Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2311.05244 · Physical Review A

Squeezing Bose-Bose liquid drops

Ares Sanuy, R. Barač, Petar Stipanović, Leandra Vranješ Markić, Jordi Boronat

Published Jan 16, 2024• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.109.013313

Related papers

Ultradilute quasi-two-dimensional Bose-Bose liquid mixtures

Leandra Vranješ Markić, Ivan Poparić, Krešimir Dželalija +2 more

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.

arXiv:2607.25558•Jul 28, 2026•0 citations

Finite-range effects in ultradilute quantum drops

Viktor Cikojević, Vranješ Markic, Leandra, Boronat Medico, Jordi

In the first experimental realization of dilute Bose–Bose liquid drops using two hyperfine states of 39K some discrepancies between theory and experiment were observed. The standard analysis of the data using the Lee–Huang–Yang beyond mean-field theory predicted critical numbers which were significantly off the experimental measurements. Also, the radial size of the drops in the experiment proved to be larger than expected from this theory. Using a new functional, which is based on quantum Monte Carlo results of the bulk phase incorporating finite-range effects, we can explain the origin of the discrepancies in the critical number. This result proves the necessity of including finite-range corrections to deal with the observed properties in this setup. The controversy on the radial size is reasoned in terms of the departure from the optimal concentration ratio between the two species of the mixture.

•Jan 1, 2020•30 citations

Breathing and quadrupole modes in squeezed Bose-Bose liquid drops

Marko Korda, Leandra Vranješ Markić, Jordi Boronat

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.

arXiv:2610.31581•Physical Review A•Oct 22, 2026•0 citations

Self-consistent description of Bose-Bose droplets: Harmonically trapped quasi-two-dimensional droplets

Paweł Zin, Maciej Pylak, Mariusz Gajda

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.

arXiv:2202.10113•Physical Review A•Jul 27, 2022•7 citations

Finite-range effects in ultradilute quantum drops

V Cikojević, L Vranješ Markić, J Boronat

Abstract In the first experimental realization of dilute Bose–Bose liquid drops using two hyperfine states of 39K some discrepancies between theory and experiment were observed. The standard analysis of the data using the Lee–Huang–Yang beyond mean-field theory predicted critical numbers which were significantly off the experimental measurements. Also, the radial size of the drops in the experiment proved to be larger than expected from this theory. Using a new functional, which is based on quantum Monte Carlo results of the bulk phase incorporating finite-range effects, we can explain the origin of the discrepancies in the critical number. This result proves the necessity of including finite-range corrections to deal with the observed properties in this setup. The controversy on the radial size is reasoned in terms of the departure from the optimal concentration ratio between the two species of the mixture.

arXiv:2001.09086•New Journal of Physics•Apr 3, 2020•38 citations

Empty and filled vortices in squeezed K 39 Bose-Bose liquid drops

Ivan Poparić, Leandra Vranješ Markić, Jordi Boronat

Using density functional theory, we have theoretically studied the formation and the stability of vortices in quantum liquid droplets composed of a mixture of hyperfine states of potassium. Following the experimental setup that produced quantum droplets for the first time, we work with squeezed drops that are compressed in one direction. By squeezing the drops even more, toward a quasi-two-dimensional geometry, we study the minimum atom number able to show a stable vortex and obtain that this number is significantly smaller than previous predictions for spherical droplets. The reduction of the critical atom number for forming a stable vortex could make their experimental observation in these droplets, which is still lacking, more feasible. Contrary to results obtained in heteronuclear mixtures, where the energetically preferred vortices are partially filled with the species not participating in the rotation, our results show a relevant stability island of fully empty vortices. Increasing the number of particles in the drop and the speed of rotation, we estimate the transition line between empty and filled vortices.

arXiv:2510.12390•Physical Review A•Nov 13, 2025•1 citation
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.
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.
In the first experimental realization of dilute Bose–Bose liquid drops using two hyperfine states of 39K some discrepancies between theory and experiment were observed. The standard analysis of the data using the Lee–Huang–Yang beyond mean-field theory predicted critical numbers which were significantly off the experimental measurements. Also, the radial size of the drops in the experiment proved to be larger than expected from this theory. Using a new functional, which is based on quantum Monte Carlo results of the bulk phase incorporating finite-range effects, we can explain the origin of the discrepancies in the critical number. This result proves the necessity of including finite-range corrections to deal with the observed properties in this setup. The controversy on the radial size is reasoned in terms of the departure from the optimal concentration ratio between the two species of the mixture.
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 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.
Abstract In the first experimental realization of dilute Bose–Bose liquid drops using two hyperfine states of 39K some discrepancies between theory and experiment were observed. The standard analysis of the data using the Lee–Huang–Yang beyond mean-field theory predicted critical numbers which were significantly off the experimental measurements. Also, the radial size of the drops in the experiment proved to be larger than expected from this theory. Using a new functional, which is based on quantum Monte Carlo results of the bulk phase incorporating finite-range effects, we can explain the origin of the discrepancies in the critical number. This result proves the necessity of including finite-range corrections to deal with the observed properties in this setup. The controversy on the radial size is reasoned in terms of the departure from the optimal concentration ratio between the two species of the mixture.
Using density functional theory, we have theoretically studied the formation and the stability of vortices in quantum liquid droplets composed of a mixture of hyperfine states of potassium. Following the experimental setup that produced quantum droplets for the first time, we work with squeezed drops that are compressed in one direction. By squeezing the drops even more, toward a quasi-two-dimensional geometry, we study the minimum atom number able to show a stable vortex and obtain that this number is significantly smaller than previous predictions for spherical droplets. The reduction of the critical atom number for forming a stable vortex could make their experimental observation in these droplets, which is still lacking, more feasible. Contrary to results obtained in heteronuclear mixtures, where the energetically preferred vortices are partially filled with the species not participating in the rotation, our results show a relevant stability island of fully empty vortices. Increasing the number of particles in the drop and the speed of rotation, we estimate the transition line between empty and filled vortices.