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Phase transitions are ubiquitous in our three-dimensional world. By contrast most conventional transitions do not occur in infinite uniform two-dimensional systems because of the increased role of thermal fluctuations. Here we explore the…

We demonstrate the spontaneous formation of a Bose-Einstein condensate (BEC) of strongly-bound harmonically-trapped dipolar $^{164}$Dy atoms on the outer curved surface of an elliptical or a circular cylinder, with a distinct topology,…

Recent experimental and theoretical work has shown that there are conditions in which a trapped, low-density Bose gas behaves like the one-dimensional delta-function Bose gas solved years ago by Lieb and Liniger. This is an intrinsically…

We analyze some issues related to the stability and free expansion of a one-dimensional logarithmic Bose-Einstein condensate, particularly its eventual relation to the formation of quantum droplet-type configurations. We prove that the…

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L…

We study properties of a trapped dipolar Bose-Einstein condensate (BEC) in a circular ring or a spherical shell using the mean-field Gross-Pitaevskii equation. In the case of the ring-shaped trap we consider different orientations of the…

We study a two-component Bose gas with a symmetric spin-orbit coupling, and find that two atoms can form a bound state with any intra- or inter-species scattering length. Consequently, in the dilute limit, the Bardeen-Cooper-Shrieffer (BCS)…

We study the statics and dynamics of a dipolar Bose-Einstein condensate (BEC) droplet bound by inter-species contact interaction in a trapped non-dipolar BEC. Our findings are demonstrated in terms of stability plots of a dipolar 164Dy…

We theoretically investigate the finite-temperature structure and collective excitations of a self-bound ultradilute Bose droplet in a flat space realized in a binary Bose mixture with attractive inter-species interactions on the verge of…

We examine the possibility of Bose-Einstein condensation (BEC) in two-dimensional (2D) system of interacting particles in a trap. We use a self-consistent mean-field theory of Bose particles interacting by a contact interaction in the Popov…

Quantum vortices in the multi-component Bose-Einstein condensation (BEC) are investigated theoretically. It is found that three kinds of the vortex configurations are possible and their physical properties are discussed in details,…

Extending the understanding of Bose-Einstein condensate (BEC) physics to new geometries and topologies has a long and varied history in ultracold atomic physics. One such new geometry is that of a bubble, where a condensate would be…

Ultracold miscible mixtures of bosonic gases have been observed to form quantum droplet states stabilized by beyond-mean-field quantum fluctuations. Here we study the properties of the droplets when subjected to harmonic trapping in one…

The structure and dynamics of one-dimensional binary Bose gases forming quantum droplets is studied by solving the corresponding amended Gross-Pitaevskii equation. Two physically different regimes are identified, corresponding to small…

We study the structure of a Bose-condensed gas after quenching interactions to unitarity. Using the method of cumulants, we decompose the evolving gas in terms of clusters. Within the quantum depletion we observe the emergence of two-body…

Here we describe a weakly interacting Bose gas on a curved manifold, which is embedded in the three-dimensional Euclidean space.~To this end we start by considering a harmonic trap in the normal direction of the manifold, which confines the…

We consider a two-dimensional self-bound quantum droplet, which consists of a mixture of two Bose-Einstein condensates. We start with the ground state, and then turn to the rotational response of this system, in the presence of an external…

We report on the formation of multiple quantum droplets in a heteronuclear $^{41}$K-$^{87}$Rb mixture released in an optical waveguide. By a sudden change of the interspecies interaction from the non-interacting to the strongly attractive…

We demonstrate that a dipolar condensate can be prepared into a three-dimensional wavepacket that remains localized when released in free-space. Such self-bound states arise from the interplay of the two-body interactions and quantum…

We study quantum coherence properties of a dilute gas at temperatures above, but not much above the transition temperature of Bose-Einstein condensation (BEC). In such a gas, a small proportion of the atoms may possess coherence lengths…