Quantum fluctuations in mixtures and dipolar systems

Abstract

Recent theoretical and experimental breakthrough results have revealed the importance of beyond-mean-field contributions in weakly-interacting systems when the mean-field energy is quasi-canceled due to the presence of competing interactions. This is in particular the case in Bose mixtures and in dipolar condensates. In this Thesis we have considered both cases, focusing on particular scenarios where quantum fluctuations result in a qualitatively new physics.

In the first part of the Thesis, we focus on binary mixtures. We consider in particular the case of a peculiar mixture in which one of the components present enhanced role of quantum fluctuations, whereas the second one is immiscible with the first. We show that this may be achieved in experiments using a three-component set up, in which two of the components are miscible and in the regime of mean-field quasi-cancellation, forming an effective scalar component, whereas a the third one is immiscible with the other two. We focus on how a quantum bubble formed by the effective scalar component, behaves in a bath formed by the third component. We show that the properties of the quantum bubble are very significantly affected by the modification introduced by quantum fluctuation in the equilibrium of pressures between bubble and bath. As a result, quantum fluctuations may significantly change the dependence of the bubble volume on the bath density. Furthermore, we show that quantum fluctuations modify the buoyancy criterion. Interestingly, once buoyancy sets in, it may be arrested by the effect of quantum fluctuations at an intermediate position between the center and the surface of the bath, in stark contrast with standard buoyancy in mean-field immiscible mixtures.

The second part of the Thesis is devoted to dipolar condensates, in which quantum fluctuations may play as well a surprisingly important role in the weakly-interacting regime. We focus in particular on the physics of dipolar condensates in quasi-one-dimensional geometries. By means of the so-called Hugenholz-Pines approach we analyze how the Lee-Huang-Yang correction resulting from quantum fluctuations experiences for growing density, a crossover from a one-dimensional dependence into a three-dimensional one. Such a crossover results from the role played by the transversal modes in the determination of the quantum correction, even if the condensate itself remains one-dimensional. We show that at low densities, quantum corrections differ very significantly from those in quasi-one-dimensional Bose-Bose mixtures due to the peculiar momentum dependence of the dipole-dipole interaction. As a result, quasi-one-dimensional dipolar condensates with a residual attractive mean-field term, may be stabilized against the formation of a bright soliton, forming rather a flat-top quantum droplet. Therefore, our results show that quantum fluctuations change radically the density profile and properties of a quasi-one-dimensional dipolar condensates.