We have studied dilute Bose-Bose mixtures of atoms with attractive interspecies and repulsive intraspecies interactions using quantum Monte Carlo methods at T = 0. Using a number of models for interactions, we determine the range of validity of the universal equation of state of the symmetric liquid mixture as a function of two parameters: the s-wave scattering length and the effective range of the interaction potential. It is shown that the Lee-Huang-Yang correction is sufficient only for extremely dilute liquids with the additional restriction that the range of the potential is small enough. Based on the quantum Monte Carlo equation of state we develop a new density functional which goes beyond the Lee-Huang-Yang term and use it together with local density approximation to determine density profiles of realistic self-bound drops.Dilute Bose and Fermi gases have proved to be a versatile tool for exploration of different phases of condensedmatter systems. For more than two decades, most of the experiments were done in the low-density gas phase, in the universal regime fixed solely by the gas parameter ρa 3 , with a the s-wave scattering length and ρ the density. The range of universality of the homogeneous Bose gas was established using different model potentials and solving the N -body problem in an exact way with quantum Monte Carlo (QMC) methods [1]. One of the most important advances in the field of ultracold atoms in the last years is the recent creation of ultradilute quantum droplets. Such self-bound quantum systems were first experimentally observed for dipolar atoms [3-6] being caused by a close cancellation of the dipolar and shortrange energies. Petrov [7] pointed out that liquid drops can be created in an even simpler setup composed by a two-component mixture of bosons with short-ranged attractive interspecies and repulsive intraspecies interactions. However, the perturbative technique employed by Petrov is valid only very close to the mean-field (MF) instability limit, that is for extremely dilute liquids. The collapse predicted on the MF level is avoided by stabilization due to the quantum fluctuations described by the Lee-Huang-Yang (LHY) correction to the energy. It was shown that a similar stabilization mechanism can be used in two-and one-dimensional geometries where the resulting liquid phase has enhanced stability [8]. Very recently, two experimental groups managed to obtain self-bound liquid drops [9, 10] which, upon releasing the trap, did not expand. The drops required a certain critical number of atoms to be bound. Importantly, measurements of the critical number and size of the smallest droplets could not be fully accounted for by the MF+LHY term [9].Recently, some of us have studied liquid Bose-Bose droplets by using the diffusion Monte Carlo (DMC) method, thus solving exactly the full many-body problem for a given Hamiltonian at zero temperature [11].Our results have confirmed the transition from a gas, with positive energy, to a self-bound droplet with negative energy. Furthermore, we ...

Using quantum Monte Carlo methods we have studied dilute Bose-Bose mixtures with attractive interspecies interaction in the limit of zero temperature. The calculations are exact within some statistical noise and thus go beyond previous perturbative estimations. By tuning the intensity of the attraction, we observe the evolution of an N -particle system from a gas to a self-bound liquid drop. This observation agrees with recent experimental findings and allows for the study of an ultradilute liquid never observed before in Nature.

In the first experimental realization of dilute Bose-Bose liquid drops using two hyperfine states of 39 K 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:2001.09086v1 [cond-mat.quant-gas]

We study a harmonically confined Bose-Bose mixture using quantum Monte Carlo methods. Our results for the density profiles are systematically compared with mean-field predictions derived through the Gross-Pitaevskii (GP) equation in the same conditions. The phase space as a function of the interaction strengths and the relation between masses is quite rich. The miscibility criterion for the homogeneous system applies rather well to the system, with some discrepancies close to the critical line for separation. We observe significant differences between the mean-field results and the Monte Carlo ones, that magnify when the asymmetry between masses increases. In the analyzed interaction regime, we observe universality of our results which extend beyond the applicability regime for the GP equation.

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Some discrepancies between experimental results on quantum droplets made of a mixture of 39 K 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 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.

Employing time-dependent density-functional theory, we have studied dynamical equilibration and binary head-on collisions of quantum droplets made of a 39 K-39 K Bose mixture. The phase space of collision outcomes is extensively explored by performing fully three-dimensional calculations with effective single-component QMC based and two-components 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. Both stationary and dynamical calculations with an initial non-optimal concentration ratio display good agreement with experiments. Calculations including three-body losses acting only on the |F, mF = |1, 0 state show dramatic differences with those obtained with the three-body term acting on the total density.