Objective comparison of methods to decode anomalous diffusion.

Deviations from Brownian motion leading to anomalous diffusion are found in transport dynamics from quantum physics to life sciences. The characterization of anomalous diffusion from the measurement of an individual trajectory is a challenging task, which traditionally relies on calculating the trajectory mean squared displacement. However, this approach breaks down for cases of practical interest, e.

One-dimensional mixtures of several ultracold atoms: a review.

Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We pay special attention to limiting cases of very strong or very weak interactions and transitions between them. For bosonic mixtures, we describe the developments in systems of three and four atoms as well as different extensions to larger numbers of particles.

Using Polarons for sub-nK Quantum Nondemolition Thermometry in a Bose-Einstein Condensate.

We introduce a novel minimally disturbing method for sub-nK thermometry in a Bose-Einstein condensate (BEC). Our technique is based on the Bose polaron model; namely, an impurity embedded in the BEC acts as the thermometer. We propose to detect temperature fluctuations from measurements of the position and momentum of the impurity.

Dipole soliton-vortices.

On universal symmetry grounds, we analyze the existence of a new type of discrete-symmetry vortex solitons that can be considered as coherent states of dipole solitons carrying a nonzero topological charge. Remarkably, they can be also interpreted as excited angular Bloch states. The stability of new soliton states is elucidated numerically.

Vortex transmutation.

Using group theory arguments and numerical simulations, we demonstrate the possibility of changing the vorticity or topological charge of an individual vortex by means of the action of a system possessing a discrete rotational symmetry of finite order. We establish on theoretical grounds a "transmutation pass" determining the conditions for this phenomenon to occur and numerically analyze it in the context of two-dimensional optical lattices. An analogous approach is applicable to the problems of Bose-Einstein condensates in periodic potentials.

Vorticity cutoff in nonlinear photonic crystals.

Using group-theory arguments, we demonstrate that, unlike in homogeneous media, no symmetric vortices of arbitrary order can be generated in two-dimensional (2D) nonlinear systems possessing a discrete-point symmetry. The only condition needed is that the nonlinearity term exclusively depends on the modulus of the field. In the particular case of 2D periodic systems, such as nonlinear photonic crystals or Bose-Einstein condensates in periodic potentials, it is shown that the realization of discrete symmetry forbids the existence of symmetric vortex solutions with vorticity higher than two.