We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a nonperpendicular polarization with respect to the system plane. For sufficiently high density, an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting direction decreases with increasing polarization angle and almost vanishes close to the instability. Exact path integral ground state Monte Carlo simulations show that this instability is indeed a quantum phase transition to a stripe phase, characterized by long-range order in the strongly interacting direction.
We present calculations of the ground state and excitations of an anisotropic dipolar Bose gas in two dimensions, realized by a nonperpendicular polarization with respect to the system plane. For sufficiently high density, an increase of the polarization angle leads to a density instability of the gas phase in the direction where the anisotropic interaction is strongest. Using a dynamic many-body theory, we calculate the dynamic structure function in the gas phase which shows the anisotropic dispersion of the excitations. We find that the energy of roton excitations in the strongly interacting direction decreases with increasing polarization angle and almost vanishes close to the instability. Exact path integral ground state Monte Carlo simulations show that this instability is indeed a quantum phase transition to a stripe phase, characterized by long-range order in the strongly interacting direction.
We analyze the ground state of a system of dipolar bosons moving in the XY plane and such that their dipolar moments are all aligned in a fixed direction in space. We focus on the general case where the polarization field forms a generic angle $\ensuremath{\alpha}$ with respect to the Z axis. We use the path-integral ground-state method to analyze the static properties of the system as both $\ensuremath{\alpha}$ and the density n vary over a wide range where the system is stable. We use the maximum of the static structure function as an order parameter to characterize the different phases and the transition lines among them. We find that, in addition to a superfluid gas and a solid phase, the system reaches a stripe phase at large tilting angles that is entirely induced by the anisotropic character of the interaction. We also show that the quantum phase transition from the gas to the stripe phase is of second order and report approximate values for the critical exponents.
Recent experimental advances in creating stable dipolar systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Here we discuss our work on homogeneous 2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for non-zero tilt angles. Using Bogoliubov-de Gennes equations, we obtain T=0 excitation spectrum of the dipolar Bose gas, and explore instabilities at varying tilt angle, density and dipolar coupling. We map out a phase diagram a function of tilt angle, dipole strength and density. We find the development of maxon-roton behavior leading to roton instabilities at large densities for small tilt angles, and at low densities for large tilt angles. The behavior is anisotropic in k-space; accordingly the roton instabilities occur in the k y direction, suggestive of inhomogeneity and stripe phase, with density mode becoming soft in the y direction. Our results compare favorably with existing Quantum Monte Carlo calculations for non-zero tilt angles.
We investigate the phases of a Bose-Einstein condensate of dipolar atoms restricted to move in a two-dimensional plane. The dipole moments are all aligned in a direction tilted with respect to the plane normal. As a result of the attractive and repulsive components of the dipole-dipole interaction, the dipolar gas has a self-bound phase, which is stabilized by quantum fluctuations. Tilting the dipoles tunes the anisotropy of the dipole-dipole interaction, which can trigger a spatial density modulation. In this work we study these two aspects and investigate the conditions for the formation of a self-bound and striped phase, which has been realized in experiments with dipolar droplets. We use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function to study the ground-state properties. This method takes into account quantum fluctuations in a nonperturbative way and thus can be used also for strongly correlated systems.
We predict a stable density-wave-type supersolid phase of a dilute gas of tilted dipolar bosons in a two-dimensional (2D) geometry. This many-body phase is manifested by the formation of the stripe pattern and elasticity coexisting together with the Bose-Einstein condensation and superfluidity at zero temperature. With the increasing of the tilting angle the type of the gas-supersolid transition changes from the first order to the second-order one despite the 2D character of the system, whereas the anisotropy and many-body stabilizing interactions play crucial roles. Our approach is based on the numerical analysis of the phase diagram using the simulated annealing method for a free-energy functional. The predicted supersolid effect can be realized in a variety of experimental setups ranging from excitons in heterostructures to cold atoms and polar molecules in optical potentials.
Recent experimental advances in creating stable dipolar bosonic systems, including polar molecules with large electric dipole moments, have led to vigorous theoretical activities. Recent reporting of observation of roton feature in dipolar erbium has provided added impetus to theoretical and experimental work. Here we discuss our mean-field theory work on 2D and quasi-2D dipolar bosons with dipoles oriented at an angle to the direction perpendicular to the confining 2D plane, i.e. for {\it non-zero tilt angles}. Using Bogoliubov-de Gennes equations, we present results on a number of T=0 properties of both 2D and quasi-2D systems, such as excitation spectra, structure functions, sound velocities, quantum depletion, etc. We explore instabilities at varying tilt angle, density and dipolar coupling. We map out phase diagrams as a function of tilt angle, dipole strength and density. We find the development of maxon-roton behavior leading to roton instabilities at large densities for small tilt angles, and at low densities for large tilt angles. The behavior is anisotropic in k-space; accordingly the roton instabilities occur first in the ky direction, suggestive of inhomogeneity and stripe phase, with density mode becoming soft in the y-direction. Beyond a critical tilt angle, at any density, the dipolar system collapses owing to a phonon instability. We discuss similarities and differences between the properties of 2D and quasi-2D dipolar systems at non-zero tilt angles.
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.