, the interaction quench dynamics from attractive to repulsive values and vice versa is investigated for various anisotropies. A closed analytical form of the expansion coefficients of the two-body wave function, during the time evolution is constructed. The response of the system is studied by means of the time-averaged fidelity, the spectra of the spatial extent of the cloud in each direction, and the one-body density. It is found that as the anisotropy increases, the system becomes less perturbed independently of the interactions, while for fixed anisotropy quenches toward the noninteracting regime perturb the system in the most efficient manner. Furthermore, we identify that in the tightly confined direction more frequencies are involved in the dynamics stemming from higher lying excited states.
We consider quantum quenches of harmonically trapped one-dimensional bosons from repulsive-to-attractive interactions. We study the resulting breathing dynamics of the so-called ``super-Tonks-Girardeau'' (STG) state at large attraction, or of its analog at moderate or small attraction. This state is highly excited compared to the ground state of the attractive gas, and is the lowest eigenstate where the particles are not bound or clustered. We analyze the dynamics from a spectral point of view, identifying the relevant eigenstates of the interacting trapped many-body system, and analyzing the nature of these quantum eigenstates. To obtain explicit eigenspectra, we use Hamiltonians with finite-dimensional Hilbert spaces to approximate the Lieb-Liniger system. We employ two very different approximate approaches: an expansion in a truncated single-particle harmonic-trap basis and a lattice (Bose-Hubbard) model. We show how the breathing frequency, identified with the energy difference between the sTG state and another particular eigenstate, varies with interaction.