arXiv subjects

Marek Trippenbach

Publications and source records attributed to Marek Trippenbach.

At least 37 records · Page 2Linked to original sources

arXiv2014

Stabilization of solitons under competing nonlinearities by external potentials

We report results of the analysis for families of one-dimensional (1D) trapped solitons, created by competing self-focusing (SF) quintic and self-defocusing (SDF) cubic nonlinear terms. Two trapping potentials are considered, the harmonic-oscillator (HO) and delta-functional ones. The models apply to optical solitons in colloidal waveguides and other photonic media, and to matter-wave solitons in Bose-Einstein condensates (BEC) loaded into a quasi-1D trap. For the HO potential, the results are obtained in an approximate form, using the variational and Thomas-Fermi approximations (VA and TFA), and in a full numerical form, including the ground state and the first antisymmetric excited one. For the delta-functional attractive potential, the results are produced in a fully analytical form, and verified by means of numerical methods. Both exponentially localized solitons and weakly localized trapped modes are found for the delta-functional potential. The most essential conclusions concern the applicability of competing Vakhitov-Kolokolov (VK) and anti-VK criteria to the identification of the stability of solitons created under the action of the competing SF and SDF terms.

nlin.PS↗

arXiv2014

Spatial control of the competition between self-focusing and self-defocusing nonlinearities in one- and two-dimensional systems

We introduce a system with competing self-focusing (SF) and self-defocusing (SDF) terms, which have the same scaling dimension. In the one-dimensional (1D) system, this setting is provided by a combination of the SF cubic term multiplied by the delta-function, $δ(x)$, and a spatially uniform SDF quintic term. This system gives rise to the most general family of 1D-Townes solitons, the entire family being unstable. However, it is completely stabilized by a finite-width regularization of the $δ$-function. The results are produced by means of numerical and analytical methods. We also consider the system with a symmetric pair of regularized $δ$-functions, which gives rise to a wealth of symmetric, antisymmetric, and asymmetric solitons, linked by a bifurcation loop, that accounts for the breaking and restoration of the symmetry. Soliton families in 2D versions of both the single- and double-delta-functional systems are also studied. The 1D and 2D settings may be realized for spatial solitons in optics, and in Bose-Einstein condensates.

physics.optics↗

arXiv2014

A class of compact entities in three component Bose - Einstein condensates

We introduce a new class of soliton-like entities in spinor three component BECs. These entities generalize well known solitons. For special values of coupling constants, the system considered is Completely Integrable and supports $N$ soliton solutions. The one-soliton solutions can be generalized to systems with different values of coupling constants. However, they no longer interact elastically. When two so generalized solitons collide, a spin component oscillation is observed in both emerging entities. We propose to call these newly found entities oscillatons. They propagate without dispersion and retain their character after collisions. We derived an exact mathematical model for oscillatons and showed that the well known one soliton solutions are a particular case.

cond-mat.quant-gas↗

arXiv2012

An extended representation of three spin component Bose Einstein Condensate solitons

We consider a three spin component Bose Einstein Condensate as described by as many coupled nonlinear Schroedinger equations. For a very special ratio of the coupling constants, exact N soliton solutions to this set of equations are known. Here we find a simple representation including the N = 1 solution based on the symmetry of the equations. This symmetry is described by a linear operator, the nonlinearity of NLS notwithstanding. Our useful representation opens the door to the nonintegrable case of general coupling constants. A new class of solutions is found.

cond-mat.quant-gas↗

arXiv2012

Cold and trapped metastable noble gases

We review experimental and theoretical work on cold, trapped metastable noble gases. We em- phasize the aspects which distinguish work with these atoms from the large body of work on cold, trapped atoms in general. These aspects include detection techniques and collision processes unique to metastable atoms. We describe several experiments exploiting these unique features in fields including atom optics and statistical physics. We also discuss precision measurements on these atoms including fine structure splittings, isotope shifts, and atomic lifetimes.

