A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
A microscopic description of the zero-energy two-body ground state and many-body static properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions at low densities is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction, on the energy per particle, comparing the results with mean-field predictions. We restrict the analysis to the regime where the interaction is always repulsive, although the strength of the repulsion depends on the orientation with respect to the polarization field. We present a series expansion of the solution of the zero-energy two-body problem, which allows us to find the scattering length of the interaction and to build a suitable Jastrow factor that we use as a trial wave function for both a variational and diffusion Monte Carlo simulation of the infinite system. We find that the anisotropy has an almost negligible impact on the ground-state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions.
A microscopic description of the many-body properties of anisotropic homogeneous gases of bosonic dipoles in two dimensions is presented and discussed. By changing the polarization angle with respect to the plane, we study the impact of the anisotropy, present in the dipole-dipole interaction on different physical quantities. We restrict the analysis to the range of polarization angles where the interaction is always repulsive, although the strength of the repulsion can be strongly dependent on the orientation with respect to the polarization field. We present a study of the zero energy two-body problem which allows us to find the scattering length of the interaction and to build a suitable Jastrow many-body wave function that will be used as a trial wave function for Monte Carlo simulations of the bulk two-dimensional system of bosonic dipoles. In the first part of this work we have studied the low-density dipolar Bose gas and we find that the anisotropy has an almost negligible impact on the ground state properties of the many-body system in the universal regime where the scattering length governs the physics of the system. We also show that scaling in the gas parameter persists in the dipolar case up to values where other isotropic interactions with the same scattering length yield different predictions. We also evaluate the excitation spectrum of the dipolar Bose gas in the context of the Feynman approximation and compare the results obtained with the Bogoliubov ones. As expected, we find that these two approximations agree at very low densities, while they start to deviate from each other as the density increases. When the density of the system is increased we find that the behavior of the system depends on the value of the polarization angle of the dipolar moments of the system. At large densities and moderate values of the polarization angle the system undergoes a first-order quantum phase transition from a gas and a crystal phase. We also find that the anisotropy of the dipole-dipole potential causes an elongation of the crystalline lattice of the system in the direction where the interaction is stronger. At large polarization angles and moderate densities the system undergoes a second-order quantum phase transition from a gas to a stripe phase. Interestingly, the critical exponents of this second order transition are nearly independent of the tilting angle and are compatible with the 3D Ising and 3D XY model universality classes within the statistical uncertainty of our simulations. Finally, at high densities and large tilting angles the system shows a first order phase transition between the crystal and stripe phases. The slope of this transition curve is extremely large indicating that, due to the anisotropy of the interaction, the crystal phase of the system is no longer stable if the dipole - dipole potential is highly anisotropic. We consider the ground state of a bilayer system of dipolar bosons, which is a configuration consisting in the continement of the particles in two paralel planes by means of a trapping potential. We consider the simplest situation where dipole moments are oriented by an external field in the direction perpendicular to the parallel planes. Quantum Monte Carlo methods are used to calculate the ground-state energy, the one-body and two-body density matrix as a function of the separation between layers. We find that by decreasing the interlayer distance for fixed value of the strength of the dipolar interaction, the behavior of all the physical observables studied are compatible with the existence of a second order phase transition modulated by the inter-layer distance. In this sense, the results presented in this work are in good agreement with some previous studies of dipolar gases in a bilayer setup En este trabajo presentamos una descripción de las propiedades de los gases homogéneos de dipolos bosónicos en dos dimensiones. Cambiando el ángulo de polarización respecto a la perpendicular al plano donde las partículas están confinadas estudiamos el impacto de la anisotropía de la interacción dipolar en diferentes magnitudes físicas. El análisis se restringe al rango de ángulos de polarización en que la interacción es repulsiva aunque la intensidad pueda depender fuertemente de la orientación respecto a la dirección de polarización. El análisis del problema a dos cuerpos a energía cero nos permite evaluar la longitud de difusión de la interacción y construir una función de onda de tipo Jastrow para el sistema de muchos cuerpos. Esta función de onda será usada como función de prueba para las simulaciones Monte Carlo del sistema homogéneo de dipolos bosónicos en dos dimensiones. En la primera parte de la tesis hemos estudiado el gas de Bose dipolar en el régimen de bajas densidades, observando que el impacto de la anisotropía es negligible en las propiedades macroscópicas en el regimen donde la longitud de difusión gobierna la física del sistema. Hemos comprobado también que el escalado en el parámetro de gas persiste en el caso dipolar hasta valores donde otras interacciones isótropas con la misma longitud de difusión llevan a distintas predicciones. Hemos evaluado el espectro de excitaciones elementales del gas de Bose dipolar en el contexto de la aproximación de Feynman, comparando los resultados con los obtenidos mediante la aproximación de Bogoliubov. Como cabría esperar, las dos aproximaciones coinciden a bajas densidades y se alejan progresivamente al aumentar la densidad. Al aumentar la densidad del sistema vemos que el comportamiento del gas depende del valor del ángulo de polarización de los momentos dipolares. A altas densidades y valores moderados del ángulo de polarización el sistema experimenta una transición de fase de primer orden pasando de una fase gaseosa a una cristalina. Hemos observado también que la anisotropía de la interacción dipolar causa una elongación de la red cristalina en la dirección de interacción más intensa. Para valores elevados del ángulo de polarización y densidades moderadas el sistema muestra transición de fase, esta vez de segundo orden, en la que el sistema pasa de la fase gaseosa a una fase de bandas. Los exponentes críticos de esta transición de fase son independientes del ángulo de polarización y, dentro de los errores estadísticos de las simulaciones, son compatibles con las clases de universalidad del modelo de Ising y XY en tres dimensiones. Finalmente, a altas densidades y valores grandes del ángulo de polarización el sistema muestra otra transición de fase de primer orden entre la fase cristalina y la fase de bandas. La pendiente de esta curva de transición es extremadamente grande indicando que, debido a la anisotropía de la interacción, la fase cristalina deja de ser estable si el potencial de interacción dipolo-dipolo es muy anisótropo. En la última parte de la tesis estudiamos el estado fundamental de un sistema bicapa de dipolos bosónicos, que es una configuración en la que se confinan las partículas en dos planos paralelos mediante un potencial externo. Consideramos la situación más simple en la que los momentos dipolares están orientados por un campo externo en la dirección perpendicular a los planos. Hemos evaluado la energía del estado fundamental y las matrices densidad a uno y dos cuerpos en función de la distancia entre capas usando métodos Monte Carlo. Hemos encontrado que disminuyendo la distancia entre planos para un valor fijo de la intensidad de la interacción, el comportamiento de todos los observables estudiados es compatible con la existencia de una transición de fase de segundo orden modulada por la distancia entre capas. En este sentido, los resultados obtenidos en este trabajo muestran buen acuerdo con estudios previos de este sistema.
