A quantum liquid in a heterogeneous mixture of $^{41}\mathrm{K}$ and $^{87}\mathrm{Rb}$ atoms is studied using the diffusion Monte Carlo method and density-functional theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals are presented. Using density-functional theory, a systematic comparison between different functionals is performed, focusing on the critical atom number, surface tension, surface width, Tolman length, and compressibility. These results are given as a function of the interspecies interaction strength, within the stability domain of the liquid mixture.
A quantum liquid in a heterogeneous mixture of 41K and 87Rb atoms is studied using the diffusion Monte Carlo method and density-functional theory. The perturbative Lee-Huang-Yang term for a heterogeneous mixture is verified and it is proved to be valid only near the gas-liquid transition. Based on the equations of state of the bulk mixture, calculated with diffusion Monte Carlo, extensions to Lee-Huang-Yang corrected mean-field energy functionals are presented. Using density-functional theory, a systematic comparison between different functionals is performed, focusing on the critical atom number, surface tension, surface width, Tolman length, and compressibility. These results are given as a function of the interspecies interaction strength, within the stability domain of the liquid mixture.
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 density functional which goes beyond the Lee-Huang-Yang term and use it together with the local density approximation to determine density profiles of realistic self-bound drops.
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.
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.
The miscibility of quantum liquids is an interesting topic in many-body physics, which has been intensively investigated in 3He-4He superfluids and the mixtures of ultracold atoms. In the context of dual species Bose-Einstein condensates, the mean-field description has been well established, according to which, the miscibility condition is density independent and determined only by the ratio of inter- and intra-species interaction strength. Recently, Nadion and Petrov proposed that [ Phys. Rev. Lett. 126 115301 ], in the vicinity of the mixing-demixing threshold, quantum fluctuations play an important role to affect the equilibrium stability, and as a result, the partially miscible state emerges. This new phase of quantum matter opens up new perspectives to explore the beyond mean-field effect in ultracold atomic gases. In this work, according to the equation of state taking the Lee-Huang-Yang correction into consideration, we investigate the ground state phase diagram of repulsive binary Bose mixtures in the interacting regime suffering a weak mean-field instability. Under the thermodynamic balance conditions, the phase boundaries between the immiscible state, partially miscible state and the homogenous state are determined. For the equal-mass case, these phase transitions only take place on condition that intra-species interactions are in an asymmetric form. In terms of interaction parameters, we explicitly derive analytical expressions of the phase boundaries, which are appropriate to describe the transitions in sufficiently dilute atomic gases. At the quantum critical point, where the partially miscible state terminates, the susceptibility tensor of the density response exhibits a divergent behavior. For the unequal-mass case, the beyond-mean-field equation of state cannot be written in a compact form, thus the determination of the phase boundaries is more involved. By expanding the Lee-Huang-Yang energy expression to the terms linear in the concentration of the minority species, we analytically obtain the threshold density for the partially miscible transition. We also propose a discriminant function, from which the configuration of the partially miscible state can be identified for the given mass ratio and interaction strength. Applications of these theoretical results to experimental systems, such as sodium, potassium, and rubidium gases, are presented.
Abstract The static and dynamic properties of self-bound quantum droplets in a one-dimensional Bose-Bose mixture are discussed in the spirit of the Hartree–Fock-Bogoliubov theory. This latter enables us to provide beyond the Lee-Huang-Yang (LHY) quantum corrections to the equation of state at both zero and finite temperatures. In the uniform case our results for the ground-state energy and the critical temperature are confirmed through comparison with Quantum Monte-Carlo simulation and with available theoretical results. The density profiles are supported by numerical simulations of the generalized Gross-Pitaevskii equation which selfconsistently includes higher-order terms originating from the normal and anomalous fluctuations under the local density approximation. We show that the density exhibits a dip near its center in the flat-top plateau region for large interspecies interactions. We exemplify the impact of the beyond LHY corrections on the spatiotemporal evolution of the self-bound droplet in the presence of excitation induced by periodic density modulation. It is found that higher-order corrections may lead to the formation of a train of small droplets. We then extend our study for the case of inhomogeneous droplets in quasi one-dimensional Bose mixtures.