quant-ph↗

arXiv2011

Symmetric and asymmetric solitons trapped in H-shaped potentials

We report results of numerical and analytical studies of the spontaneous symmetry breaking in solitons, both two- and one-dimensional, which are trapped in H-shaped potential profiles, built of two parallel potential troughs linked by a narrow rung in the transverse direction. This system can be implemented in self-attractive Bose-Einstein condensates (BECs), as well as in a nonlinear bulk optical waveguide.We demonstrate that the introduction of the transverse link changes the character of the symmetry-breaking bifurcation (SBB) in the system from subcritical to supercritical (in terms of the corresponding phase transition, it is a change between the first and second kinds). A noteworthy feature of the SBB in this setting is a non-monotonous dependence of the soliton's norm at the bifurcation point on the strength of the transverse link. In the full 2D system, the results are obtained in a numerical form. An exact analytical solution is found for the bifurcation in the 1D version of the model, with the transverse rung modeled by the local linear coupling between the parallel troughs with the Delta-functional longitudinal profile. Replacing the Delta-function by its finite-width Gaussian counterpart, similar results are obtained by means of the variational approximation (VA). The VA is also applied to the 1D system with a mixed linear and nonlinear transverse localized coupling. Comparison of the results produced by the different varieties of the system clearly reveals basic features of the symmetry-breaking transition in it.

cond-mat.quant-gas↗

arXiv2010

Revivals in the attractive BEC in a double-well potential and their decoherence

We study the dynamics of ultracold attractive atoms in a weakly linked two potential wells. We consider an unbalanced initial state and monitor dynamics of the population difference between the two wells. The average imbalance between wells undergoes damped oscillations, like in a classical counterpart, but then it revives almost to the initial value. We explain in details the whole behavior using three different models of the system. Furthermore we investigate the sensitivity of the revivals on the decoherence caused by one- and three-body losses. We include the dissipative processes using appropriate master equations and solve them using the stochastic wave approximation method.

cond-mat.quant-gas↗

arXiv2010

Oscillating solitons in a three component BEC

We investigate the properties of three component BEC systems with spin exchange interactions. We consider different coupling constants from those leading to exact solutions known in the literature. When two solitons collide, an oscillation of the emerging entities is observed. This behavior seems to be generic. A mathematical model is derived for the emerging solitons. It describes the new oscillatory phenomenon extremely well. Surprisingly, the model is exact as a solution to the initial equations. This comes as a bonus.

cond-mat.quant-gas↗

arXiv2010

Two - dimensional solitons in media with the stripe - shaped nonlinearity modulation

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. In recent works, it was concluded that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. The double stripe with the rectangular profile admit stable solitons of three distinct types: symmetric and asymmetric ones with a single peak, and double-peak symmetric solitons. The shape and stability of single-peak solitons of either type are accurately predicted by the VA. Collisions between stable solitons are briefly considered too, by means of direct simulations. Depending on the relative velocity we observe excitation, decay or catastrophic self focusing.

nlin.PS↗

arXiv2010

Spontaneous Four-Wave Mixing of de Broglie Waves: Beyond Optics

We investigate the atom-optical analog of degenerate four-wave mixing of photons by colliding two Bose-Einstein condensates (BECs) of metastable helium and measuring the resulting momentum distribution of the scattered atoms with a time and space resolved detector. For the case of photons, phase matching conditions completely define the final state of the system, and in the case of two colliding BECs, simple analogy implies a spherical momentum distribution of scattered atoms. We find, however, that the final momenta of the scattered atoms instead lie on an ellipsoid whose radii are smaller than the initial collision momentum. Numerical and analytical calculations agree well with the measurements, and reveal the interplay between many-body effects, mean-field interaction, and the anisotropy of the source condensate.

cond-mat.quant-gas↗

arXiv2009

Thermal effects in light scattering from ultracold bosons in an optical lattice

We study the scattering of a weak and far-detuned light from a system of ultracold bosons in 1D and 3D optical lattices. We show the connection between angular distributions of the scattered light and statistical properties of a Bose gas in a periodic potential. The angular patterns are determined by the Fourier transform of the second-order correlation function, and thus they can be used to retrieve information on particle number fluctuations and correlations. We consider superfluid and Mott insulator phases of the Bose gas in a lattice, and we analyze in detail how the scattering depends on the system dimensionality, temperature and atom-atom interactions.

