arXiv subjects

B. A. Malomed

Publications and source records attributed to B. A. Malomed.

At least 127 records · Page 7Linked to original sources

arXiv2008

Effects of Axial Vorticity in Elongated Mixtures of Bose-Einstein Condensates

We consider a meniscus between rotating and nonrotating species in the Bose-Einstein condensate (BEC) with repulsive inter-atomic interactions, confined to a pipe-shaped trap. In this setting, we derive a system of coupled one-dimensional (1D) nonpolynomial Schrodinger equations (NPSEs) for two mean-field wave functions. Using these equations, we analyze the phase separation/mixing in the pipe with periodic axial boundary conditions, i.e. in a toroidal configuration. We find that the onset of the mixing, in the form of suction, i.e., filling the empty core in the vortical component by its nonrotating counterpart, crucially depends on the vorticity of the first component, and on the strengths of the inter-atomic interactions.

cond-mat.other↗

arXiv2008

Semi-discrete solitons in arrayed waveguide structures with Kerr nonlinearity

We construct families of optical semi-discrete composite solitons (SDCSs), with one or two independent propagation constants, supported by a planar slab waveguide, XPM-coupled to a periodic array of stripes. Both structures feature the cubic nonlinearity and support intrinsic modes with mutually orthogonal polarizations. We report three species of SDCSs, odd, even, and twisted ones, the first type being stable. Transverse motion of phase-tilted solitons, with potential applications to beam steering, is considered too.

physics.optics↗

arXiv2008

Two-Component Nonlinear Schrodinger Models with a Double-Well Potential

We introduce a model motivated by studies of Bose-Einstein condensates (BECs) trapped in double-well potentials. We assume that a mixture of two hyperfine states of the same atomic species is loaded in such a trap.The analysis is focused on symmetry-breaking bifurcations in the system, starting at the linear limit and gradually increasing the nonlinearity. Depending on values of the chemical potentials of the two species, we find numerous states, as well as symmetry-breaking bifurcations, in addition to those known in the single-component setting. These branches, which include all relevant stationary solutions of the problem, are predicted analytically by means of a two-mode approximation, and confirmed numerically. For unstable branches, outcomes of the instability development are explored in direct simulations.

nlin.PS↗

arXiv2008

Double barrier potentials for matter-wave gap solitons

We investigate collisions of solitons of the gap type, supported by a lattice potential in repulsive Bose-Einstein condensates, with an effective double-barrier potential that resembles a Fabry-Perot cavity. We identify conditions under which the trapping of the entire incident soliton in the cavity is possible. Collisions of the incident soliton with an earlier trapped one are considered too. In the latter case, many outcomes of the collisions are identified, including merging, release of the trapped soliton with or without being replaced by the incoming one, and trapping of both solitons.

cond-mat.other↗

arXiv2008

Multistable Solitons in Higher-Dimensional Cubic-Quintic Nonlinear Schroedinger Lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schroedinger lattices with a combination of cubic self-focusing and quintic self-defocusing onsite nonlinearities. Several species of stationary solutions are constructed, and bifurcations linking their families are investigated using parameter continuation starting from the anti-continuum limit, and also with the help of a variational approximation. In particular, a species of hybrid solitons, intermediate between the site- and bond-centered types of the localized states (with no counterpart in the 1D model), is analyzed in 2D and 3D lattices. We also discuss the mobility of multi-dimensional discrete solitons that can be set in motion by lending them kinetic energy exceeding the appropriately crafted Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.

nlin.PS↗

arXiv2008

Trapping of two-component matter-wave solitons by mismatched optical lattices

We consider a one-dimensional model of a two-component Bose-Einstein condensate in the presence of periodic external potentials of opposite signs, acting on the two species. The interaction between the species is attractive, while intra-species interactions may be attractive too [the system of the right-bright (BB) type], or of opposite signs in the two components [the gap-bright (GB) model]. We identify the existence and stability domains for soliton complexes of the BB and GB types. The evolution of unstable solitons leads to the establishment of oscillatory states. The increase of the strength of the nonlinear attraction between the species results in symbiotic stabilization of the complexes, despite the fact that one component is centered around a local maximum of the respective periodic potential.

nlin.PS↗

arXiv2008

Tightly bound gap solitons in a Fermi gas

Within the framework of the mean-field-hydrodynamic model of a degenerate Fermi gas (DFG), we study, by means of numerical methods and variational approximation (VA), the formation of fundamental gap solitons (FGSs) in a DFG (or in a BCS superfluid generated by weak interaction between spin-up and spin-down fermions), which is trapped in a periodic optical-lattice (OL) potential. An effectively one-dimensional (1D) configuration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG (which amounts to the known quintic equation for the Tonks-Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL-induced spectrum (unless they are very close to edges of the gaps) feature a tightly-bound shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly-bound subfundamental solitons (SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of $\sim 10^4 - 10^5$ atoms, can be created by available experimental techniques in the DFG of $^6$Li atoms.

