Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Determination of surface properties by means of large signal photovoltage pulses and the influence of trapping

Large signal photovoltage pulses, measured on real surfaces of high-resistivity p-type silicon as a function of excitation intensity and induced charge, show characteristic features, especially smooth minima in the negative pulses. It is shown how the results can be used for a determination of surface potentials (band bendings) and surface- or interface-state distributions. Comparisons between theoretically and experimentally determined photovoltages show that the exchange of charge carriers between surface states and space charge layer during electron-hole nonequilibrium was not negligible and has to be taken into account for an accurate determination of surface potentials. The influence of such trapping processes is analysed graphically and analytically for continuously distributed surface states and the modifications due to trapping are determined. It is shown that the bands become asymptotically flat for the limit of large excitation even when strong trapping in a system of continuously distributed surface states with arbitrarily large concentrations prevails.     

Localized nonlinear vector matter waves in two-component Bose–Einstein condensates with spatially modulated nonlinearities

Exact localized nonlinear vector matter waves in the form of soliton–soliton and vortex–vortex pairs in two-component Bose–Einstein condensates with spatially modulated nonlinearity coefficients and harmonic trapping potentials are reported. It is shown that there exists an infinite number of exact vector pairs sharing the same chemical potential with soliton–soliton ones for odd integer n while vortex–vortex ones for even integer n  . The stability of the vector pairs found is investigated by means of direct numerical simulations and a linear stability analysis; the results show that the stable vortex–vortex pairs (±l,±l)$(\pm l,\pm l)$ with large topological charges can be supported by the spatially modulated interaction when the harmonic trapping potential is presented in this system.     

Energy bounds of linked vortex states

Energy bounds of knotted and linked vortex states in a charged two-component system are considered. It is shown that a set of local minima of free energy contains new classes of universality. When the mutual linking number of vector order parameter of vortex lines is less than the Hopf invariant, these states have lower lying energies.     

Photon-photon gates in Bose-Einstein condensates

It has recently been shown that light can be stored in Bose-Einstein condensates for over a second. Here we propose a method for realizing a controlled phase gate between two stored photons. The photons are both stored in the ground state of the effective trapping potential inside the condensate. The collision-induced interaction is enhanced by adiabatically increasing the trapping frequency and by using a Feshbach resonance. A controlled phase shift of π can be achieved in 1 s or less.     

Dynamical creation of fractionalized vortices and vortex lattices

We investigate the dynamic creation of fractionalized half-quantum vortices in Bose-Einstein condensates of sodium atoms. Our simulations show that both individual half-quantum vortices and vortex lattices can be created in rotating optical traps when additional pulsed magnetic trapping potentials are applied. We also find that a distinct periodically modulated spin-density-wave spatial structure is always embedded in square half-quantum vortex lattices. This structure can be conveniently probed by taking absorption images of ballistically expanding cold atoms in a Stern-Gerlach field.     

Topological excitations in rotating spin–orbit-coupled spin-1 Bose–Einstein condensates with in-plane gradient magnetic field

We investigate the topological excitations of rotating spin-1 ferromagnetic Bose–Einstein condensates with spin–orbit coupling (SOC) in an in-plane quadrupole field. Such a system sustains a rich variety of exotic vortex structures due to the spinor order parameter and the interplay among in-plane quadrupole field, SOC, rotation, and interatomic interaction. For the nonrotating case, with the increase of the quadrupole field strength, the system experiences a transition from a coreless polar-core vortex with a bright soliton to a singular polar-core vortex with a density hole. Without rotation but with a fixed quadrupole field, when the SOC strength increases, the system transforms from a central Mermin–Ho vortex into a criss-crossed vortex–antivortex string lattice. For the rotating case, we give a phase diagram with respect to the quadrupole field strength and the SOC strength. It is shown that the rotating system supports four typical quantum phases: vortex necklace, diagonal vortex chain cluster, single diagonal vortex chain, and few vortex states. Furthermore, the system favors novel spin textures and skyrmion excitations including an antiskyrmion, a criss-crossed half-skyrmion–half-antiskyrmion lattice, a skyrmion-meron necklace, a symmetric half-skyrmion lattice, and an asymmetric skyrmion-meron lattice.     

Energy barriers for vortex nucleation in dipolar condensates

We consider singly-quantized vortex states in a condensate of ⁵²Cr atoms in a pancake trap. We obtain the vortex solutions by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. The behavior of the condensate is studied under three different situations concerning the interactions: only s-wave, s-wave plus dipolar and only dipolar. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis in the three cases. These results are compared to those obtained for contact interaction condensates in the Thomas-Fermi approximation, and to a pseudo-analytical model, showing this latter a very good agreement with the numerical calculation.     

Entanglement production with multimode Bose-einstein condensates in optical lattices

Deep optical lattices are considered, in each site of which there are many Bose condensed atoms. By the resonant modulation of trapping potentials, it is possible to transfer a macroscopic portion of atoms to the collective nonlinear states corresponding to topological coherent modes. Entanglement can be generated between these modes. By varying the resonant modulating field, it is possible to effectively regulate entanglement production in this multimode multitrap system of Bose condensates.     

Solitary waves on vortex lines in Ginzburg-Landau models for the example of Bose-Einstein condensates

Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum (p)-substitution energy (Epsilon) plane with p-->0.09 rho kappa(3)/c(2), Epsilon-->0.091 rho kappa(3)/c as U-->c, where rho is the density, c is the speed of sound, kappa is the quantum of circulation, and U is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particular, it is shown that during collapse the vortex core becomes significantly compressed, and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line.     

