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arXiv:2209.01887 · Journal of Physics B Atomic Molecular and Optical Physics

Phase diagram and elementary excitations of strongly interacting droplets with non-local interactions

Maciej Łebek, Jakub Kopyciński, Wojciech Górecki, Rafał Ołdziejewski, Krzysztof Pawłowski

Published Feb 26, 2025• 1 citation
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Abstract

Abstract A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks–Girardeau limit of infinitely strong contact repulsion. We show that the main system features are the same for a broad class of non-local interaction potentials. Then, we focus on a limiting case, the one of slowly varying density profiles, to find approximate formulas for the surface and bulk energies of a droplet. We further characterise the system by numerically finding the excitation spectrum. It consists of two families: phononic-like excitations inside droplets and scattering modes. Analysis within the linearised regime is supplemented with the full, nonlinear dynamics of small perturbations.

DOI
10.1088/1361-6455/adba9d

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Abstract A one-dimensional bosonic gas with strong contact repulsion and attractive non-local interactions may form a quantum droplet with a flat-top density profile. We focus on a system in the Tonks–Girardeau limit of infinitely strong contact repulsion. We show that the main system features are the same for a broad class of non-local interaction potentials. Then, we focus on a limiting case, the one of slowly varying density profiles, to find approximate formulas for the surface and bulk energies of a droplet. We further characterise the system by numerically finding the excitation spectrum. It consists of two families: phononic-like excitations inside droplets and scattering modes. Analysis within the linearised regime is supplemented with the full, nonlinear dynamics of small perturbations.
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We analyze the dynamics of one-dimensional quantum gases with strongly attractive contact interactions. We specify a class of initial states for which attractive forces effectively act as strongly repulsive ones during the time evolution. Our findings extend the theoretical results on the super-Tonks-Girardeau gas to a highly nonequilibrium dynamics. The mechanism is illustrated on the prototypical problem of the domain stability in a two-component Fermi gas. We also discuss finite-range interactions and analyze the universality of the presented results. Moreover, we use our conclusions to argue for the existence of metastable quantum droplets in the regime of strongly attractive contact and attractive dipolar interactions.
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Abstract Using the Bose–Fermi mapping method, we obtain the exact ground state wavefunction of one-dimensional (1D) Bose gas with the zero-range dipolar interaction in the strongly repulsive contact interaction limit. Its ground state density distributions for both repulsive and attractive dipole interactions are exhibited. It is shown that in the case of the finite dipole interaction the density profiles do not change obviously with the increase of dipole interaction and display the typical shell structure of Tonks–Girardeau gases. As the repulsive dipole interaction is greatly strong, the density decreases at the center of the trap and displays a sunken valley. As the attractive dipole interaction increases, the density displays more oscillations and sharp peaks appear in the strong attraction limit, which mainly originate from the atoms occupying the low single particle levels.