cond-mat.quant-gas↗

arXiv2008

Matter wave soliton collisions in the quasi one dimensional potential

We consider soliton solutions of a two-dimensional nonlinear system with the self-focusing nonlinearity and a quasi-1D confining potential, taking harmonic potential as an example. We investigate a single soliton in detail and find criterion for possible collapse. This information is then used to investigate the dynamics of the two soliton collision. In this dynamics we identify three regimes according to the relation between nonlinear interaction and the excitation energy: elastic collision, excitation and collapse regime. We show that surprisingly accurate predictions can be obtained from variational analysis.

nlin.PS↗

arXiv2007

Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice

We consider effects of inter-species attraction on two-component gap solitons (GSs) in the binary BEC with intra-species repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations (GPEs) corroborate an assumption that, because the effective mass of GSs is negative, the inter-species attraction may \emph{split} the two-component soliton. Two critical values, $κ_{1} $ and $κ_{2}$, of the OL strength ($κ$) are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices ($κ>κ_{1}$). In an intermediate region, $κ_{1}>κ>κ_{2}$, the soliton splits into a double-humped state with separated components. Finally, in weak lattices ($κ<κ_{2}$%), the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of $κ_{1}$ and $κ_{2}$ on thenumber of atoms (total norm), and on the relative strength of the competing inter-species attraction and intra-species repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry.

cond-mat.other↗

arXiv2006

Simple and efficient generation of gap solitons in Bose-Einstein condensates

We suggest an efficient method for generating matter-wave gap solitons in a repulsive Bose-Einstein condensate, when the gap soliton is formed from a condensate cloud in a harmonic trap after turning on a one-dimensional optical lattice. We demonstrate numerically that this approach does not require preparing the initial atomic wave packet in a specific state corresponding to the edge of the Brillouin zone of the spectrum, and losses that occur during the soliton generation process can be suppressed by an appropriate adiabatic switching of the optical lattice.

nlin.PS↗

arXiv2005

Elastic scattering losses from colliding BEC's

Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently Ziń {\it et al.} (Phys. Rev. Lett. {\bf 94}, 200401 (2005)) have introduced a model of two counter-propagating atomic Gaussian wavepackets incorporating dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first order approximation we derive analytical expressions for the density matrix and anomalous density which provides excellent insight into correlation properties of scattered atoms.

cond-mat.other↗

arXiv2005

Crossover from self-defocusing to discrete trapping in nonlinear waveguide arrays

We predict a sharp crossover from nonlinear self-defocusing to discrete self-trapping of a narrow Gaussian beam with the increase of the refractive index contrast in a periodic photonic lattice. We demonstrate experimentally nonlinear discrete localization of light with defocusing nonlinearity by single site excitation in LiNbO$_3$ waveguide arrays.

nlin.PS↗

arXiv2003

Highly Nonlinear Dynamics of Third-Harmonic Generation by Focused Beams

Beams that experience third-harmonic generation (THG) also experience Kerr effects. With Kerr effects, beams do not take simple Gaussian shapes, but exhibit nonlinear dynamics. These nonlinear dynamics have an effect on the THG accumulated by focusing and then diverging beams. We formulate a self-consistent and complete set of nonlinear Schroedinger equations for a pair of coupled beams -- a fundamental and its third-harmonic. Numerical simulations show that the Kerr nonlinearities allow some third-harmonic to propagate to the far-field even for zero or negative phase-mismatch. This is because the nonlinear dynamics break the beams' reflection symmetry about the focal plane and therefore increases far-field THG by changing some of the interference from destructive to constructive. THG conversion efficiencies are computed as functions of several beam parameters.

physics.optics↗

arXiv2002

Spontaneous emission of atoms via collisions of Bose-Einstein condensates

The widely used Gross-Pitaevskii equation treats only coherent aspects of the evolution of a Bose-Einstein condensate. However, inevitably some atoms scatter out of the condensate. We have developed a method, based on the field theory formulation, describing the dynamics of incoherent processes which are due to elastic collisions. We can therefore treat processes of spontaneous emission of atoms into the empty modes, as opposed to stimulated processes, which require non-zero initial occupation. In this article we study two counter-propagating plane waves of atoms, calculating the full dynamics of mode occupation, as well as the statistics of scattered atoms. The more realistic case of Gaussian wavepackets is also analyzed.

cond-mat↗