Effect of quantum fluctuations on bose-einstein condensation of bilayer atomic gases in rapid rotation

We investigate vortex states and quantum fluctuations of bilayer atomic gases in rapid rotation. Among mean-field solutions of the Gross-Pitaevskii equation, we consider two types of vortex configurations: the vortex core positions of the layers are coincident or staggered. It is found that the coincident type is energetically preferred in the practical parameter regime. We also calculate the dispersion relations of collective modes and the filling factor for bosons outside the condensates. In the double layer system, quantum depletion is found to be suppressed due to interlayer tunneling. This means that Bose-Einstein condensation is stabilized compared to the single layer case.     

Black Holes in Bose–Einstein Condensates

It is shown that there exist both dynamically stable and unstable dilute-gas Bose–Einstein condensates that, in the hydrodynamic limit, exhibit a behavior completely analogous to that of gravitational black holes. The dynamical instabilities involve creation of quasiparticle pairs in positive and negative energy states. We illustrate these features in two qualitatively different one-dimensional models. We have also simulated the creation of a stable sonic black hole by solving the Gross–Pitaevskii equation numerically for a condensate subject to a trapping potential that is adiabatically deformed. A sonic black hole could in this way be created experimentally with state-of-the-art or planned technology.     

Manifestations of the roton mode in dipolar Bose-Einstein condensates

We investigate the structure of trapped Bose-Einstein condensates (BECs) with long-range anisotropic dipolar interactions. We find that a small perturbation in the trapping potential can lead to dramatic changes in the condensate's density profile for sufficiently large dipolar interaction strengths and trap aspect ratios. By employing perturbation theory, we relate these oscillations to a previously identified "rotonlike" mode in dipolar BECs. The same physics is responsible for radial density oscillations in vortex states of dipolar BECs that have been predicted previously.     

Damping and frequency shift in the oscillations of two colliding Bose-Einstein condensates

We have investigated the center-of-mass oscillations of a ⁸⁷Rb Bose-Einstein condensate in an elongated magneto-static trap. We start from a trapped condensate and we transfer part of the atoms to another trapped level, by applying a radio-frequency pulse. The new condensate is produced far from its equilibrium position in the magnetic potential, and periodically collides with the parent condensate. We discuss how both the damping and the frequency shift of the oscillations are affected by the mutual interaction between the two condensates, in a wide range of trapping frequencies. The experimental data are compared with the prediction of a mean-field model. Received 28 May 2001     

Solitary wave complexes in two-component condensates

Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components; (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component; (3) two coupled rarefaction waves; (4) either a vortex ring or a rarefaction pulse coupled to a localized disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability, and solitary wave complexes in two dimensions are discussed.     

Vortex chains travelling with discrete velocities

It has been shown that Swihart waves slowing down caused by Josephson junction spatial dispersion leads to the new field periodic nonlinear vortex states moving with discrete velocities. Swihart waves trapping by periodic vortex structures is discovered.     

Decay of a negative molecular ion in a constant electric field

The problem of the shift and broadening of the electron energy levels in the field of two 3D short-range potentials (e.g., the model of a negative molecular ion) by a constant electric field F is considered. The interaction of an electron with attraction centers is taken into account in the effective range approximation. We analyze the cases when both centers maintain weakly bound s states and when the electron state in the field of one of the centers is a p state. Exact numerical results for the shift and the width of the energy levels of a quasi-molecule as functions of field F, distance R between atomic centers, and the orientation of the quasi-molecule axis relative to vector F are presented, as well as the results of analytic treatment for a number of limiting cases. The exact values of complex energies of the quasi-molecule are compared with analytic results for a weak field in the case of identical s centers [26], as well as nonequivalent s centers and s-p centers; the applicability boundaries of the weak field approximation are established. It is shown that for large values of R, the position and width of the levels in a strong field are correctly described in perturbation theory in the exchange interaction. We analyze the field-induced quasi-intersection of molecular energy levels of the system with nonequivalent atomic centers and peculiarities in the energy level widths associated with this intersection. The results make it possible to qualitatively interpret the results of numerical calculations of the probability of homo- and heteronuclear molecules being ionized by a low-frequency laser field.     

二元玻色-爱因斯坦凝聚体中矢量孤子的转化行为

考虑种内和种间相互作用均为排斥作用,研究了局限于谐振外部势阱中的二元玻色-爱因斯坦凝聚体中灰-灰和黑-黑孤子的动力学行为.结果表明:当谐振势阱的轴向囚禁频率为零时,灰-灰和黑-黑孤子均能保持局域稳定;而当轴向囚禁频率不为零时,凝聚体中的原子向势阱中心聚集,发现灰-灰孤子可以转化成亮-亮孤子.     

Magnetooptical properties of a molecular D<Stack><Subscript>2</Subscript><Superscript>−</Superscript></Stack>-ion in a quantum wire

In the framework of a model of zero-range potential, the problem of bound states of an electron in the field of two D0 centers (a two-center problem) in a semiconductor quantum wire is considered in the presence of a longitudinal magnetic field. It is shown that the magnetic field produces a significant shift of g and u terms and stabilizes the D ₂ ^? states in quantum wires. It is found that, in the case of transverse polarization of light, the spectral dependence of the photoionization cross section of a D ₂ ^? center exhibits the quantum-confined Zeeman effect with strongly pronounced oscillations of interference nature.