arXiv subjects

Boris A. Malomed

Publications and source records attributed to Boris A. Malomed.

At least 505 records · Page 28Linked to original sources

arXiv2007

Spontaneous soliton symmetry breaking in two-dimensional coupled Bose-Einstein condensates supported by optical lattices

Models of two-dimensional (2D) traps, with the double-well structure in the third direction, for Bose-Einstein condensate (BEC) are introduced, with attractive or repulsive interactions between atoms. The models are based on systems of linearly coupled 2D Gross-Pitaevskii equations (GPEs), where the coupling accounts for tunneling between the wells. Each well carries an optical lattice (OL) (stable 2D solitons cannot exist without OLs). The main subject of the work is spontaneous symmetry breaking (SSB) in two-component 2D solitons and localized vortices. We demonstrate that, in the system with attraction or repulsion, SSB occurs in families of symmetric or antisymmetric solitons (or vortices), respectively. The corresponding bifurcation destabilizes the original solution branch and gives rise to a stable branch of asymmetric solitons or vortices. In the model with attraction, all stable branches eventually terminate due to the onset of collapse. Stable asymmetric solitons in higher finite bandgaps, and vortices with a multiple topological charge are found too. The models also give rise to first examples of \textit{embedded solitons%} and \textit{embedded vortices}(the states located inside Bloch bands) in two dimensions. In the linearly-coupled system with opposite signs of the nonlinearity in the two cores, two distinct types of stable solitons and vortices are found, dominated by either the self-attractive component or the self-repulsive one. In the system with a mismatch between the two OLs, a \textit{pseudo-bifurcation} is found: when the mismatch attains its largest value ($π$), the bifurcation does not happen, as branches of different solutions asymptotically approach each other but fail to merge.

nlin.PS↗

arXiv2007

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of ``gap-acoustic'' solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.

nlin.PS↗

arXiv2007

Guiding-center solitons in rotating potentials

We demonstrate that rotating quasi-one-dimensional potentials, periodic or parabolic, support solitons in settings where they are otherwise impossible. Ground-state and vortex solitons are found in defocusing media, if the rotation frequency exceeds a critical value. The revolving periodic potentials exhibit the strongest stabilization capacity at a finite optimum value of their strength, while the rotating parabolic trap features a very sharp transition to stability with the increase of rotation frequency.

physics.optics↗

arXiv2007

Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices

We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps, equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling. Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral bandgaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bi-stability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. The impact of a phase mismatch, between the OLs in the two cores is also studied. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing different spin states of the same atom) are coupled by linear interconversion. In that case, the symmetry-breaking bifurcations in the AA and RR models switch their character, if the inter-species nonlinear interaction becomes stronger than the intra-species nonlinearity.

nlin.PS↗

arXiv2007

Three-dimensional vortex solitons in self-defocusing media

We demonstrate that families of vortex solitons are possible in a bi-dispersive three-dimensional nonlinear Schrodinger equation. These solutions can be considered as extensions of two-dimensional dark vortex solitons which, along the third dimension, remain localized due to the interplay between dispersion and nonlinearity. Such vortex solitons can be observed in optical media with normal dispersion, normal diffraction, and defocusing nonlinearity.

nlin.PS↗

arXiv2007

Modulated Amplitude Waves in Collisionally Inhomogeneous Bose-Einstein Condensates

We investigate the dynamics of an effectively one-dimensional Bose-Einstein condensate (BEC) with scattering length $a$ subjected to a spatially periodic modulation, $a=a(x)=a(x+L)$. This "collisionally inhomogeneous" BEC is described by a Gross-Pitaevskii (GP) equation whose nonlinearity coefficient is a periodic function of $x$. We transform this equation into a GP equation with constant coefficient $a$ and an additional effective potential and study a class of extended wave solutions of the transformed equation. For weak underlying inhomogeneity, the effective potential takes a form resembling a superlattice, and the amplitude dynamics of the solutions of the constant-coefficient GP equation obey a nonlinear generalization of the Ince equation. In the small-amplitude limit, we use averaging to construct analytical solutions for modulated amplitude waves (MAWs), whose stability we subsequently examine using both numerical simulations of the original GP equation and fixed-point computations with the MAWs as numerically exact solutions. We show that "on-site" solutions, whose maxima correspond to maxima of $a(x)$, are significantly more stable than their "off-site" counterparts.

nlin.PS↗

arXiv2006

Transitions between symmetric and asymmetric solitons in dual-core systems with cubic-quintic nonlinearity

