Quantum entanglement and classical bifurcations in a coupled two-component Bose-Einstein condensate

We investigate the relation between quantum states and classical fixed-point bifurcations in a coupled two-component Bose-Einstein condensate (BEC). It is shown that the classical bifurcations are closely related to a topological change of the corresponding quantum levels, and such a structure change can be manifested in the entanglement properties of the corresponding quantum states. That is, the entanglement of the quantum states displays some peaks near the classical bifurcation points.     

Bifurcations in the growth process of a vortex sheet in rotating superfluid

Vortex-sheet growth is considered. Broken symmetry bifurcations are found in the growth process. The collective elasticity theory for a well-developed vortex sheet is presented, which is similar to that of smectic liquid crystals. The bifurcations in the limit of a much folded vortex sheet correspond to the Helfrich instability in smectics and cholesterics.     

The appearance of gap solitons in a nonlinear Schrödinger lattice

We study the appearance of discrete gap solitons in a nonlinear Schrödinger model with a periodic on-site potential that possesses a gap evacuated of plane-wave solutions in the linear limit. For finite lattices supporting an anti-phase (q=π/2) gap edge phonon as an anharmonic standing wave in the nonlinear regime, gap solitons are numerically found to emerge via pitchfork bifurcations from the gap edge. Analytically, modulational instabilities between pairs of bifurcation points on this “nonlinear gap boundary” are found in terms of critical gap widths, turning to zero in the infinite-size limit, which are associated with the birth of the localized soliton as well as discrete multisolitons in the gap. Such tunable instabilities can be of relevance in exciting soliton states in modulated arrays of nonlinear optical waveguides or Bose-Einstein condensates in periodic potentials. For lattices whose gap edge phonon only asymptotically approaches the anti-phase solution, the nonlinear gap boundary splits in a bifurcation scenario leading to the birth of the discrete gap soliton as a continuable orbit to the gap edge in the linear limit. The instability-induced dynamics of the localized soliton in the gap regime is found to thermalize according to the Gibbsian equilibrium distribution, while the spontaneous formation of persisting intrinsically localized modes (discrete breathers) from the extended out-gap soliton reveals a phase transition of the solution.     

Optical vortex solitons and soliton clusters in photonic crystal fibres

We study higher-order nonlinear modes in the form of vortex solitons and soliton clusters propagating in the waveguides created in photonic crystal fibers made of a material with the focusing Kerr nonlinearity. We find numerically different families of such nonlinear modes with a nontrivial topology and study their bifurcations. We also study the soliton stability to propagation. We demonstrate that waveguides in photonic crystal fibers may support a variety of soliton clusters with the symmetries that may differ from the lattice symmetry. We also discuss briefly the case of a dual-core coupler created by two neighboring cores in a photonic crystal fiber and find numerically the profiles of symmetric and asymmetric nonlinear modes.     

Two-component nonlinear Schrödinger 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.     

Spatial symmetry breaking and coexistence of attractors in a nonlinear ring cavity

We consider a passive optical system consisting of a ring cavity and a homogeneously broadened two-level medium. We find that a spatial modulation of the input beam imposes processes of competition between the external modulation frequency and the internal space frequencies which emerge from modulation instabilities. This leads to symmetry breaking phenomena when both the amplitude and the wavelength of the modulation are increased and results in the coexistence of periodic attractors. We numerically analyze the corresponding bifurcations and find that they can be explained by a generalization of the concept of cooperative frequency locking although the bifurcating attractors are periodic and are not related to linear resonator modes.     

Magnetic bistability of Co nanodots

Size-dependent magnetic single-domain versus vortex state stability of Co/Ru(0001) nanodots is explored with spin-polarized low-energy electron microscopy, analytical modeling, and micromagnetic simulations. We show that both single-domain and vortex states can be stabilized in a broad region near the phase boundary. The calculated width of the bistability region and temperature dependent heights of the energy barriers between both states agree well with our experimental findings.     

