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A nonrelativistic Bose gas is represented as a grand-canonical ensemble of fluctuating closed spacetime strings of arbitrary shape and length. The loops are characterized by their string tension and the number of times they wind around the…

We theoretically examine the vortex states of a gas of trapped quasi-two-dimensional ultracold bosons subject to a density-dependent gauge potential, realizing an effective nonlinear rotation of the atomic condensate, which we also show is…

We study the effect of different heating rates of a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms.…

Open quantum systems can be systematically controlled by making changes to their environment. A well-known example is the spontaneous radiative decay of an electronically excited emitter, such as an atom or a molecule, which is…

Motivated by the recent experiment at ENS [ V. Bretin, S. Stock, Y. Seurin and, J. Dalibard, Phys. Rev. Lett. {\bf 92}, 050403 (2004)], we study a rotating (non-)interacting atomic Bose-Einstein condensate confined in a…

We experimentally and theoretically study the peak fraction of a Bose-Einstein condensate loaded into a cubic optical lattice as the lattice potential depth and entropy per particle are varied. This system is well-described by the…

We consider the dynamics of Bose-Einstein condensates in a corral-like potential. Compared to the electronic quantum corrals, the atomic quantum corrals have the advantage of allowing direct and convenient observation of the wave dynamics.…

The recent experimental condensation of ultracold atoms in a triangular optical lattice with negative effective tunneling energies paves the way to study frustrated systems in a controlled environment. Here, we explore the critical behavior…

The Bose-Einstein condensates recently created in trapped atomic gases are mesoscopic systems, in two senses: (a) Their size fall between macroscopic and microscopic systems; (b) They have a quantum phase that can be manipulated in…

We analyze the dynamical stability of gap solitons formed in a quasi one-dimensional Bose-Einstein condensate in an optical lattice. Using two different numerical methods we show that, under realistic assumptions for experimental…

The possibility, envisaged in 1925 by Einstein following the suggestion of Bose, of a dilute gas of atoms being condensed into a single quantum state was experimentally achieved in 1995 following decades of research. An avalanche of…

We study the dynamics of a Bose-Einstein condensate in a one-dimensional optical lattice in the limit of weak atom-atom interactions, including an approximate model for quantum fluctuations. A pulsating dynamical instability in which atoms…

We present a model which predicts the temperature of Bose-Einstein condensation in atomic alkali gases and find excellent agreement with recent experimental observations. A system of bosons confined by a harmonic oscillator potential is not…

We examine the phase diagram of a Bose-Einstein condensate of atoms, interacting with an attractive pseudopotential, in a quadratic-plus-quartic potential trap rotating at a given rate. Investigating the behavior of the gas as a function of…

We study the effects of a position-dependent artificial gauge field on an atomic Bose--Einstein condensate in quasi-one-dimensional and two-dimensional ring settings. The inhomogeneous artificial gauge field can induce global and local…

We study the non-equilibrium evolution of binary Bose-Einstein condensates in the presence of weak random potential with a Gaussian correlation function using the time-dependent perturbation theory. We apply this theory to construct a…

We suggest the possibility of observing and studying bright vortex solitons in attractive Bose-Einstein condensates in three dimensions with a radial trap. Such systems lie on the verge of critical stability and we discuss the conditions of…

Motivated by a recent experiment [K.C. Wright et. al. Phys. Rev. Lett. 110, 025302 (2013)], we investigate deterministic discontinuous jumps between quantized circulation states in a toroidally trapped Bose-Einstein condensate. These phase…

We study bright solitons in a Bose-Einstein condensate with a spin-orbit coupling that has been realized experimentally. Both stationary bright solitons and moving bright solitons are found. The stationary bright solitons are the ground…

This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already…