It is well known that a symmetric soliton in coupled nonlinear Schroedinger (NLS) equations with the cubic nonlinearity loses its stability with the increase of its energy, featuring a transition into an asymmetric soliton via a subcritical bifurcation. A similar phenomenon was found in a dual-core system with quadratic nonlinearity, and in linearly coupled fiber Bragg gratings, with a difference that the symmetry-breaking bifurcation is supercritical in those cases. We aim to study transitions between symmetric and asymmetric solitons in dual-core systems with saturable nonlinearity. We demonstrate that a basic model of this type, viz., a pair of linearly coupled NLS equations with the intra-core cubic-quintic (CQ) nonlinearity, features a bifurcation loop: a symmetric soliton loses its stability via a supercritical bifurcation, which is followed, at a larger value of the energy, by a reverse bifurcation that restores the stability of the symmetric soliton. If the linear-coupling constant is small enough, the second bifurcation is subcritical, and there is a broad interval of energies in which the system is bistable, with coexisting stable symmetric and asymmetric solitons. At larger values of the coupling constant, the reverse bifurcation is supercritical, and the bifurcation loop disappears if the linear coupling is very strong. Collisions between moving solitons are studied too. Symmetric solitons always collide elastically, while collisions between asymmetric solitons turns them into breathers, that subsequently undergo dynamical symmetrization.

nlin.PS↗

arXiv2006

Miscibility in a degenerate fermionic mixture induced by linear coupling

We consider a one-dimensional mean-field-hydrodynamic model of a two-component degenerate Fermi gas in an external trap, each component representing a spin state of the same atom. We demonstrate that the interconversion between them (linear coupling), imposed by a resonant electromagnetic wave, transforms the immiscible binary gas into a miscible state, if the coupling constant, $κ$, exceeds a critical value, $ κ_{\mathrm{cr}}$. The effect is predicted in a variational approximation, and confirmed by numerical solutions. Unlike the recently studied model of a binary BEC with the linear coupling, the components in the immiscible phase of the binary fermion mixture never fill two separated domains with a wall between them, but rather form anti-locked ($π$ -phase-shifted) density waves. Another difference from the bosonic mixture is spontaneous breaking of symmetry between the two components in terms of numbers of atoms in them, $N_{1}$ and $N_{2}$. The latter effect is characterized by the parameter $ν\equiv (N_{1}-N_{2})/(N_{1}+N_{2}) $ (only $N_{1}+N_{2}$ is a conserved quantity), the onset of miscibility at $κ\geq κ_{\mathrm{cr}}$ meaning a transition to $ν\equiv 0$. At $κ<κ_{\mathrm{cr}}$, $ν$ features damped oscillations as a function of $κ$. We also briefly consider an asymmetric model, with a chemical-potential difference between the two components.

cond-mat.soft↗

arXiv2006

Vector solitons in nearly-one-dimensional Bose-Einstein condensates

We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of the variational approximation, starting from the coupled 3D Gross-Pitaevskii equations and assuming, as usual, the factorization of 3D wave functions. The system can be obtained in a tractable form under a natural condition of symmetry between the two species. A family of vector (two-component) soliton solutions is constructed. Collisions between orthogonal solitons (ones belonging to the different components) are investigated by means of simulations. The collisions are essentially inelastic. They result in strong excitation of intrinsic vibrations in the solitons, and create a small orthogonal component ("shadow") in each colliding soliton. The collision may initiate collapse, which depends on the mass and velocities of the solitons.

cond-mat.other↗

arXiv2006

Partially incoherent gap solitons in Bose-Einstein condensates

We construct families of incoherent matter-wave solitons in a repulsive degenerate Bose gas trapped in an optical lattice (OL), i.e., gap solitons, and investigate their stability at zero and finite temperature, using the Hartree-Fock-Bogoliubov equations. The gap solitons are composed of a coherent condensate, and normal and anomalous densities of incoherent vapor co-trapped with the condensate. Both intragap and intergap solitons are constructed, with chemical potentials of the components falling in one or different bandgaps in the OL-induced spectrum. Solitons change gradually with temperature. Families of intragap solitons are completely stable (both in direct simulations, and in terms of eigenvalues of perturbation modes), while the intergap family may have a very small unstable eigenvalue (nevertheless, they feature no instability in direct simulations). Stable higher-order (multi-humped) solitons, and bound complexes of fundamental solitons are found too.

cond-mat.other↗

arXiv2006

An effective potential for one-dimensional matter-wave solitons in an axially inhomogeneous trap

We demonstrate that a tight transverse trap with the local frequency, $% ω_{\perp}$, gradually varying in the longitudinal direction ($x$) induces an effective potential for one-dimensional solitons in a self-attractive Bose-Einstein condensate. An analytical approximation for this potential is derived by means of a variational method. In the lowest approximation, the potential is $N(S+1)ω_{\perp}(x)$, with $N$ the soliton's norm (number of atoms), and $S$ its intrinsic vorticity (if any). The results can be used to devise nonuniform traps helping to control the longitudinal dynamics of the solitons. Numerical verification of the analytical predictions will be presented elsewhere.

cond-mat.soft↗

arXiv2006

Gap solitons in quasiperiodic optical lattices

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three bandgaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.

cond-mat.soft↗

arXiv2006

Deviation from one-dimensionality in stationary properties and collisional dynamics of matter-wave solitons

