Anisotropic interactions and self-bound solutions in Bose-Einstein condensates

Abstract

[eng] Bose-Einstein condensation is a direct consequence of quantum statistical effects. It occurs in ultradilute gases at very low temperatures: most atoms condense into the lowest-energy state and behave as a single matter wave. In this thesis, we study Bose- Einstein condensates (BECs) of dilute and weakly interacting atoms within the meanfield framework and focus on two topics: anisotropic interactions and self-bound states. In ultracold dilute gases, the most common atom-atom interactions are short-range and isotropic. However, the interactions can also be anisotropic, for instance, when the gas is either formed of atoms with a large magnetic moment or subject to an artificial gauge field, exhibiting dipolar and chiral interactions, respectively. The interacting nature of the system gives rise to two possible solutions that do not require external confinement: quantum droplets and solitons. Droplets emerge from the balance between quantum fluctuations and the mean-field interactions, while solitons are localized excitations sustained by the competition between the dispersion and nonlinearity of the medium. We begin the thesis by developing the theoretical framework. First, we present single and multicomponent BECs, the mean-field regime and its constraints, and the conditions of existence for droplets and solitons. Then, we introduce dipolar interactions, their effect on the stability and geometry of the system, and how dipolar droplets, as well as crystals of droplets, may form due to the stabilizing effect of quantum fluctuations. Last, we present BECs coupled to artificial density-dependent gauge potentials, which have effective interactions that are chiral (i.e., depend on the direction of motion of the atoms). The first system under consideration is a BEC confined in a shell-shaped potential in the presence of gravitational sag. We explore both the dipolar and nondipolar cases and study the interplay between the anisotropy of the dipolar interactions (or the lack thereof) and the privileged direction set by gravity. We study the ground-state configurations of the system and the dynamics when changing perturbatively the orientation or the strength of the gravitational force. Afterward, we move to binary mixtures of nondipolar and dipolar BECs to investigate, respectively, the formation of solitons and droplets. In the first case, we consider a quasi-1D bosonic mixture within the immiscible regime. We examine the dynamics of a dark soliton moving through the domain wall between components, which may generate, in some cases, a dark--bright soliton. The resulting dark-bright soliton follows a harmonic-like trajectory. Concerning the dipolar case, we propose a two-component BEC with antiparallel dipoles, which forms self-bound structures when unconfined. In the presence of confinement in the dipole direction, the mixture can form incoherent stripes if the interactions are symmetric and droplet crystals if they are asymmetric. These droplet crystals are composed of an array of incoherent droplets in one component surrounded by an interstitial superfluid in the other. In both cases, the resulting structures are self-bound in the transversal plane. To study the effect of chiral interactions, we regard a quasi-1D BEC confined in a rotating ring geometry and coupled to a density-dependent gauge potential, which produces chiral currents. We give an analytical description of the general stationary states of the system (plane waves and solitons) and test their dynamical stability. Finally, we split the system into two components employing a double-well potential to obtain a 1/2-spinor condensate. Besides the linear coupling between the two spin states, the system also presents an effective spin-orbit coupling due to the chiral nature of the interactions. The solutions of the scalar case are also solutions of the spinor case, but now the system also supports states that may have nonzero polarization, leading, for instance, to Josephson vortices.

[cat] En aquesta tesi estudiem condensats de Bose-Einstein de gasos diluïts amb interaccions febles, i ens centrem en dos temes: interaccions anisotròpiques i estats autolligats. Les interaccions més comunes en gasos ultrafreds són isotròpiques i de curt abast. Tanmateix, poden ser anisotròpiques, per exemple, quan el gas està format per àtoms altament magnètics o quan se sotmet a un camp de gauge artificial. Les interaccions són, respectivament, dipolars o quirals. El caràcter interactuant del sistema dona lloc a dues possibles solucions autolligades: gotes quàntiques i solitons. Les gotes es formen gràcies al balanç entre les fluctuacions quàntiques i les interaccions de camp mitjà, mentre que els solitons són pertorbacions localitzades que mantenen la seva forma per la competició entre la dispersió i la no-linealitat del medi. Comencem la tesi desenvolupant el marc teòric. Primer, presentem els condensats formats per una o més components, el règim de camp mitjà, les gotes i els solitons. Seguidament, introduïm les interaccions dipolars, les gotes dipolars i els cristalls de gotes. Per acabar, presentem condensats acoblats a potencials de gauge dependents de la densitat, on les interaccions efectives esdevenen quirals. El primer sistema que considerem és un condensat dipolar confinat en un potencial amb forma de closca sota l'efecte de la gravetat. A continuació, ens centrem en les barreges binàries per investigar la formació de solitons i gotes. En el primer cas, considerem una barreja immiscible quasi-unidimensional i no-dipolar, i analitzem la formació dinàmica d'un solitó fosc-brillant. En el segon, proposem una barreja dipolar amb dipols antiparal·lels, on observem estructures autolligades. Quan el sistema està confinat al llarg de la direcció dels dipols, la barreja pot formar franges incoherents i cristalls de gotes segons si les interaccions són simètriques o asimètriques. Respecte a les interaccions quirals, considerem un condensat confinat en un anell en rotació i acoblat a un potencial de gauge depenent de la densitat, de manera que es produeixen corrents persistents quirals. Finalment, separem el sistema en dues components amb un doble pou per obtenir un condensat espinor que, per la naturalesa quiral de les interaccions, presenta un acoblament espí-òrbita efectiu.