An optimal principle in fluid-structure interaction

We study the steady terminal orientation of a fore-aft symmetric body as it settles in a viscous fluid. An optimal principle for the settling behavior is discussed based upon entropy production in the system, both in the Stokes limit and the case of near equilibrium states when inertial effects emerge. We show that in the Stokes limit, the entropy production in the system is zero allowing any possible terminal orientation while in the presence of inertia, the particle assumes a horizontal position which coincides with the state of maximum entropy production. Our results are seen to agree well with experimental observations.     

Chaos and hyperchaos in a gyrotron

We study oscillation in a gyrotron with allowance for reflections from an output horn. Regions with different system behaviors, such as stationary oscillation, self-modulation, and complex-dynamics regimes are found in the parameter plane. The scenarios of appearance of chaotic oscillations are considered. It is shown that they can emerge via either a sequence of period-doubling bifurcations or destruction of quasiperiodic motion. For chaotic attractors, Lyapunov exponents are calculated and their dimensions are estimated on the basis of the Kaplan-Yorke formula. The dimension values turn out to be anomalously large, which is stipulated by the presence of a large number of high-Q eigenmodes in the gyrotron cavity due to operation near the cutoff frequency of an electrodynamic system. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 49, No. 10, pp. 887–899, October 2006.     

幺正极限附近费米气体反常激发模式的涡旋

在幺正极限附近研究了处于旋转外势中费米气体的量子化涡旋动力学. 选取适当的试探波函数并利用含时变分法, 得到了小振幅涡旋运动方程及描述其反常激发模式的解. 详细讨论了在幺正极限附近的反常模式产生的条件. 结果显示系统囚禁外势的临界转动频率在幺正极限附近随粒子间相互作用参数的增加而变大, 而涡旋进动的周期则随着粒子间相互作用参数的增加而减小. 关键词： 费米气体 涡旋 幺正极限     

Vortex induced rotation of clusters of localized states in the complex Ginzburg-Landau equation

We report existence of a qualitatively distinct class of spiral waves in the two-dimensional cubic-quintic complex Ginzburg-Landau equation. These are stable clusters of localized states rotating around a central vortex core emerging due to interference of the tails of the individual states involved. We also develop an asymptotic theory allowing calculation of the angular frequency and stability analysis of the rotating clusters.     

Sequential escapes: onset of slow domino regime via a saddle connection

We explore sequential escape behaviour of coupled bistable systems under the influence of stochastic perturbations. We consider transient escapes from a marginally stable “quiescent” equilibrium to a more stable “active” equilibrium. The presence of coupling introduces dependence between the escape processes: for diffusive coupling there is a strongly coupled limit (fast domino regime) where the escapes are strongly synchronised while for intermediate coupling (slow domino regime) without partially escaped stable states, there is still a delayed effect. These regimes can be associated with bifurcations of equilibria in the low-noise limit. In this paper, we consider a localized form of non-diffusive (i.e. pulse-like) coupling and find similar changes in the distribution of escape times with coupling strength. However, we find transition to a slow domino regime that is not associated with any bifurcations of equilibria. We show that this transition can be understood as a codimension-one saddle connection bifurcation for the low-noise limit. At transition, the most likely escape path from one attractor hits the escape saddle from the basin of another partially escaped attractor. After this bifurcation, we find increasing coefficient of variation of the subsequent escape times.     

Spatially Periodic Inhomogeneous States in a Nonlinear Crystal with a Nonlinear Defect

Spatially periodic inhomogeneous stationary states are shown to exist near a thin defect layer with nonlinear properties separating nonlinear Kerr-type crystals. The contacts of nonlinear self-focusing and defocusing crystals have been analyzed. The spatial field distribution obeys a time-independent nonlinear Schrödinger equation with a nonlinear (relative to the field) potential modeling the thin defect layer with nonlinear properties. Both symmetric and asymmetric states relative to the defect plane are shown to exist. It has been established that new states emerge in a self-focusing crystal, whose existence is attributable to the defect nonlinearity and which do not emerge in the case of a linear defect. The dispersion relations defining the energy of spatially periodic inhomogeneous stationary states have been derived. The expressions for the energies of such states have been derived in an explicit analytical form in special cases. The conditions for the existence of periodic states and their localization, depending on the defect and medium characteristics, have been determined.     