cond-mat.other↗

arXiv2008

Spontaneous symmetry breaking of gap solitons in double-well traps

We introduce a two dimensional model for the Bose-Einstein condensate with both attractive and repulsive nonlinearities. We assume a combination of a double well potential in one direction, and an optical lattice along the perpendicular coordinate. We look for dual core solitons in this model, focusing on their symmetry-breaking bifurcations. The analysis employs a variational approximation, which is verified by numerical results. The bifurcation which transforms antisymmetric gap solitons into asymmetric ones is of supercritical type in the case of repulsion; in the attraction model, increase of the optical latttice strength leads to a gradual transition from subcritical bifurcation (for symmetric solitons) to a supercritical one.

cond-mat.other↗

arXiv2007

Anisotropic solitons in dipolar Bose-Einstein Condensates

Starting with a Gaussian variational ansatz, we predict anisotropic bright solitons in quasi-2D Bose-Einstein condensates consisting of atoms with dipole moments polarized \emph{perpendicular} to the confinement direction. Unlike isotropic solitons predicted for the moments aligned with the confinement axis [Phys. Rev. Lett. \textbf{95}, 200404 (2005)], no sign reversal of the dipole-dipole interaction is necessary to support the solitons. Direct 3D simulations confirm their stability.

cond-mat.other↗

arXiv2007

Bright-Dark Soliton Complexes in Spinor Bose-Einstein Condensates

We present bright-dark vector solitons in quasi-one-dimensional spinor (F=1) Bose-Einstein condensates. Using a multiscale expansion technique, we reduce the corresponding nonintegrable system of three coupled Gross-Pitaevskii equations (GPEs) to a completely integrable Yajima-Oikawa system. In this way, we obtain approximate solutions for small-amplitude vector solitons of dark-dark-bright and bright-bright-dark types, in terms of the $m_{F}=+1,-1,0$ spinor components, respectively. By means of numerical simulations of the full GPE system, we demonstrate that these states indeed feature soliton properties, i.e., they propagate undistorted and undergo quasi-elastic collisions. It is also shown that, in the presence of a parabolic trap of strength $ω$, the bright component(s) is (are) guided by the dark one(s), and, as a result, the small-amplitude vector soliton as a whole performs harmonic oscillations of frequency $ω/ \sqrt{2}$ in the shallow soliton limit. We investigate numerically deviations from this prediction, as the depth of the solitons is increased, as well as when the strength of the spin-dependent interaction is modified.

cond-mat.other↗

arXiv2007

Two-dimensional discrete solitons in rotating lattices

We introduce a two-dimensional (2D) discrete nonlinear Schrödinger (DNLS) equation with self-attractive cubic nonlinearity in a rotating reference frame. The model applies to a Bose-Einstein condensate stirred by a rotating strong optical lattice, or light propagation in a twisted bundle of nonlinear fibers. Two species of localized states are constructed: off-axis fundamental solitons (FSs), placed at distance $R$ from the rotation pivot, and on-axis (R=0) vortex solitons (VSs), with vorticities $% S=1$ and 2. At a fixed value of rotation frequency $Ω$, a stability interval for the FSs is found in terms of the lattice coupling constant $C$, $% 0<C<C_{\mathrm{cr}}(R)$, with monotonically decreasing $C_{\mathrm{cr}}(R)$. VSs with S=1 have a stability interval, $\tilde{C}_{\mathrm{cr}%}^{(S=1)}(Ω)<C<C_{\mathrm{cr}}^{(S=1)}(Ω)$, which exists for $% Ω$ below a certain critical value, $Ω_{\mathrm{cr}}^{(S=1)}$. This implies that the VSs with S=1 are \emph{destabilized} in the weak-coupling limit by the rotation. On the contrary, VSs with S=2, that are known to be unstable in the standard DNLS equation, with $Ω=0$, are \emph{stabilized} by the rotation in region $0<C<C_{\mathrm{cr}}^{(S=2)}$%, with $C_{\mathrm{cr}}^{(S=2)}$ growing as a function of $Ω$. Quadrupole and octupole on-axis solitons are considered too, their stability regions being weakly affected by $Ω\neq 0$.

nlin.PS↗

arXiv2007

Bose-Einstein condensates under a spatially-modulated transverse confinement

We derive an effective nonpolynomial Schrodinger equation (NPSE) for self-repulsive or attractive BEC in the nearly-1D cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. Besides the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form (using both the effective NPSE and the full 3D Gross-Pitaevskii equation) and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.

cond-mat.other↗

arXiv2007

Polarized States and Domain Walls in Spinor Bose-Einstein Condensates

We study spin-polarized states and their stability in anti-ferromagnetic states of spinor (F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including: patterns of the Thomas-Fermi type; structures with a pulse-shape in one component inducing a hole in the other components; states with holes in all three components; and domain walls. A Bogoliubov-de Gennes analysis reveals that families of these states contain intervals of a weak oscillatory instability, except for the domain walls, which are always stable. The development of the instabilities is examined by means of direct numerical simulations.

