Quenching small quantum gases: Genesis of the orthogonality catastrophe

We study the dynamics of two strongly interacting bosons with an additional impurity atom trapped in a harmonic potential. Using exact numerical diagonalization we are able to fully explore the dynamical evolution when the interaction between the two distinct species is suddenly switched on (quenched). We examine the behavior of the densities, the entanglement, the Loschmidt echo and the spectral function for a large range of inter-species interactions and find that even in such small systems evidence of Anderson's orthogonality catastrophe can be witnessed.Comment: 6 pages, 5 figures, Accepted for publication in Physical Review

Bose polaron as an instance of quantum Brownian motion

We study the dynamics of a quantum impurity immersed in a Bose-Einstein condensate as an open quantum system in the framework of the quantum Brownian motion model. We derive a generalized Langevin equation for the position of the impurity. The Langevin equation is an integrodifferential equation that contains a memory kernel and is driven by a colored noise. These result from considering the environment as given by the degrees of freedom of the quantum gas, and thus depend on its parameters, e.g. interaction strength between the bosons, temperature, etc. We study the role of the memory on the dynamics of the impurity. When the impurity is untrapped, we find that it exhibits a super-diffusive behavior at long times. We find that back-flow in energy between the environment and the impurity occurs during evolution. When the particle is trapped, we calculate the variance of the position and momentum to determine how they compare with the Heisenberg limit. One important result of this paper is that we find position squeezing for the trapped impurity at long times. We determine the regime of validity of our model and the parameters in which these effects can be observed in realistic experiments.Comment: 16 pages, 9 figure

Photonic Nambu-Goldstone bosons

We predict the existence of a Nambu-Goldstone excitation in the propagation of light in nonlinear periodic lattices. We use methods of condensed matter physics that emphasize the peculiarities stemming from the interplay between the nonlinearity and the lattice periodicity. By means of nonlinear Bloch and Wannier functions we provide an explicit construction of the effective free energy of the system, valid for long-range, or, equivalently, low-energy excitations around Bloch solutions. Using then Landau mean field theory for phase transitions we determine the possible stable ground states of the optical system and their stability conditions. Low energy excitations above a stable ground state are fully controlled by the U(1) phase of the optical field, which appear as a Nambu-Goldstone boson, analogous to those predicted in condenser matter and particle physics systems. We support these results by numerical simulations both for spatially periodic and finite nonlinear Bloch wave solutions. We demonstrate how finite-sized nonlinear Bloch light structures embedded in a linear periodic lattice act as tunable metawaveguides for the phase Nambu-Goldstone waves.Ciencias Experimentale

Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.Comment: 6 pages, 2 figure

Non-equilibrium thermodynamics of harmonically trapped bosons

We apply the framework of non-equilibrium quantum thermodynamics to the physics of quenched small-sized bosonic quantum gases in a one-dimensional harmonic trap. We show that dynamical orthogonality can occur in these few-body systems with strong interactions after a quench and we find its occurrence analytically for an infinitely repulsive pair of atoms. We further show this phenomena is related to the fundamental excitations that dictate the dynamics from the spectral function. We establish a clear qualitative link between the amount of (irreversible) work performed on the system and the establishment of entanglement. We extend our analysis to multipartite systems by examining the case of three trapped atoms. We show the initial (pre-quench) interactions play a vital role in determining the dynamical features, while the qualitative features of the two particle case appear to remain valid. Finally, we propose the use of the atomic density profile as a readily accessible indicator of the non-equilibrium properties of the systems in question.Comment: Short supplementary section available in source files. Close to published version. v4 included an omitted referenc

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 non-linearity 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.Comment: 4 pages, 5 figures; minor changes in address and reference

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 rule'' determining the conditions for this phenomenon to occur and numerically analize it in the context of two-dimensional optical lattices or, equivalently, in that of Bose-Einstein condensates in periodic potentials.Comment: 4 pages, 4 figure