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arXiv:2105.01439

Ab-initio Quantum Monte Carlo study of ultracold atomic mixtures

Viktor Cikojević

Published May 4, 2021• 0 citations
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Abstract

In this thesis, 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.

DOI
10.48550/arxiv.2105.01439

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Ab-initio quantum Monte Carlo study of ultracold atomic mixtures

Viktor Cikojević

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.

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In this thesis, the properties of mixtures of Bose-Einstein condensates at T=0T = 0T=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.
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.
In this Thesis we will theoretically address some issues concerning the Physics of ultracold Fermi gases, all of them with experimental relevance. The field of ultracold gases, and more recently of ultracold Fermi gases, is gathering a lot of experimental and theoretical interest for two main reasons: the great control on the relevant parameters of the problem and the relative simplicity of the minimal theory which is able to correctly describe the system. Building upon this solid background, ultracold gases provided an ideal laboratory for testing more refined theories and also for addressing fundamental issues of quantum mechanics as well as for simulating more complex physical systems such as those encountered in condensed matter. Even if the effective hamiltonian of ultracold gases can be simple, due to the diluteness of the system and the low temperature, which imply low energy physics, the solution of the quantum mechanic equations governing the state of these systems is not always simple. For the static properties usually mean-field solutions exist or perturbative expansions can be produced in some regimes. However Quantum Monte Carlo (QMC) techniques provide more accurate results especially in the strongly interacting regimes. For confined systems it is possible to use QMC only for a few particles, so that, for large number of particles, a fruitful combined use of Density Functional Theory (DFT) and QMC is necessary. The study of the dynamics of ultracold gases has received little attention with QMC techniques, due to the intrinsic computational difficulty of the many-body problem, so that general hydrodynamic equations are often used for studying the propagation of smoothly varying perturbations. In this Thesis we use QMC techniques for studying the problem of ferromagnetism in repulsive or effectively repulsive ultracold gases without a lattice and the problem of the Bardeen-Cooper-Schrieffer to Bose-Einstein-Condensation (BCS-BEC) crossover in two dimensions. We use DFT in the Local Density Approximation (LDA) for calculating the density profiles of ultracold Fermi gases in harmonic magneto-optical traps, starting from QMC equations of state. We study the propagation of first and second sound in ultracold Fermi gases in cylindrical geometry, using the hydrodynamic equations of superfluids.
In this thesis we investigate the properties of mixtures of Bose gases in one dimensions at zero temperature using quantum Monte-Carlo methods. First we investigate the limiting case of an impurity interacting with an atomic bath. We characterize the impurity, by calculating its effective mass, binding energy as well as the contact parameter between the impurity and the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. Then we describe uniform balanced mixtures with repulsive interactions. We investigate the miscibility phase diagram of the two components and find that correlations do not alter the phase diagram predicted by mean-field theories. We investigate the Andreev-Bashkin effect , a non-dissipative drag between the the two components of the gas and find that the drag becomes very large in the strongly interacting regime. In non-homogeneous systems we also investigate the frequency of the spin-dipole mode. Finally we describe mixtures with attractive inter-species interactions, where one can obtain a liquid ground state because of the competition between the inter-species attraction and intra-species repulsion. We characterize the the liquid and we find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intra-species repulsive interactions exceeds a critical value.
We study thermal properties of a trapped Bose-Bose mixture in a dilute regime using quantum Monte Carlo methods. Our main aim is to investigate the dependence of the superfluid density and the condensate fraction on temperature for the mixed and separated phases. To this end we use the diffusion Monte Carlo method in the zero-temperature limit and the path-integral Monte Carlo method for finite temperatures. The results obtained are compared with solutions of the coupled Gross-Pitaevskii equations for the mixture at zero temperature. We notice the existence of an anisotropic superfluid density in some phase-separated mixtures. Our results also show that the temperature evolution of the superfluid density and condensate fraction is slightly different, showing noteworthy situations where the superfluid fraction is smaller than the condensate fraction.