Nonlinear optics of intense few-cycle pulses: A overview of recent theoretical and experimental developments

We provide a brief overview of recent theoretical and experimental studies in the field of nonlinear optics of intense few-cycle pulses, which were performed in a series of relevant physical settings

Positive and Negative Mass Solitons in Spin-Orbit Coupled Bose-Einstein Condensates

We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals “negative mass” regimes, where corresponding “negative mass” bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOC-BEC. Numerical results are found to be in excellent agreement with our analytical predictions

Dynamics of Dark-Bright Solitons in Cigar-Shaped Bose-Einstein Condensates

We explore the stability and dynamics of dark-bright solitons in two-component elongated Bose-Einstein condensates by developing effective 1D vector equations as well as solving the corresponding 3D Gross-Pitaevskii equations. A strong dependence of the oscillation frequency and of the stability of the dark-bright (DB) soliton on the atom number of its components is found. Spontaneous symmetry breaking leads to oscillatory dynamics in the transverse degrees of freedom for a large occupation of the component supporting the dark soliton. Moreover, the interactions of two DB solitons are investigated with special emphasis on the importance of their relative phases. Experimental results showcasing dark-bright soliton dynamics and collisions in a BEC consisting of two hyperfine states of $^{87}$Rb confined in an elongated optical dipole trap are presented.Comment: 4 pages, 5 figure

On the Emergence of Unstable Modes in an Expanding Domain for Energy-Conserving Wave Equations

Motivated by recent work on instabilities in expanding domains in reaction-diffusion settings, we propose an analog of such mechanisms in energy-conserving wave equations. In particular, we consider a nonlinear Schr{\"o}dinger equation in a finite domain and show how the expansion or contraction of the domain, under appropriate conditions, can destabilize its originally stable solutions through the modulational instability mechanism. Using both real and Fourier spacediagnostics, we monitor and control the crossing of the instability threshold and, hence, the activation of the instability. We also consider how the manifestation of this mechanism is modified in a spatially inhomogeneous setting, namely in the presence of an external parabolic potential, which is relevant to trapped Bose-Einstein condensates

Dynamics of trapped bright solitons in the presence of localized inhomogeneities

We examine the dynamics of a bright solitary wave in the presence of a repulsive or attractive localized ``impurity'' in Bose-Einstein condensates (BECs). We study the generation and stability of a pair of steady states in the vicinity of the impurity as the impurity strength is varied. These two new steady states, one stable and one unstable, disappear through a saddle-node bifurcation as the strength of the impurity is decreased. The dynamics of the soliton is also examined in all the cases (including cases where the soliton is offset from one of the relevant fixed points). The numerical results are corroborated by theoretical calculations which are in very good agreement with the numerical findings.Comment: 8 pages, 5 composite figures with low res (for high res pics please go to http://www.rohan.sdsu.edu/~rcarrete/ [Publications] [Publication#41

Bose-Einstein Condensation: Twenty Years After

The aim of this introductory article is two-fold. First, we aim to offer a general introduction to the theme of Bose-Einstein condensates, and briefly discuss the evolution of a number of relevant research directions during the last two decades. Second, we introduce and present the articles that appear in this Special Volume of Romanian Reports in Physics celebrating the conclusion of the second decade since the experimental creation of Bose-Einstein condensation in ultracold gases of alkali-metal atoms

Collisional-inhomogeneity-induced generation of matter-wave dark solitons

We propose an experimentally relevant protocol for the controlled generation of matter-wave dark solitons in atomic Bose-Einstein condensates (BECs). In particular, using direct numerical simulations, we show that by switching-on a spatially inhomogeneous (step-like) change of the s-wave scattering length, it is possible to generate a controllable number of dark solitons in a quasi-one-dimensional BEC. A similar phenomenology is also found in the two-dimensional setting of "disk-shaped" BECs but, as the solitons are subject to the snaking instability, they decay into vortex structures. A detailed investigation of how the parameters involved affect the emergence and evolution of solitons and vortices is provided.Comment: 8 pages, 5 Figures, Physics Letters A (in press

Dynamics of Vortex Dipoles in Confined Bose-Einstein Condensates

We present a systematic theoretical analysis of the motion of a pair of straight counter-rotating vortex lines within a trapped Bose-Einstein condensate. We introduce the dynamical equations of motion, identify the associated conserved quantities, and illustrate the integrability of the ensuing dynamics. The system possesses a stationary equilibrium as a special case in a class of exact solutions that consist of rotating guiding-center equilibria about which the vortex lines execute periodic motion; thus, the generic two-vortex motion can be classified as quasi-periodic. We conclude with an analysis of the linear and nonlinear stability of these stationary and rotating equilibria.Comment: 8 pages, 3 figures, to appear in Phys. Lett.

Matter wave solitons at finite temperatures

We consider the dynamics of a dark soliton in an elongated harmonically trapped Bose-Einstein condensate. A central question concerns the behavior at finite temperatures, where dissipation arises due to the presence of a thermal cloud. We study this problem using coupled Gross-Pitaevskii and $N$-body simulations, which include the mean field coupling between the condensate and thermal cloud. We find that the soliton decays relatively quickly even at very low temperatures, with the decay rate increasing with rising temperature.Comment: 6 pages, 2 figures, submitted to the Proceedings of QFS '0

Spontaneous Symmetry Breaking in Photonic Lattices: Theory and Experiment

We examine an example of spontaneous symmetry breaking in a double-well waveguide with a symmetric potential. The ground state of the system beyond a critical power becomes asymmetric. The effect is illustrated numerically, and quantitatively analyzed via a Galerkin truncation that clearly shows the bifurcation from a symmetric to an asymmetric steady state. This phenomenon is also demonstrated experimentally when a probe beam is launched appropriately into an optically induced photonic lattice in a photorefractive material.Comment: 4 pages, 3 figure