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arXiv:2607.25558

Ultradilute quasi-two-dimensional Bose-Bose liquid mixtures

Leandra Vranješ Markić, Ivan Poparić, Krešimir Dželalija, Petar Stipanović, Jordi Boronat

Published Jul 28, 2026• 0 citations
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Abstract

We study ultradilute $^{39}$K 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 $T=0$, using interaction potentials that include information on the $s$-wave scattering length $a$ and the effective range $r_{\rm eff}$. 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 $a$ and $r_{\rm eff}$. 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 $a$ and $r_{\rm eff}$ 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.

DOI
10.48550/arxiv.2607.25558

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We describe a quantum droplet of a Bose-Bose mixture squeezed by an external harmonic force in one spatial direction. Our approach is based on the self-consistent method formulated in Zin et al. (arXiv:2202.10109) The true spatial droplet profile in the direction of confinement is accounted for; however, the local density approximation is assumed in the free directions. We define a numerical approach to find the beyond-mean-field contribution to the chemical potential (Lee-Huang-Yang chemical potential)---the quantity that determines the droplet's profile. In addition to the numerical approach, we find the Lee-Huang-Yang potential in the analytic form in two limiting cases: a perturbative result for a strong confinement and a semiclassical expression when confinement is very weak.
We investigate the properties of self-bound ultradilute Bose-Bose mixtures, beyond the Lee-Huang-Yang description. Our approach is based on the determination of the beyond mean-field corrections to the phonon modes of the mixture in a self-consistent way and calculation of the associated equation of state. The newly obtained ground state energies show excellent agreement with recent quantum Monte Carlo calculations, providing a simple and accurate description of the self-bound mixtures with contact type interaction. We further show numerical results for the equilibrium properties of the finite size droplet, by adjusting the Gross-Pitaevskii equation. Our analysis is extended to the one-dimensional mixtures where an excellent agreement with quantum Monte Carlo predictions is found for the equilibrium densities. Finally, we discuss the effects of temperature on the stability of the liquid phase.
We study liquid quantum droplets in a mixture of two-component Bose-Einstein condensates under variable confinement introduced along one or two spatial dimensions. Although the atom-atom scattering has a three-dimensional character, discreteness of the available modes in the reduced dimension(s) strongly influences the zero-point energy, which for a weakly interacting three-dimensional system is given by the Lee-Huang-Yang term. Here, we generalize the result of Lee, Huang, and Yang and calculate the higher order corrections to the mean-field energy for a single component Bose-Einstein condensate under condition of a tight confinement in one or two spatial directions. We apply our results to the two-component mixture of bosonic species under conditions favorable for the creation of quantum liquid droplets, which constitute a perfect playground for studies of the beyond mean-field effects. Our findings allow one to analyze the properties of quantum droplets at the dimensional crossover and provide demanding conditions for accessing quasilow dimensions. They also pave a way for experimental exploration of this state of matter in reduced dimensions.
The ultracold and ultradilute bosonic heteronuclear mixture (41K - 87Rb) of Bose-Einstein condensates with tunable interspecies interaction at zero temperature is studied in the self-bound regime, using numerical simulations based on Density Functional Theory within the Local Density Approximation. In particular, the beyond mean-field effects embodied in the Lee-Huang-Yang energy contribution are explicitly included in the total energy functional. The thermodynamic properties of the homogeneous system are investigated to set the stability conditions of the self-bound droplet. The surface properties are discussed with (i) a variational approach, (ii) a numerical method and (iii) by solving the two coupled Gross-Pitaevskii equations associated to the two components of the mixture. The validity of the liquid-drop model is verified by computing the total ground state energy for systems with a different number of particles and, after the confinement in a quasi-1D configuration by means of an optical waveguide, we also discuss the transition between quantum droplets and bright solitons, two localized states of different nature.