The properties of mixtures of Bose-Einstein condensates at T=0 have been investigated using quantum Monte Carlo (QMC) methods and Density Functional Theory (DFT) with the aim of understanding physics beyond the mean-field theory in Bose-Bose mixtures. In particular, quantum liquid droplets with attractive intraspecies and repulsive interspecies attraction were studied, for which we observed significant contributions beyond Lee Huang Yang (LHY) theory that affect the energy, saturation density, and surface tension. The critical atom number in droplets in free space for total number of atoms N between N=30 and N=2000 was obtained. Results of the surface tension for three values of the attractive interspecies interactions are presented. For a homogeneous system, extensive calculations of the equations of state were performed and we report the influence of finite-range effects in beyond-Bogoliubov theory. In systems interacting with a small (large) effective range, we observe repulsive (attractive) beyond-LHY contributions to the energy. For the droplets in a mixture of 39K atoms, which were observed experimentally for the first time, the calculations of equations of state were performed. Combining QMC-built functionals with DFT, the discrepancy in the estimation of critical atom number between the mean-field theory and experimental results was explained by the proper inclusion of the effective range in inter-particle interaction models. The influence of finite-range effects on breathing and quadrupole modes in 39K quantum droplets was investigated. We predicted a significant deviation in the excitation frequencies when entering a more correlated regime. Finally, the phase diagram of repulsive Bose-Bose mixtures in a spherical harmonic trap using Quantum Monte Carlo calculations was studied. Density profiles were obtained reported and we found the occurrence of three phases: separation of condensates in two blobs, fully mixed and shell-separated phase. A comparison with the Gross-Pitaevskii solutions showed a large deviation in the regime of large mass imbalance and strong interactions. We showed the universality in the density profiles with respect to the s-wave scattering length and found numerical evidence for Gross-Pitaevskii scaling present beyond the regime of applicability of Gross-Pitaevskii equations. Hemos investigado las propiedades de las mezclas de condensados de Bose-Einstein en el límite de temperatura cero. Para ello hemos usado métodos cuánticos de Monte Carlo (QMC) y la teoría del funcional de la densidad (DFT) con el objetivo de comprender la física más allá de la teoría del campo medio en las mezclas bosónicas. En particular, se estudiaron las gotas de líquido cuántico originadas con interacciones atractivas entre especies distinats y repulsivas entre especies iguales. Observamos contribuciones significativas más allá de la teoría de Lee Huang Yang (LHY) que afectan a la energía, la densidad de saturación y la tensión superficial. Calculamos el número crítico de átomos en gotitas en el espacio libre para un número total de átomos N entre N = 30 y N = 2000. Obtuvimos resultados de la tensión superficial para tres valores de las interacciones atractivas entre especies. Para un sistema homogéneo, se realizaron cálculos extensos de las ecuaciones de estado y reportamos la influencia de los efectos de rango finito en la teoría, más allá de Bogoliubov. En sistemas que interactúan con un rango efectivo pequeño (grande), observamos contribuciones repulsivas (atractivas) a la energia más allá de LHY. Para las gotitas en una mezcla de 39K átomos, que se observaron experimentalmente por primera vez en ICFO, se realizaron los cálculos de ecuaciones de estado. Combinando funciones obtenidas de QMC con DFT, explicamos la discrepancia en la estimación del número crítico de átomos, entre la teoría de campo medio y los resultados experimentales, mediante la inclusión adecuada del rango efectivo en los modelos de interacción entre partículas. Se investigó la influencia de los efectos de rango finito en los modos monopolar y cuadrupolar en gotas cuánticas de 39K. Predijimos una desviación significativa en las frecuencias de excitación al entrar en un régimen más correlacionado. Finalmente, se estudió el diagrama de fase de mezclas bosóncas repulsivas en una trampa armónica esférica utilizando cálculos de Quantum Monte Carlo. Se obtuvieron los perfiles de densidad y se probó la existencia de tres fases: separación de condensados en dos lóbulos, una fase completamente mezclada y una fase separada con capas esféricas. Una comparación con las soluciones de Gross-Pitaevskii mostró una gran desviación en el régimen de gran desequilibrio de masas e interacciones fuertes. Finalmente, mostramos la presencia de universalidad en los perfiles de densidad, con respecto a la longitud de dispersión en onda S, y encontramos evidencia numérica del factor de escala de Gross-Pitaevskii más allá del régimen de aplicabilidad de las propias ecuaciones de Gross-Pitaevskii. Ultrahladne atomske mješavine istražene ab-initio kvantnom Monte Carlo metodom. Svojstva smjesa Bose-Einsteinovih kondenzata pri T = 0 istražena su korištenjem metoda kvantnog Monte Carla (QMC) i teorije funkcionala gustoće (DFT) s ciljem proučavanja fizike izvan teorije srednjeg polja u bozonskim mješavinama. Proučili smo kvantne kapljice s jednakim i odbojnim interakcijama između atoma istovrsne komponente te privlačnim interakcijama atoma različitih komponenti u interakciji i opazili smo značajne doprinose povrh Lee Huang Yang (LHY) teorije koji utječu na energiju, saturacijsku gustoću i površinsku napetost. Odredili smo kritični broj atoma za kapljice u slobodnom prostoru za broj atoma u kapljici N između N = 30 i N = 2000. Izračunali smo površinsku napetost za tri vrijednosti privlačnih međuatomskih interakcija. Izvršili smo opsežne proračune jednadžbi stanja iznimno rijetke tekućine bozonske mješavine i uočili utjecaj efekata konačnog dosega koji nije predviđen Bogoliubovljevom teorijom. U sustavima koji interagiraju s malim (velikim) efektivnim dosegom, opaženi su odbojni (privlačni) doprinosi koje ne predviđa LHY teorija. Izračunali smo jednadžbe stanja za kapljice bozonskih mješavina koje su po prvi put eksperimentalno uočene u smjesi 39K atoma. Kombinirajući funkcionale gustoće izgrađene pomoću kvantnog Monte Carla s DFT-om, neslaganje u procjeni kritičnog broja atoma između teorije srednjeg polja i eksperimentalnih rezultata je objašnjeno preko pravilnog uključivanja efektivnog dosega u modele međudjelovanja čestica. Istražen je utjecaj efektivnog dosega na pobuđenja kapljice 39K, i to na mod disanja i kvadrupolni mod. Dobiveni rezultati prikazuju značajno odstupanje frekvencija pobude pri ulasku u korelirani režim. Detaljno smo proučili fazni dijagram odbojnih Bose-Bose mješavina u sfernoj harmonijskoj zamci koristeći kvantne Monte Carlo račune. Dobiveni su profili gustoće koji pokazuju pojavu tri faze: separacija kondenzata u dvije nakupine, potpuno miješanje i separacije u obliku ljuske. Usporedba s riješenjima Gross-Pitaevskii jednadžbi pokazuje veliko odstupanje u režimu velike masene neravnoteže i jakih interakcija. Pokazali smo univerzalnost profila gustoće s obzirom na s-valnu duljinu raspršenja te postojanje Gross-Pitaevskii skaliranja prisutnog izvan dosega primjenjivosti Gross-Pitaevskii jednadžbi.