Make Slow Fast -- how to speed up interacting disordered matter

Anderson and dynamical localization have been experimentally observed with ultra-cold atomic matter. Feshbach resonances are used to efficiently control the strength of interactions between atoms. This allows to study the delocalization effect of interactions for localized wave packets. The delocalization processes are subdiffusive and slow, thereby limiting the quantitative experimental and numerical analysis. We propose an elegant solution of the problem by proper ramping the interaction strength in time. We demonstrate that subdiffusion is speeded up to normal diffusion for interacting disordered and kicked atomic systems. The door is open to test these theoretical results experimentally, and to attack similar computational quests in higher space dimension

Localized modes in mini-gaps opened by periodically modulated intersite coupling in two-dimensional nonlinear lattices

Spatially periodic modulation of the intersite coupling in two-dimensional (2D) nonlinear lattices modifies the eigenvalue spectrum by opening mini-gaps in it. This work aims to build stable localized modes in the new bandgaps. Numerical analysis shows that single-peak and composite two- and four-peak discrete static solitons and breathers emerge as such modes in certain parameter areas inside the mini-gaps of the 2D superlattice induced by the periodic modulation of the intersite coupling along both directions.The single-peak solitons and four-peak discrete solitons are stable in a part of their existence domain, while unstable stationary states (in particular, two-soliton complexes) may readily transform into robust localized breathers.Comment: Chaos, in pres

Nonlinear symmetry breaking of Aharonov-Bohm cages

We study the influence of mean field cubic nonlinearity on Aharonov-Bohm caging in a diamond lattice with synthetic magnetic flux. For sufficiently weak nonlinearities the Aharonov-Bohm caging persists as periodic nonlinear breathing dynamics. Above a critical nonlinearity, symmetry breaking induces a sharp transition in the dynamics and enables stronger wavepacket spreading. This transition is distinct from other flatband networks, where continuous spreading is induced by effective nonlinear hopping or resonances with delocalized modes, and is in contrast to the quantum limit, where two-particle hopping enables arbitrarily large spreading. This nonlinear symmetry breaking transition is readily observable in femtosecond laser-written waveguide arrays.Comment: 6 pages, 5 figure

Influence of different disorder types on Aharonov-Bohm caging in the diamond chain

The linear diamond chain with fine-tuned effective magnetic flux has a completely flat energy spectrum and compactly-localized eigenmodes, forming an Aharonov-Bohm cage. We study numerically how this localization is affected by different types of disorder (static and time-evolving) relevant to recent realizations of Aharonov-Bohm cages in periodically-modulated optical waveguide arrays. We demonstrate robustness of localization under static and periodically-evolving disorder, while in contrast non-quenched (time-dependent) disorder leads to wavepacket spreading and delocalization.Comment: 13 figure

Soliton stability and collapse in the discrete nonpolynomial Schrodinger equation with dipole-dipole interactions

The stability and collapse of fundamental unstaggered bright solitons in the discrete Schrodinger equation with the nonpolynomial on-site nonlinearity, which models a nearly one-dimensional Bose-Einstein condensate trapped in a deep optical lattice, are studied in the presence of the long-range dipole-dipole (DD) interactions. The cases of both attractive and repulsive contact and DD interaction are considered. The results are summarized in the form of stability/collapse diagrams in the parametric space of the model, which demonstrate that the the attractive DD interactions stabilize the solitons and help to prevent the collapse. Mobility of the discrete solitons is briefly considered too.Comment: 6 figure

Transition to miscibility in linearly coupled binary dipolar Bose-Einstein condensates

We investigate effects of dipole-dipole (DD) interactions on immiscibility-miscibility transitions (IMTs) in two-component Bose-Einstein condensates (BECs) trapped in the harmonic-oscillator (HO) potential, with the components linearly coupled by a resonant electromagnetic field (accordingly, the components represent two different spin states of the same atom). The problem is studied by means of direct numerical simulations. Different mutual orientations of the dipolar moments in the two components are considered. It is shown that, in the binary BEC formed by dipoles with the same orientation and equal magnitudes, the IMT cannot be induced by the DD interaction alone, being possible only in the presence of the linear coupling between the components, while the miscibility threshold is affected by the DD interactions. However, in the binary condensate with the two dipolar components polarized in opposite directions, the IMT can be induced \emph{without} any linear coupling. Further, we demonstrate that those miscible and immiscible localized states, formed in the presence of the DD interactions, which are unstable evolve into robust breathers, which tend to keep the original miscibility or immiscibility, respectively. An exception is the case of a very strong DD attraction, when narrow stationary modes are destroyed by the instability. The binary BEC composed of co-polarized dipoles with different magnitudes are briefly considered too.Comment: 10 figure

