Microscopic description of two dimensional dipolar quantum gases

by Adrián Macía Rey

Institution: Universitat Politècnica de Catalunya
Year: 2015
Record ID: 1127032
Full text PDF: http://hdl.handle.net/10803/286784


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…