Breathing mode of quantum droplets in dipolar quantum gases: A sum-rule analysis

• URL: http://arxiv.org/abs/2606.29370v1
• Date: Sun, 28 Jun 2026 12:23:25 GMT
• Title: Breathing mode of quantum droplets in dipolar quantum gases: A sum-rule analysis
• Abstract summary: We theoretically investigate the ground-state properties and breathing-mode collective excitations of three-dimensional dipolar Bose gases in anisotropic harmonic traps.<n>Our work offers a rigorous and highly accurate framework to characterize collective excitations in dipolar quantum gases.
• Score: 7.809635348931763
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We theoretically investigate the ground-state properties and breathing-mode collective excitations of three-dimensional dipolar Bose gases in anisotropic harmonic traps incorporating quantum fluctuations. Combining a Gaussian variational ansatz with a non-perturbative sum-rule analysis, we derive explicit analytical expressions for both axial and radial breathing-mode frequencies, which are validated by numerical solutions of the time-dependent extended Gross-Pitaevskii equation. Our theoretical predictions show excellent agreement with existing experimental data for $^{166}$Er and $^{162}$Dy gases. By constructing comprehensive phase diagrams across the parameter space of the $s$-wave scattering length, atom number, and trap aspect ratio, we reveal both discontinuous first-order phase transitions and smooth crossovers between the dilute Bose-Einstein condensate and dense quantum droplet phases. We confirm that the enhanced incompressibility induced by quantum fluctuations significantly elevates the breathing-mode frequencies in the droplet phase compared to conventional weakly interacting Bose gases. Furthermore, the system undergoes a phase transition and a crossover over the scattering length under the quasi-two-dimensional and quasi-one-dimensional confinements, characterized by discontinuous jumps and continuous crossovers in peak density and atomic cloud sizes, respectively. Our work offers a rigorous and highly accurate framework to characterize collective excitations in dipolar quantum gases, providing quantitative insights for forthcoming ultracold atom experiments in lanthanide atoms and polar molecules.

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