Motivated by the recent achievement of space-based Bose-Einstein condensates (BEC) with ultracold alkali-metal atoms under microgravity and by the proposal of bubble traps which confine atoms on a thin shell, we investigate the BEC thermodynamics on the surface of a sphere. We determine analytically the critical temperature and the condensate fraction of a noninteracting Bose gas. Then we consider the inclusion of a zero-range interatomic potential, extending the noninteracting results at zero and finite temperature. Both in the noninteracting and interacting cases the crucial role of the finite radius of the sphere is emphasized, showing that in the limit of infinite radius one recovers the familiar two-dimensional results. We also investigate the Berezinski-Kosterlitz-Thouless transition driven by vortical configurations on the surface of the sphere, analyzing the interplay of condensation and superfluidity in this finite-size system.

The recent developments of microgravity experiments with ultracold atoms have produced a relevant boost in the study of shell-shaped ellipsoidal Bose-Einstein condensates. For realistic bubble-trap parameters, here we calculate the critical temperature of Bose-Einstein condensation, which, if compared to the one of the bare harmonic trap with the same frequencies, shows a strong reduction. We simulate the zero-temperature density distribution with the Gross-Pitaevskii equation, and we study the free expansion of the hollow condensate. While part of the atoms expands in the outward direction, the condensate selfinterferes inside the bubble trap, filling the hole in experimentally observable times. For a mesoscopic number of particles in a strongly interacting regime, for which more refined approaches are needed, we employ quantum Monte Carlo simulations, proving that the nontrivial topology of a thin shell allows superfluidity. Our work constitutes a reliable benchmark for the forthcoming scientific investigations with bubble traps.

Recent experimental and theoretical results show that weakly interacting atomic Bose-Bose mixtures with attractive interspecies interaction are stabilized by beyond-mean-field effects. Here we consider the peculiar properties of these systems in a strictly one-dimensional configuration, taking also into account the nontrivial role of spin-orbit and Rabi couplings. We show that when the value of interand intraspecies interaction strengths are such that mean-field contributions to the energy cancel, a self-bound bright soliton fully governed by quantum fluctuations exists. We derive the phase diagram of the phase transition between a single-peak soliton and a multipeak (striped) soliton, produced by the interplay between spin-orbit, Rabi couplings and beyond-mean-field effects, which also affect the breathing mode frequency of the atomic cloud. Finally, we prove that a phase imprinting of the single-peak soliton leads to a self-confined propagating solitary wave even in the presence of spin-orbit coupling.

We investigate an ultracold and dilute Bose gas by taking into account a finite-range two-body interaction. The coupling constants of the resulting Lagrangian density are related to measurable scattering parameters by following the effective-field-theory approach. A perturbative scheme is then developed up to the Gaussian level, where both quantum and thermal fluctuations are crucially affected by finite-range corrections. In particular, the relation between spontaneous symmetry breaking and the onset of superfluidity is emphasized by recovering the renowned Landau's equation for the superfluid density in terms of the condensate one.resulting picture is only qualitative since, for instance, it does not even manage to capture the peculiar rotonic minimum of the excitation spectrum.In 1995, the experimental realization of a Bose-Einstein condensates [13] changed the scenario in a crucial way: for the first time, the predictions of the Bogoliubov theory [16] have been checked in actual weaklyinteracting quantum gases. At the same time, within a field-theory approach, it is possible to recover the Landau main results moving from a microscopic Lagrangian for ultracold atoms.The several successful theoretical studies based on the Bogoliubov framework move from the crucial assumption that the true atom-atom interaction can be replaced by a contact (i.e. zero-range) pseudopotential whose strength is given by the s-wave scattering length a s [17,18]. The resulting thermodynamics is universal since there is no dependence on the potential shape, with only a s playing a relevant role. The same point can be made for transport quantities as the superfluid fraction. Despite the many achievements of this strategy, current experiments deal with higher density setups, reduced dimensionalities and more complex interactions [19,20]. Thus, it is pressing to extend the usual two-body zero-range framework in order to capture more realistic and interesting experimental regimes. Within a functional integration formalism, atoms are represented by a bosonic field whose dynamics is governed by a microscopic interacting Lagrangian density. The coupling constants of the finite-range theory can be determined in terms of the s-wave scattering parameters, namely a s and the corresponding effective range r e . In [21][22][23][24], the finite-range thermodynamics is derived up to the Gaussian level for a three-dimensional uniform Bose gas, while the non-trivial case of two spatial dimensions is addressed in [25,26]. In figure 1 we report a visual summary of the major analytical approaches to modeling bosonic quantum gases.A similar analysis concerning the superfluid properties of a finite-range theory is still missing and it is the main subject of this work. By adopting a functional integration point of view as in [23,25], we are going to show that both condensate and superfluid depletion are modified by the finite-range character of the two-body interaction. Moreover, they are not independent from each other but the familiar Landau equation for t...