The energy of ultra-dilute quantum many-body systems is known to exhibit a universal dependence on the gas parameter x=n a_0^d x = n a 0 d , with n n the density, d d the dimensionality of the space ( d=1,2,3 d = 1 , 2 , 3 ) and a_0 a 0 the s s -wave scattering length. The universal regime typically extends up to x\approx 0.001 x ≈ 0.001 , while at larger values specific details of the interaction start to be relevant and different model potentials lead to different results. Dipolar systems are peculiar in this regard since the anisotropy of the interaction makes a_0 a 0 depend on the polarization angle \alpha α , so different combinations of n and \alpha α can lead to the same value of the gas parameter x. In this work we analyze the scaling properties of dipolar bosons in two dimensions as a function of the density and polarization dependent scattering length up to very large gas parameter values. Using Quantum Monte Carlo (QMC) methods we study the energy and the main structural and coherence properties of the ground state of a gas of dipolar bosons by varying the density and scattering length for a fixed gas parameter. We find that the dipolar interaction shows relevant scaling laws up to unusually large values of x x that hold almost to the boundaries in the phase diagram where a transition to a stripe phase takes place.
The low-density expansions for the energy, chemical potential, and condensate depletion of the homogeneous dilute dipolar Bose gas are obtained by regularizing the dipole-dipole interaction at long distances. It is shown that the leading term, proportional to the density, allows a simple physical interpretation and consistently describes the thermodynamic stability of the system. The long-range asymptotics are obtained analytically for the normal and anomalous one-particle correlation functions and the pair distribution function. We discuss the properties of the two-body scattering with zero relative momentum for the dipole-dipole interaction; in particular, we derive the asymptotics of the wave function and a correction to the scattering length for small values of the dipolar range. We show how the density expansions can be derived within the Bogoliubov model of weakly interacting particles without any divergence from the assumption of universality of the expansions at low densities.
We studied the miscibility of two dipolar quantum gases in the limit of zero temperature. The system under study is composed of a mixture of two Bose gases with dominant dipolar interaction in a two-dimensional harmonic confinement. The dipolar moments are all considered to be perpendicular to the plane, turning the dipolar potential in a purely repulsive and isotropic model. Our analysis is carried out by using the diffusion Monte Carlo method, which allows for an exact solution to the many-body problem within some statistical noise. Our results show that the miscibility between the two species is rather constrained as a function of the relative dipolar moments and masses of the two components. A narrow regime is predicted where both species mix and we introduce an adimensional parameter whose value quite accurately predicts the miscibility of the two dipolar gases.
We theoretically investigate various beyond mean-field effects on Bose gases at zero temperature featuring the anisotropic and long-range dipole-dipole interaction in addition to the isotropic and short-range contact interaction. Within the realm of the Bogoliubov--de Gennes theory, we consider static properties and low-lying excitations of both homogeneous and harmonically trapped dipolar bosonic gases. For the homogeneous system, the condensate depletion, the ground-state energy, the equation of state, and the speed of sound are discussed in detail. Making use of the local density approximation, we extend these results in order to study the properties of a dipolar Bose gas in a harmonic trap and in the regime of large particle numbers. After deriving the equations of motion for the general case of a triaxial trap, we analyze the influence of quantum fluctuations on important properties of the gas, such as the equilibrium configuration and the low-lying excitations in the case of a cylinder-symmetric trap. In addition to the monopole and quadrupole oscillation modes, we also discuss the radial quadrupole mode. We find that the latter acquires a quantum correction exclusively due to the dipole-dipole interaction. As a result, we identify the radial quadrupole as a reasonably accessible source for the signature of dipolar many-body effects and stress the enhancing character that dipolar interactions have for quantum fluctuations in the other oscillation modes.
We investigate the zero-temperature properties of a diluted homogeneous Bose gas made of N particles interacting via a two-body square-well potential by performing Monte Carlo simulations. We tune the interaction strength to achieve arbitrary positive values of the scattering length and compute by Monte Carlo quadrature the energy per particle E/N and the condensate fraction N0/N of this system by using a Jastrow ansatz for the many-body wave function, which avoids the formation of the self-bound ground state and describes instead a (metastable) gaseous state with uniform density. In the unitarity limit, where the scattering length diverges while the range of the interatomic potential is much smaller than the average distance between atoms, we find a finite energy per particle [$E/N=0.70\phantom{\rule{4pt}{0ex}}{\ensuremath{\hbar}}^{2}{(6{\ensuremath{\pi}}^{2}n)}^{2/3}/2m$, with n the number density] and a quite large condensate fraction (N0/N=0.83).