arXiv subjects

D. J. Frantzeskakis

Publications and source records attributed to D. J. Frantzeskakis.

At least 109 records · Page 6Linked to original sources

arXiv2011

Vector solitons in nonlinear isotropic chiral metamaterials

Starting from the Maxwell equations, we used the reductive perturbation method to derive a system of two coupled nonlinear Schrödinger (NLS) equations for the two Beltrami components of the electromagnetic field propagating along a fixed direction in an isotropic nonlinear chiral metamaterial. With single-resonance Lorentz models for the permittivity and permeability and a Condon model for the chirality parameter, in certain spectral regimes, one of the two Beltrami components exhibits a negative real refractive index when nonlinearity is ignored and the chirality parameter is sufficiently large.We found that, inside such a spectral regime, there may exist a subregime wherein the system of the NLS equations can be approximated by the Manakov system. Bright-bright, dark-dark, and dark-bright vector solitons can be formed in that spectral subregime.

nlin.PS↗

arXiv2011

Statics and dynamics of atomic dark-bright solitons in the presence of delta-like impurities

Adopting a mean-field description for a two-component atomic Bose-Einstein condensate, we study the stat- ics and dynamics of dark-bright solitons in the presence of localized impurities. We use adiabatic perturbation theory to derive an equation of motion for the dark-bright soliton center. We show that, counter-intuitively, an attractive (repulsive) delta-like impurity, acting solely on the bright soliton component, induces an effective localized barrier (well) in the effective potential felt by the soliton; this way, dark-bright solitons are reflected from (transmitted through) attractive (repulsive) impurities. Our analytical results for the small-amplitude oscil- lations of solitons are found to be in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Transfer and scattering of wave packets by a nonlinear trap

In the framework of a one-dimensional model with a tightly localized self-attractive nonlinearity, we study the formation and transfer (dragging) of a trapped mode by "nonlinear tweezers", as well as the scattering of coherent linear wave packets on the stationary localized nonlinearity. The use of the nonlinear trap for the dragging allows one to pick up and transfer the relevant structures without grabbing surrounding "garbage". A stability border for the dragged modes is identified by means of of analytical estimates and systematic simulations. In the framework of the scattering problem, the shares of trapped, reflected, and transmitted wave fields are found. Quasi-Airy stationary modes with a divergent norm, that may be dragged by the nonlinear trap moving at a constant acceleration, are briefly considered too.

nlin.PS↗

arXiv2011

Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

We study a discrete nonlinear Schrödinger lattice with a parabolic trapping potential. The model, describing, e.g., an array of repulsive Bose-Einstein condensate droplets confined in the wells of an optical lattice, is analytically and numerically investigated. Starting from the linear limit of the problem, we use global bifurcation theory to rigorously prove that - in the discrete regime - all linear states lead to nonlinear generalizations thereof, which assume the form of a chain of discrete dark solitons (as the density increases). The stability of the ensuing nonlinear states is studied and it is found that the ground state is stable, while the excited states feature a chain of stability/instability bands. We illustrate the mechanisms under which discreteness destabilizes the dark-soliton configurations, which become stable only inside the continuum regime. Continuation from the anti-continuum limit is also considered, and a rich bifurcation structure is revealed.

cond-mat.quant-gas↗

arXiv2011

Dark-bright solitons in Bose-Einstein condensates at finite temperatures

We study the dynamics of dark-bright solitons in binary mixtures of Bose gases at finite temperature using a system of two coupled dissipative Gross-Pitaevskii equations. We develop a perturbation theory for the two-component system to derive an equation of motion for the soliton centers and identify different temperature-dependent damping regimes. We show that the effect of the bright ("filling") soliton component is to partially stabilize "bare" dark solitons against temperature-induced dissipation, thus providing longer lifetimes. We also study analytically thermal effects on dark-bright soliton "molecules" (i.e., two in- and out-of-phase dark-bright solitons), showing that they undergo expanding oscillations while interacting. Our analytical findings are in good agreement with results obtained via a Bogoliubov-de Gennes analysis and direct numerical simulations.