Role of the Majorana fermion and the edge mode in chiral superfluidity near a p-wave Feshbach resonance

The visualization of chiral p-wave superfluidity in Fermi gases near p-wave Feshbach resonances is theoretically examined. It is proposed that the superfluidity becomes detectable in the entire BCS-BEC regimes through (i) vortex visualization by the density depletion inside the vortex core and (ii) intrinsic angular momentum in vortex-free states. It is revealed that both (i) and (ii) are closely connected with the Majorana zero energy mode of the vortex core and the edge mode, which survive until the strong coupling BCS regime is approached from the weak coupling limit and vanish in the Bose-Einstein condensation regime.     

Multistable solitons in higher-dimensional cubic-quintic nonlinear Schrödinger lattices

We study the existence, stability, and mobility of fundamental discrete solitons in two- and three-dimensional nonlinear Schrödinger 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 defined Peierls-Nabarro barrier; however, they eventually come to a halt, due to radiation loss.     

Resonant two-magnon Raman scattering and photoexcited States in two-dimensional mott insulators

We investigate the resonant two-magnon Raman scattering in two-dimensional (2D) Mott insulators by using a half-filled 2D Hubbard model in the strong coupling limit. By performing numerical diagonalization calculations for small clusters, we find that the Raman intensity is enhanced when the incoming photon energy is not near the optical absorption edge but well above it, being consistent with experimental data. The absence of resonance near the gap edge is associated with the presence of background spins, while photoexcited states for resonance are found to be characterized by the charge degree of freedom. The resonance mechanism is different from those proposed previously.     

Vortex-core structure in neutral fermion superfluids with population imbalance

Quantized vortex-core structure is theoretically investigated in fermion superfluids with population imbalance for two atom species of neutral atom clouds near a Feshbach resonance. In contrast with the vortex core in balance case where the quantum depletion makes a vortex visible through the density profile measurement, the vortex core is filled in and becomes less visible because the quantized discrete bound states are occupied exclusively by the majority species. Yet it is shown that the core can be visible through the minority density profile experiment using phase contrast imaging, revealing an interesting opportunity to examine low-lying fermionic core bound states unexplored so far.     

Solitary coherent structures in viscoelastic shear flow: computation and mechanism

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed "diwhirl" patterns. Based on the computed velocity and stress fields, we elucidate a heuristic, fully nonlinear mechanism for these flows. We propose that these localized, fully nonlinear structures comprise fundamental building blocks for complex spatiotemporal dynamics in the flow of elastic liquids.     

Rotating optical soliton clusters

We introduce the concept of soliton clusters--multisoliton bound states in a homogeneous bulk optical medium--and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.     

Non-Abelian vortex in four dimensions as a critical superstring

We discuss recent progress in describing a certain non-Abelian vortex string as a critical superstring on a conifold and clarify some subtle points. This particular solitonic vortex is supported in four-dimensional supersymmetric QCD with the gauge group, N _f = 4 quark flavors and the Fayet–Iliopoulos term. Under certain conditions, the non-Abelian vortex can become infinitely thin and can be interpreted as a critical ten-dimensional superstring. In addition to four translational moduli, the non-Abelian vortex under consideration carries six orientational and size moduli. The vortex moduli dynamics are described by a twodimensional sigma model with the target space ?⁴ × Y ₆, where Y ₆ is a non-compact Calabi–Yau conifold. The closed string states that emerge in four dimensions (4D) are identified with hadrons of 4D bulk N= 2 QCD. It turns out that most of the states arising from the ten-dimensional graviton spectrum are non-dynamical in 4D. A single dynamical massless hypermultiplet associated with the deformation of the complex structure of the conifold is found. It is interpreted as a monopole–monopole baryon of the 4D theory (at strong coupling).