By means of analytical and numerical methods, we study how the residual three-dimensionality affects dynamics of solitons in an attractive Bose-Einstein condensate loaded into a cigar-shaped trap. Based on an effective 1D Gross-Pitaevskii equation that includes an additional quintic self-focusing term, generated by the tight transverse confinement, we find a family of exact one-soliton solutions and demonstrate stability of the entire family, despite the possibility of collapse in the 1D equation with the quintic self-focusing nonlinearity. Simulating collisions between two solitons in the same setting, we find a critical velocity, $V_{c}$, below which merger of identical in-phase solitons is observed. Dependence of $V_{c} $ on the strength of the transverse confinement and number of atoms in the solitons is predicted by means of the perturbation theory and investigated in direct simulations. Symmetry breaking in collisions of identical solitons with a nonzero phase difference is also shown in simulations and qualitatively explained by means of an analytical approximation.

cond-mat.other↗

arXiv2006

Mobility of Discrete Solitons in Quadratically Nonlinear Media

We study the mobility of solitons in second-harmonic-generating lattices. Contrary to what is known for their cubic counterparts, discrete quadratic solitons are mobile not only in the one-dimensional (1D) setting, but also in two dimensions (2D). We identify parametric regions where an initial kick applied to a soliton leads to three possible outcomes, namely, staying put, persistent motion, or destruction. For the 2D lattice, it is found that, for the solitary waves, the direction along which they can sustain the largest kick and can attain the largest speed is the diagonal. Basic dynamical properties of the discrete solitons are also discussed in the context of an analytical approximation, in terms of an effective Peierls-Nabarro potential in the lattice setting.

nlin.PS↗

arXiv2006

Stable circulation modes in a dual-core matter-wave soliton laser

We consider a model of a matter-wave laser generating a periodic array of solitary-wave pulses. The system, a general version of which was recently proposed in Ref. [5], is composed of two parallel tunnel-coupled cigar-shaped traps (a reservoir and a lasing cavity), solitons being released through a valve at one edge of the cavity. We report a stable lasing mode accounted for by circulations of a narrow soliton in the cavity, which generates an array of strong pulses (with 1,000 - 10,000 atoms in each, the array's duty cycle ~ 30%) when the soliton periodically hits the valve.

nlin.PS↗

arXiv2006

Matter-wave solitons in radially periodic potentials

We investigate two-dimensional (2D) states of Bose-Einstein condensates (BEC) with self-attraction or self-repulsion, trapped in an axially symmetric optical-lattice potential periodic along the radius. Unlike previously studied 2D models with Bessel lattices, no localized states exist in the linear limit of the present model, hence all localized states are truly nonlinear ones. We consider the states trapped in the central potential well, and in remote circular troughs. In both cases, a new species, in the form of \textit{radial gap solitons}, are found in the repulsive model (the gap soliton trapped in a circular trough may additionally support stable dark-soliton pairs). In remote troughs, stable localized states may assume a ring-like shape, or shrink into strongly localized solitons. The existence of stable annular states, both azimuthally uniform and weakly modulated ones, is corroborated by simulations of the corresponding Gross-Pitaevskii equation. Dynamics of strongly localized solitons circulating in the troughs is also studied. While the solitons with sufficiently small velocities are stable, fast solitons gradually decay, due to the leakage of matter into the adjacent trough under the action of the centrifugal force. Collisions between solitons are investigated too. Head-on collisions of in-phase solitons lead to the collapse; $π$-out of phase solitons bounce many times, but eventually merge into a single soliton without collapsing. The proposed setting may also be realized in terms of spatial solitons in photonic-crystal fibers with a radial structure.

cond-mat.other↗

arXiv2006

Vortex stability in nearly two-dimensional Bose-Einstein condensates with attraction

We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity S=1 are stable in a third of their existence region, $0 $ $\allowbreak 0.43N_{\max}^{(S=1)}$, the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full 3D Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio $\sqrt{10}$, the stability interval of the S=1 vortices occupies $\approx 40%$ of their existence region, hence the 2D limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to 2. All vortices with $S\geq 2$ are unstable.

cond-mat.other↗

arXiv2006

Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (non-integrable) model of a spinor (three-component) model of the Bose-Einstein condensate (BEC), based on a system of three nonlinearly coupled Gross-Pitaevskii equations. The stability of the solitons is studied by means of direct simulations, and, in a part, analytically, using linearized equations for small perturbations. Global stability of the solitons is considered by means of the energy comparison. As a result, ground-state and metastable soliton states of the FM and polar types are identified. For the special integrable version of the model, we develop the Darboux transformation (DT). As an application of the DT, analytical solutions are obtained that display full nonlinear evolution of the modulational instability (MI) of a continuous-wave (CW) state seeded by a small spatially periodic perturbation. Additionally, by dint of direct simulations, we demonstrate that solitons of both the polar and FM types, found in the integrable system, are structurally stable, i.e., they are robust under random changes of the relevant nonlinear coefficient in time.

nlin.PS↗