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arXiv:2104.09102 · Physical Review Research

Dynamics of equilibration and collisions in ultradilute quantum droplets

Viktor Cikojević, Leandra Vranješ Markić, Martí Pi, M. Barranco, Francesco Ancilotto, Jordi Boronat

Published Nov 29, 2021• 23 citations
arXivHTMLPDF

Abstract

Employing time-dependent density-functional theory, we have studied dynamical equilibration and binary head-on collisions of quantum droplets taking as a case of study droplets made of a $^{39}\mathrm{K}\text{\ensuremath{-}}^{39}\mathrm{K}$ Bose mixture. The phase space of collision outcomes is extensively explored by performing fully three-dimensional calculations with effective single-component Quantum Monte Carlo-based and two-component LHY-corrected mean-field functionals. We exhaustively explored the important effect---not considered in previous studies---of the initial population ratio deviating from the optimal mean-field value ${N}_{2}/{N}_{1}=\sqrt{{a}_{11}/{a}_{22}}$. Both stationary and dynamical calculations indicate sensitivity to an initial nonoptimal concentration. When three-body losses (3BL) are present our two-component approach allows to theoretically address situations in which they mainly act on one of the components of the mixture. Our approach also allows to simultaneously explore the effect on the simulation of population imbalance and 3BL, which are coupled when they act.

DOI
10.1103/physrevresearch.3.043139

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Employing time-dependent density-functional theory, we have studied dynamical equilibration and binary head-on collisions of quantum droplets taking as a case of study droplets made of a 39K\ensuremath-39K^{39}\mathrm{K}\text{\ensuremath{-}}^{39}\mathrm{K}39K\ensuremath-39K Bose mixture. The phase space of collision outcomes is extensively explored by performing fully three-dimensional calculations with effective single-component Quantum Monte Carlo-based and two-component LHY-corrected mean-field functionals. We exhaustively explored the important effect---not considered in previous studies---of the initial population ratio deviating from the optimal mean-field value N2/N1=a11/a22{N}_{2}/{N}_{1}=\sqrt{{a}_{11}/{a}_{22}}N2​/N1​=a11​/a22​​. Both stationary and dynamical calculations indicate sensitivity to an initial nonoptimal concentration. When three-body losses (3BL) are present our two-component approach allows to theoretically address situations in which they mainly act on one of the components of the mixture. Our approach also allows to simultaneously explore the effect on the simulation of population imbalance and 3BL, which are coupled when they act.
A quantum droplet is a self-bound state balanced by the mean-field interaction and Lee–Huang–Yang correction in a Bose–Bose mixture. In this paper, we study the collisional dynamics of two-dimensional quantum droplets with a vortex. By adjusting the initial momentum, the initial phase difference, the topological charge of the quantum droplets, and the total number of particles, we identify three dynamic mechanisms of collisions, namely, splitting, no-splitting, and their crossover according to the states after collision, which are significantly different from the merging, separation, and evaporation of the collisional dynamics of vortex-free droplets. The initial phase difference of the two droplets changes the interference fringes and the manner of splitting of the droplets. We also show that the three-body loss of atoms does not affect the result.
A theoretical analysis of binary collisions of quantum droplets under feasible experimental conditions is reported. Droplets formed from degenerate dilute Bose gases made up from binary mixtures of ultracold atoms are considered. Reliable expressions for the surface tension of the droplets are introduced based on a study of low energy excitations of their ground state within the random phase approximation. Their relevance is evaluated considering an estimation of the expected excitation energy having in mind the Thouless variational theorem. The surface tension expressions allow calculating the Weber number of the droplets involved in the collisions. Several regimes on the outcomes of the binary frontal collisions that range from the coalescence of the quantum droplets to their disintegration into smaller droplets are identified. Atoms losses of the droplets derived from self-evaporation and three-body scattering are quantified for both homo- and hetero-nuclear mixtures. Their control is mandatory for the observation of some interesting effects arising from droplets collisions.
Ultradilute quantum droplets are an intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in three-, one-, and two-dimensional two-component Bose-Bose mixtures by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the interspecies attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In three dimensions, we predict the existence of a strongly interacting Bose droplet at the crossover from Bose-Einstein condensates (BECs) to BCS superfluids and map out the bosonic BEC-BCS crossover phase diagram. In one dimension, we find that the energy of the one-dimensional Bose droplet calculated by the pairing theory is in excellent agreement with the latest diffusion Monte Carlo simulation [L. Parisi et al., Phys. Rev. Lett. 122, 105302 (2019)] for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that Bose droplets disappear and may turn into a solitonlike many-body bound state, when the interspecies attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by D. S. Petrov and G. E. Astrakharchik [Phys. Rev. Lett. 117, 100401 (2016)]. The predicted energies from both theories are higher than the diffusion Monte Carlo results due to the weak interspecies attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets in various dimensions, including their shape and collective oscillations.
Recently achieved two-component dipolar Bose-Einstein condensates open exciting possibilities for the study of mixtures of ultradilute quantum liquids. While nondipolar self-bound (without external confinement) mixtures are necessarily miscible with an approximately fixed ratio between the two densities, the density ratio for the dipolar case is free. Therefore, self-bound dipolar mixtures present qualitatively novel and much richer physics, characterized by three possible ground-state phases: miscible, symmetric immiscible, and asymmetric immiscible, which may in principle occur at any population imbalance. Self-bound immiscible droplets are possible due to mutual nonlocal intercomponent attraction, which results in the formation of a droplet molecule. Moreover, our analysis of the impurity regime shows that quantum fluctuations in the majority component crucially modify the miscibility of impurities. Our work opens intriguing perspectives for the exploration of spinor physics in ultradilute liquids, which should resemble to some extent that of ^{4}He-^{3}He droplets and impurity-doped helium droplets.
We use exact quantum Monte Carlo techniques to study the properties of quantum droplets in two-component bosonic mixtures with contact interactions in one spatial dimension. We systematically study the surface tension, the density profile and the breathing mode as a function of the number of particles in the droplet and of the ratio of coupling strengths between intraspecies repulsion and interspecies attraction. We find that deviations from the predictions of the generalized Gross-Pitaevskii equation are small in most cases of interest.
Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in low-dimensional two-component Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the inter-species attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In one dimension, we find that the energy calculated by the pairing theory is in an excellent agreement with the latest diffusion Monte Carlo simulation {[}Phys. Rev. Lett. \textbf{122}, 105302 (2019){]}, for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that quantum droplets disappear and may turn into a soliton-like many-body bound state, when the inter-species attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by Petrov and Astrakharchik {[}Phys. Rev. Lett. \textbf{117}, 100401 (2016){]}. The predicted energies from both theories are higher than the diffusion Monte Carlo results, due to the weak inter-species attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets, including their shape and collective oscillations.