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arXiv:2610.31581 · Physical Review A

Breathing and quadrupole modes in squeezed Bose-Bose liquid drops

Marko Korda, Leandra Vranješ Markić, Jordi Boronat

Published Oct 22, 2026• 0 citations
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Abstract

We investigate the lowest excitation modes of binary $^{39}$K ultradilute droplets confined harmonically in one direction, which reduces the critical number of particles needed to sustain a self-bound state. Using the density functional built from first-principles quantum Monte Carlo calculations (QMC), which incorporates the effects of finite range interactions, we study the crossover of the oscillation modes from three to two dimensions. For weak squeezing, we observe the coupling between breathing and quadrupole modes, resulting from the breaking of spherical symmetry. Increasing the squeezing, the higher-frequency mode corresponding to three-dimensional breathing mode becomes unstable. For squeezings stronger and comparable to experiments, we analyze the dependence of the excitation modes on the droplet size for several interactions and show the reduction of the number of particles needed to sustain stable oscillations. The differences between the results obtained with the QMC functional and the extended Gross-Pitaevskii theory are increased with respect to the case of previously studied spherical droplets.

DOI
10.1103/qh9m-rxhz

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We investigate the lowest excitation modes of binary 39^{39}39K ultradilute droplets confined harmonically in one direction, which reduces the critical number of particles needed to sustain a self-bound state. Using the density functional built from first-principles quantum Monte Carlo calculations (QMC), which incorporates the effects of finite range interactions, we study the crossover of the oscillation modes from three to two dimensions. For weak squeezing, we observe the coupling between breathing and quadrupole modes, resulting from the breaking of spherical symmetry. Increasing the squeezing, the higher-frequency mode corresponding to three-dimensional breathing mode becomes unstable. For squeezings stronger and comparable to experiments, we analyze the dependence of the excitation modes on the droplet size for several interactions and show the reduction of the number of particles needed to sustain stable oscillations. The differences between the results obtained with the QMC functional and the extended Gross-Pitaevskii theory are increased with respect to the case of previously studied spherical droplets.
We explore ultradilute Bose-Bose liquid droplets squeezed by an external harmonic potential in one spatial direction. Our theoretical study is based on a functional that is built using quantum Monte Carlo results of the bulk phase and incorporates finite-range effects. A characteristic feature of these drops is the existence of a critical atom number, which is the minimum number of particles to have a many-body bound state. We report results on the critical atom numbers for different magnetic fields and applying confinement strengths towards a quasi-two-dimensional setup. In the regime where the local-density approximation is expected to be valid, we find that the critical atom number decreases linearly with the harmonic oscillator length of the confining potential. With the largest squeezing explored in our work, we predict stable drops containing from approximately 1000 to 2000 atoms for magnetic fields from 56.230 to 56.574 G, respectively. Our functional reduces the critical numbers for any confinement and applied magnetic field with respect to the estimations based on the Lee-Huang-Yang model. We observe saturated drops when the number of atoms in the drop is much larger than the critical value, their central density being higher for the quantum Monte Carlo functional than for the Lee-Huang-Yang one.
Some discrepancies between experimental results on quantum droplets made of a mixture of 39K^{39}\mathrm{K}39K atoms in different hyperfine states and their analysis within extended Gross-Pitaevskii theory (which incorporates beyond mean-field corrections) have been recently solved by introducing finite-range effects into the theory. Here we study the influence of these effects on the monopole and quadrupole excitation spectrum of extremely dilute quantum droplets using a density functional built from first-principles quantum Monte Carlo calculations, which can be easily introduced in the existing Gross-Pitaevskii numerical solvers. Our results show differences of up to 2020%20 with those obtained within the extended Gross-Pitaevskii theory, likely providing another way to observe finite-range effects in mixed quantum droplets by measuring their lowest excitation frequencies.
We study ultradilute 39^{39}39K Bose-Bose bulk mixtures and droplets in an external harmonic potential that confines them in one spatial direction towards the two-dimensional (2D) limit. Equations of state for several confinements are obtained with quantum Monte Carlo (QMC) at T=0T=0T=0, using interaction potentials that include information on the sss-wave scattering length aaa and the effective range reffr_{\rm eff}reff​. Performing the calculations using two different interaction potential models we have determined the range of confinements for which equations of state are universal in terms of aaa and reffr_{\rm eff}reff​. Based on the QMC equation of state, we develop a 2D QMC density functional for each confinement strength and use it together with the local density approximation to determine properties of the self-bound drops. For moderate squeezing, energies and droplet profiles obtained using the 2D QMC functional agree well with those obtained using 3D functionals, while offering a substantial reduction in computational cost, and a consistent approach in crossover to 2D. Noticeably, our results approach 2D mean-field (MF) + Lee-Huang-Yang (LHY) predictions only for the most strongly confined systems for which universality in terms of aaa and reffr_{\rm eff}reff​ is observed. This implies a very narrow range of confinements for which 2D LHY functionals are applicable, which has important consequences for the study of vortices.
The collective excitation modes in quantum droplets trapped in a two-dimensional harmonic potential in the context of symmetric weakly interacting binary bosonic mixtures are studied. By utilizing the linearization technique, the time-dependent extended Gross--Pitaevskii equation, and a sum-rule approach with a variational approximation, the ground-state properties and collective excitations of such a two-dimensional quantum system are investigated for various system parameters. We present comprehensive analysis and calculations on the effect of the confinement strength and anisotropy of the trapping potential, the number of atoms in the droplet, and the collective excitation modes. The radius of the droplet, as well as the chemical potential, is nonmonotonically related to the number of atoms in the droplet, and the confinement tends to shift the minimum values towards the ideal-gas limit. The excitation frequency peaks, which are prominent in a self-bounded droplet, become less pronounced and smoother when subjected to a strong trapping potential. The sum-rule approach fails to reproduce the breathing mode frequency for a moderate number of atoms in a weak trapping potential, however, works perfectly well in a strong confinement. It was found that the anisotropy in the trap eliminates the degeneracy between the quadrupole and scissors modes that occurs in an isotropic trap, causing the frequencies of these two modes to immediately diverge from each other for any degree of anisotropy. These findings provide valuable insights into the unique characteristics and behavior of quantum droplets, offering potential implications for future research and applications in the dynamic behaviors of intriguing quantum droplets.
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^{166}166Er and 162^{162}162Dy gases. By constructing comprehensive phase diagrams across the parameter space of the sss-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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