Composite localized modes in discretized spin-orbit-coupled Bose-Einstein condensates

We introduce a discrete model for binary spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC) trapped in a deep one-dimensional optical lattice. Two different types of the couplings are considered, with spatial derivatives acting inside each species, or between the species. The discrete system with inter-site couplings dominated by the SOC, while the usual hopping is negligible, \textit{emulates} condensates composed of extremely heavy atoms, as well as those with opposite signs of the effective atomic masses in the two components.\ Stable localized composite states of miscible and immiscible types are constructed. The effect of the SOC on the immiscibility-miscibility transition in the localized complexes, which emulates the phase transition between insulating and conducting states in semiconductors, is studied.Comment: Journal of Physics B , in pres

Neural network modeling methods for predicting the air parameters in the city of Tuzla

According to the report of the World Health Organization, the city of Tuzla is the second in the world, and the first in Europe in terms of the number of diseases caused by air pollution. Tuzla Canton since 2003 has continuous air monitoring. Concentrations of individual pollutants exceed hourly, daily and annual limit values. In this paper, based on the existing results of air monitoring and meteorological data, using statistical methods and neural network modeling methods, unique and reliable models for predicting the concentration of NO2 in the air for the City of Tuzla have been developed. The results obtained using these models can be used in strategic decision-making processes and activities related to air quality control and management. This paper, on the example of the City of Tuzla, showed that using existing air monitoring data, concentrations of pollutants can be predicted for a longer period of time, using artificial intelligence methods. Reliable models with a high correlation coefficient can be obtained. In the case of a short or long interruption of the measurement of pollutant concentrations for the City of Tuzla with the help of models, which are the result of this work, it is possible to predict the concentrations of pollutants and plan to take measures based on them

Coupled vortex generator in active multi-core fibers

Optical vortex is a coherent localized structure carrying energy around the pivot point. It is characterized by an optical angular momentum (OAM) mathematically described by azimuthal phase term exp(ilφ). Here, the integer number l stands for the winding number or topological charge of the vortex [1]. Particularly interesting are vortices generated in discrete systems [2]. They are specified by quantized topological charge and exhibit inherent robustness on perturbations within the system [3]. One of the structures that support discrete vortices is multi-core fiber (MCF) [4]. Here, we study MCF structure composed of two concentric hexagonal rings, A and B (Fig. 1). Beside equal coupling constants among nearest sites of A and B ring, we also consider a presence of artificial flux (Φ) which affects coupling between sites in the A ring [5]. The presence of artificial flux does not change the topological charge of vortices, only shifts their corresponding eigenvalues. Moreover, vortex excitation in one of the rings produces a regular periodical energy exchange between A and B rings in a form of stable breathing coupled-vortex structure. In passive MCF the vortex excitation is necessary to propagate vortex through the system. However, including the saturable gain and linear loss in the MCF, the vortices of different topological charge can be excited even from the uniform background by tuning the flux value. Numerical simulations show high robustness of newly formed vortices, which offers possibility to utilize the proposed setup as highly controllable vortex generator. Moreover, this can be of particular importance in the ring array based lasers [6,7].IX International School and Conference on Photonics : PHOTONICA2023 : book of abstracts; August 28 - September 1, 2023; Belgrad

Stable periodic density waves in dipolar Bose-Einstein condensates trapped in optical lattices

Density-wave patterns in (quasi-) discrete media with local interactions are known to be unstable. We demonstrate that \emph{stable} double- and triple- period patterns (DPPs and TPPs), with respect to the period of the underlying lattice, exist in media with nonlocal nonlinearity. This is shown in detail for dipolar Bose-Einstein condensates (BECs), loaded into a deep one-dimensional (1D) optical lattice (OL), by means of analytical and numerical methods in the tight-binding limit. The patterns featuring multiple periodicities are generated by the modulational instability of the continuous-wave (CW) state, whose period is identical to that of the OL. The DPP and TPP emerge via phase transitions of the second and first kind, respectively. The emerging patterns may be stable provided that the dipole-dipole (DD) interactions are repulsive and sufficiently strong, in comparison with the local repulsive nonlinearity. Within the set of the considered states, the TPPs realize a minimum of the free energy. Accordingly, a vast stability region for the TPPs is found in the parameter space, while the DPP\ stability region is relatively narrow. The same mechanism may create stable density-wave patterns in other physical media featuring nonlocal interactions, such as arrayed optical waveguides with thermal nonlinearity.Comment: 7 pages, 4 figures, Phys. Rev. Lett., in pres