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For most kinds of already known Bose-Einstein condensates experimental evidence for the existence of a macroscopic coherent quantum state has been provided, e.g., from the observation of interference phenomena, the formation vortices, the…
We investigate the expansion dynamics of spin-orbit-coupled Bose-Einstein condensates subjected to a synthetic magnetic field, after their release from an external harmonic trap. Our findings reveal that the condensate experiences a…
We review the topic of quantized vortices in multicomponent Bose-Einstein condensates of dilute atomic gases, with an emphasis on that in two-component condensates. First, we review the fundamental structure, stability and dynamics of a…
Vortices are expected to exist in a supersolid but experimentally their detection can be difficult because the vortex cores are localized at positions where the local density is very low. We address here this problem by performing numerical…
We make use of Shannon entropy ($S$) and Fisher information ($I$) to study the response of atomic density profiles of a spin-orbit coupled Bose-Einstein condensate to changes in the wave number ($\kappa_L$) of the Raman laser that couples…
We study topological excitations in spin-1 Bose-Einstein condensates trapped in an elongated double-well optical potential. This system hosts a new topological defect, the spin Josephson vortex (SJV), which forms due to the competition…
Spinorial or multi-component Bose-Einstein condensates may sustain fractional quanta of circulation, vorticant topological excitations with half integer windings of phase and polarization. Matter-light quantum fluids, such as microcavity…
We study the superfluid properties of a system of fully polarized dipolar bosons moving in the $xy$ plane. We focus on the general case where the polarization field forms an arbitrary angle $\alpha$ with respect to the $z$ axis, while the…
We investigate the phases of a Bose-Einstein condensate of dipolar atoms restricted to move in a two-dimensional plane. The dipole moments are all aligned in a direction tilted with respect to the plane normal. As a result of the attractive…
We report the first numerical prediction of a "spin microemulsion" -- a phase with undulating spin domains resembling classical bicontinuous oil-water-surfactant emulsions -- in two-dimensional systems of spinor Bose-Einstein condensates…
We demonstrate the formation of stable spatially-ordered states in a {\it uniform} and also {\it trapped} quasi-two-dimensional (quasi-2D) Rashba or Dresselhaus spin-orbit (SO) coupled pseudo spin-1/2 Bose-Einstein condensate using the…
We numerically investigate low-energy stationary states of pseudospin-1 Bose-Einstein condensates in the presence of Rashba-Dresselhaus-type spin-orbit coupling. We show that for experimentally feasible parameters and strong spin-orbit…
We study the real-time dynamics of vortex lines in a large elongated Bose-Einstein condensate (BEC) of sodium atoms using a stroboscopic technique. Vortices are spontaneously produced via the Kibble-Zurek mechanism in a quench across the…
Realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates are discussed. It is shown that, contrary to common intuition, rotation of the trap containing a spin-orbit condensate does not lead to an equilibrium…
Bose-Einstein condensates of dilute atomic gases, characterized by a macroscopic population of the quantum mechanical ground state, are a new, weakly interacting quantum fluid. In most experiments condensates in a single weak field seeking…
We analyze the formation of transient patterns and spin-spin correlations in quasi-two-dimensional spin-1 homogeneous Bose-Einstein condensates subjected to parametric driving of $s$-wave scattering lengths. The dynamics for an initial…
For many years, $^4$He typified Bose-Einstein superfluids, but recent advances in dilute ultra-cold alkali-metal gases have provided new neutral superfluids that are particularly tractable because the system is dilute. This chapter starts…
We investigate the ground-state properties of spin-orbit coupled Bose-Einstein condensates in spin-dependent optical lattices. The competition between the spin-orbit coupling strength and the depth of the optical lattice leads to a rich…
We show that many observable properties of high temperature superconductors can be obtained in the frameworks of one-dimensional self-consistent model with included superconducting correlations. Analytical solutions for spin, charge and…
The recently realized multicomponent Bose-Einstein condensates provide opportunities to explore the rich physics brought about by the spin degrees of freedom. For instance, we can study spin waves and phase separation, macroscopic quantum…