cond-mat.quant-gas↗

arXiv2011

Dark-bright ring solitons in Bose-Einstein condensates

We study dark-bright ring solitons in two-component Bose-Einstein condensates. In the limit of large densities of the dark component, we describe the soliton dynamics by means of an equation of motion for the ring radius. The presence of the bright, "filling" species is demonstrated to have a stabilizing effect on the ring dark soliton. Near the linear limit, we discuss the symmetry-breaking bifurcations of dark-bright soliton stripes and vortex-bright soliton clusters from the dark-bright ring and relate the stabilizing effect of filling to changes in the bifurcation diagram. Finally, we show that stabilization by means of a second component is not limited to the radially symmetric structures, but can also be observed in a cross-like dark-bright soliton configuration.

cond-mat.quant-gas↗

arXiv2011

Guiding-center dynamics of vortex dipoles in Bose-Einstein condensates

A quantized vortex dipole is the simplest vortex molecule, comprising two counter-circulating vortex lines in a superfluid. Although vortex dipoles are endemic in two-dimensional superfluids, the precise details of their dynamics have remained largely unexplored. We present here several striking observations of vortex dipoles in dilute-gas Bose-Einstein condensates, and develop a vortex-particle model that generates vortex line trajectories that are in good agreement with the experimental data. Interestingly, these diverse trajectories exhibit essentially identical quasi-periodic behavior, in which the vortex lines undergo stable epicyclic orbits.

cond-mat.quant-gas↗

arXiv2011

Fluctuating and dissipative dynamics of dark solitons in quasi-condensates

The fluctuating and dissipative dynamics of matter-wave dark solitons within harmonically trapped, partially condensed Bose gases is studied both numerically and analytically. A study of the stochastic Gross-Pitaevskii equation, which correctly accounts for density and phase fluctuations at finite temperatures, reveals dark soliton decay times to be lognormally distributed at each temperature, thereby characterizing the previously predicted long lived soliton trajectories within each ensemble of numerical realizations (S.P. Cockburn {\it et al.}, Phys. Rev. Lett. 104, 174101 (2010)). Expectation values for the average soliton lifetimes extracted from these distributions are found to agree well with both numerical and analytic predictions based upon the dissipative Gross-Pitaevskii model (with the same {\it ab initio} damping). Probing the regime for which $0.8 k_{B}T < μ< 1.6 k_{B}T$, we find average soliton lifetimes to scale with temperature as $τ\sim T^{-4}$, in agreement with predictions previously made for the low-temperature regime $k_{B}T\llμ$. The model is also shown to capture the experimentally-relevant decrease in the visibility of an oscillating soliton due to the presence of background fluctuations.

cond-mat.quant-gas↗

arXiv2011

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.

cond-mat.quant-gas↗

arXiv2011

Multiple dark-bright solitons in atomic Bose-Einstein condensates

We present experimental results and a systematic theoretical analysis of dark-br ight soliton interactions and multiple-dark-bright soliton complexes in atomic t wo-component Bose-Einstein condensates. We study analytically the interactions b etween two-dark-bright solitons in a homogeneous condensate and, then, extend ou r considerations to the presence of the trap. An effective equation of motion is derived for the dark-bright soliton center and the existence and stability of stationary two-dark-bright soliton states is illustrated (with the bright components being either in- or out-of-phase). The equation of motion provides the characteristic oscillation frequencies of the solitons, in good agreement with the eigenfrequencies of the anomalous modes of the system.

cond-mat.quant-gas↗

arXiv2011

Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide

We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{ö}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasi-discrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments.

nlin.PS↗

arXiv2011

Nonlinear Excitations, Stability Inversions and Dissipative Dynamics in Quasi-one-dimensional Polariton Condensates

We consider the existence, stability and dynamics of the ground state and nonlinear excitations, in the form of dark solitons, for a quasi-one-dimensional polariton condensate in the presence of pumping and nonlinear damping. We find a series of remarkable features that can be directly contrasted to the case of the typically energy-conserving ultracold alkali-atom Bose-Einstein condensates. For some sizeable parameter ranges, the nodeless ("ground") state becomes {\it unstable} towards the formation of {\em stable} nonlinear single or {\em multi} dark-soliton excitations. It is also observed that for suitable parametric choices, the instability of single dark solitons can nucleate multi-dark-soliton states. Also, for other parametric regions, {\em stable asymmetric} sawtooth-like solutions exist. Finally, we consider the dragging of a defect through the condensate and the interference of two initially separated condensates, both of which are capable of nucleating dark multi-soliton dynamical states.