cond-mat.other↗

arXiv2007

Symmetry Breaking in Linearly Coupled Dynamical Lattices

We examine one- and two-dimensional (1D and 2D) models of linearly coupled lattices of the discrete-nonlinear-Schr{ö}dinger type. Analyzing ground states of the systems with equal powers in the two components, we find a symmetry-breaking phenomenon beyond a critical value of the squared $l^2$-norm. Asymmetric states, with unequal powers in their components, emerge through a subcritical pitchfork bifurcation, which, for very weakly coupled lattices, changes into a supercritical one. We identify the stability of various solution branches. Dynamical manifestations of the symmetry breaking are studied by simulating the evolution of the unstable branches. The results present the first example of spontaneous symmetry breaking in 2D lattice solitons. This feature has no counterpart in the continuum limit, because of the collapse instability in the latter case.

nlin.PS↗

arXiv2007

Spontaneous symmetry breaking of solitons trapped in a double-channel potential

We consider a two-dimensional (2D) nonlinear Schrodinger equation with self-focusing nonlinearity and a quasi-1D double-channel potential, i.e., a straightforward 2D extension of the well-known double-well potential. The model may be realized in terms of nonlinear optics and Bose-Einstein condensates. The variational approximation (VA) predicts a bifurcation breaking the symmetry of 2D solitons trapped in the double channel, the bifurcation being of the subcritical type. The predictions of the VA are confirmed by numerical simulations. The work presents the first example of the spontaneous symmetry breaking (SSB) of 2D solitons in any dual-core system.

nlin.PS↗

arXiv2007

Nearly-one-dimensional self-attractive Bose-Einstein condensates in optical lattices

Within the framework of the mean-field description, we investigate atomic Bose-Einstein condensates (BECs), with attraction between atoms, under the action of strong transverse confinement and periodic (optical-lattice, OL) axial potential. Using a combination of the variational approximation (VA), one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE), and direct numerical solutions of the underlying 3D Gross-Pitaevskii equation (GPE), we show that the ground state of the condensate is a soliton belonging to the semi-infinite bandgap of the periodic potential. The soliton may be confined to a single cell of the lattice, or extend to several cells, depending on the effective self-attraction strength, $g$ (which is proportional to the number of atoms bound in the soliton), and depth of the potential, $V_{0}$, the increase of $V_{0}$ leading to strong compression of the soliton. We demonstrate that the OL is an effective tool to control the soliton's shape. It is found that, due to the 3D character of the underlying setting, the ground-state soliton collapses at a critical value of the strength, $g=g_{c}$, which gradually decreases with the increase of the depth of the periodic potential, $V_{0}$; under typical experimental conditions, the corresponding maximum number of $^{7}$Li atoms in the soliton, $N_{\max}$, ranges between $8,000$ and $4,000$. Examples of stable multi-peaked solitons are also found in the first finite bandgap of the lattice spectrum. The respective critical value $g_{c}$ again slowly decreases with the increase of $V_{0}$, corresponding to $N_{\max }\simeq 5,000$.

cond-mat.other↗

arXiv2007

Cerenkov-like radiation in a binary Schr{ö}dinger flow past an obstacle

We consider the dynamics of two coupled miscible Bose-Einstein condensates, when an obstacle is dragged through them. The existence of two different speeds of sound provides the possibility for three dynamical regimes: when both components are subcritical, we do not observe nucleation of coherent structures; when both components are supercritical they both form dark solitons in one dimension (1D) and vortices or rotating vortex dipoles in two dimensions (2D); in the intermediate regime, we observe the nucleation of a structure in the form of a dark-antidark soliton in 1D; subcritical component; the 2D analog of such a structure, a vortex-lump, is also observed.

cond-mat.soft↗

arXiv2006

Mismatch management for optical and matter-wave quadratic solitons

We propose a way to control solitons in $χ^{(2)}$ (quadratically-nonlinear) systems by means of periodic modulation imposed on the phase-mismatch parameter ("mismatch management", MM). It may be realized in the co-transmission of fundamental-frequency (FF) and second-harmonic (SH) waves in a planar optical waveguide via a long-period modulation of the usual quasi-phase-matching pattern of ferroelectric domains. The MM may also be implemented by dint of the Feshbach resonance in a harmonically-modulated magnetic field in a hybrid atomic-molecular Bose-Einstein condensate (BEC), with the atomic and molecular mean fields (MFs) playing the roles of the FF and SH, respectively. The problem is analyzed by two methods. First, we identify stability regions for spatial solitons in the MM system, in terms of the MM amplitude and period, using the MF equations for spatially-inhomogeneous configurations. In particular, an instability enclave is found inside the stability area.The robustness of the solitons is also tested against variation of the shape of the input pulse, and a threshold for the formation of stable solitons is found in terms of its power. Interactions between solitons are virtually unaffected by the MM. The second method (\textit{parametric approximation}), going beyond the MF description, is developed for spatially-homogeneous states. It demonstrates that the MF description is valid for large modulation periods, while at smaller periods the non-MF component acquires gain, which implies destruction of MF under the action of the high-frequency MM.

physics.optics↗