cond-mat.quant-gas↗

arXiv2011

Control of the symmetry breaking in double-well potentials by the resonant nonlinearity management

We introduce a one-dimensional model of Bose-Einstein condensates (BECs), combining the double-well potential, which is a well-known setting for the onset of spontaneous-symmetry-breaking (SSB) effects, and time-periodic modulation of the nonlinearity, which may be implemented by means of the Feshbach-resonance-management (FRM) technique. Both cases of the nonlinearity which is repulsive or attractive on the average are considered. In the former case, the main effect produced by the application of the FRM is spontaneous self-trapping of the condensate in either of the two potential wells in parameter regimes where it would remain untrapped in the absence of the management. In the weakly nonlinear regime, the frequency of intrinsic oscillations in the FRM-induced trapped state is very close to half the FRM frequency, suggesting that the effect is accounted for by a parametric resonance. In the case of the attractive nonlinearity, the FRM-induced effect is the opposite, i.e., enforced detrapping of a state which is self-trapped in its unmanaged form. In the latter case, the frequency of oscillations of the untrapped mode is close to a quarter of the driving frequency, suggesting that a higher-order parametric resonance may account for this effect.

cond-mat.quant-gas↗

arXiv2010

Emergence and Stability of Vortex Clusters in Bose-Einstein Condensates: a Bifurcation Approach near the Linear Limit

We study the existence and stability properties of clusters of alternating charge vortices in Bose-Einstein condensates. It is illustrated that such states emerge from cascades of symmetry-breaking bifurcations that can be analytically tracked near the linear limit of the system via weakly nonlinear few-mode expansions. We present the resulting states that emerge near the first few eigenvalues of the linear limit, and illustrate how the nature of the bifurcations can be used to understand their stability. Rectilinear, polygonal and diagonal vortex clusters are only some of the obtained states while mixed states, consisting of dark solitons and vortex clusters, are identified as well.

cond-mat.quant-gas↗

arXiv2010

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.

cond-mat.quant-gas↗

arXiv2010

Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier

We study possibilities to suppress the transverse modulational instability (MI) of dark-soliton stripes in two-dimensional (2D) Bose-Einstein condensates (BECs) and self-defocusing bulk optical waveguides by means of quasi-1D structures. Adding an external repulsive barrier potential (which can be induced in BEC by a laser sheet, or by an embedded plate in optics), we demonstrate that it is possible to reduce the MI wavenumber band, and even render the dark-soliton stripe completely stable. Using this method, we demonstrate the control of the number of vortex pairs nucleated by each spatial period of the modulational perturbation. By means of the perturbation theory, we predict the number of the nucleated vortices per unit length. The analytical results are corroborated by the numerical computation of eigenmodes of small perturbations, as well as by direct simulations of the underlying Gross-Pitaevskii/nonlinear Schrödinger equation.

cond-mat.quant-gas↗

arXiv2010

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.

cond-mat.quant-gas↗

arXiv2010

Effects of Long-Range Nonlinear Interactions in Double-Well Potentials

We consider the interplay of linear double-well-potential (DWP) structures and nonlinear longrange interactions of different types, motivated by applications to nonlinear optics and matter waves. We find that, while the basic spontaneous-symmetry-breaking (SSB) bifurcation structure in the DWP persists in the presence of the long-range interactions, the critical points at which the SSB emerges are sensitive to the range of the nonlocal interaction. We quantify the dynamics by developing a few-mode approximation corresponding to the DWP structure, and analyze the resulting system of ordinary differential equations and its bifurcations in detail. We compare results of this analysis with those produced by the full partial differential equation, finding good agreement between the two approaches. Effects of the competition between the local self-attraction and nonlocal repulsion on the SSB are studied too. A far more complex bifurcation structure involving the possibility for not only supercritical but also subcritical bifurcations and even bifurcation loops is identified in that case.

nlin.PS↗