Parabolic Trap Research Articles

A variational approach to the modulational instability of a Bose–Einstein condensate in a parabolic trap

By means of the time-dependent variational approach, we study the modulational instability of Bose–Einstein condensates (BECs), with both two- and three-body interatomic interactions, trapped in an external parabolic potential. Within this framework, we derive and analyse ordinary differential equations for the explicit time evolution of the amplitude and phase of modulational perturbation. The effect of the trapping coefficients as well as the quintic nonlinear interaction on the dynamics of the BEC are examined. Numerical simulations are carried out in order to support our theoretical findings.

Normal modes of a small bilayer system of binary classical charged particles trapped in a parabolic confinement potential

The normal modes and the melting character of a bilayer system consisting of binary charged particles with different charge and/or different mass, interacting through a Coulomb potential and confined in a parabolic trap are investigated. The normal mode spectrum is discussed as a function of the charge ratio (CR) and mass ratio (MR) of the two kinds of charged particles as well as the interlayer separation. We show that the dependence of the normal modes on the excited states can be tuned by varying the CR, the MR, and the interlayer distance. Once the interlayer distance is larger than a critical value, the first excited state corresponds only to the intershell rotation mode. In addition, the intershell rotation melting temperature is discussed as a function of the CR and MR as well as the interlayer separation.

Ground state and normal-mode spectra of a two-dimensional system of dipole particles confined in a parabolic trap

The ordered configurations of a monolayer of interacting magnetic dipoles confined in a circular parabolic potential are investigated as a function of the dipole moment of the particles. Despite the circular confinement, we find very asymmetric ordered structures like chains and Y-shaped configurations when a magnetic field is applied parallel to the plane of the particles. The normal-mode spectrum of the particles and its dependence on the magnetic field and the strength of the dipole moment of the particles are studied. The vibrational and rotational modes of the spectrum, which are associated with the stability of the system, are investigated in detail. The number of particles is varied and we found different ordering of the particles for different values of the dipole moment and the magnetic field. A ring structure with a large number of particles is observed for high values of the dipole moment of the particles.

Stable three-dimensional spatially modulated vortex solitons in Bose-Einstein condensates

We present exact numerical solutions in the form of spatially localized three-dimensional (3D) nonrotating and rotating (azimuthon) multipole solitons in the Bose-Einstein condensate (BEC) confined by a parabolic trap. We numerically show that the 3D azimuthon solutions exist as a continuous family parametrized by the angular velocity (or, equivalently, the modulational depth). By a linear stability analysis we show that 3D azimuthons with a sufficiently large phase modulational depth can be stable. The results are confirmed by direct numerical simulations of the Gross-Pitaevskii equation.

Elastic light scattering by the atoms of a Bose gas confined in a parabolic trap

It is shown that the emergence of a condensate fraction in a gas confined in a trap leads to a sharp increase in the intensity of elastic scattering (scattering not accompanied by a change in the quantum numbers describing the motion of gas atoms in the trap) of light. Under typical experimental conditions, this intensity may be thousands of times greater than the intensity of inelastic scattering, which is hardly affected by the condensate. The angular distribution of elastic scattering of light allows one to determine the size of the condensate, and its intensity makes it possible to determine the number of particles trapped in the condensate.

Genetic algorithm approach to calculation of the ground-state configurations of 2D clusters of non-uniformly charged classical particles

We study a system consisting of two different types of particles, having charge, equal to 1 or q interacting through a pure Coulomb potential and confined in a parabolic trap. The ground-state and metastable state configurations of the classical non-uniformly point-charge particles have been calculated using a new genetic algorithm-based approach. The geometrical structures and structural phase transitions found by the recent Monte Carlo simulations have been confirmed but the localization of a second-order phase transition point has been estimated more accurately at q = 0.488.

Influence of the trap shape on the detection of the superfluid—Mott-insulator transition

The coexistence of superfluid and Mott insulator, due to the quadratic confinement potential in current optical lattice experiments, makes the accurate detection of the superfluid-Mott transition difficult. Studying alternative trapping potentials which are experimentally realizable and have a flatter center, we find that the transition can be better resolved, but at the cost of a more difficult tuning of the particle filling. When mapping out the phase diagram using local probes and the local density approximation we find that the smoother gradient of the parabolic trap is advantageous.

Reentrant quantum phase transition in double-well optical lattices

We study the quantum phases of bosons confined to a combined potential of a one-dimensional double-well optical lattice and a parabolic trap (two-legged ladders). We apply the time-evolving block decimation method to the corresponding ladders described by a two-legged Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in the double-well optical lattice exhibits a reentrant quantum phase transition between Mott insulator and superfluid phases at unit filling as the tilt of the double wells is increased. We show that this reentrant phase transition still occurs in the presence of a parabolic trap, and we suggest that it can be detected experimentally by measuring matter-wave interference patterns.

Bosons in one-dimensional incommensurate superlattices

We investigate numerically the zero-temperature physics of the one-dimensional Bose-Hubbard model in an incommensurate cosine potential, recently realized in experiments with cold bosons in optical superlattices [L. Fallani et al., Phys. Rev. Lett. 98, 130404 (2007)]. An incommensurate cosine potential has intermediate properties between a truly periodic and a fully random potential, displaying a characteristic length scale (the quasiperiod) which is shown to set a finite lower bound to the excitation energy of the system at special incommensurate fillings. This leads to the emergence of gapped incommensurate band-insulator (IBI) phases along with gapless Bose-glass (BG) phases for strong quasiperiodic potential for both hard-core and soft-core bosons. Enriching the spatial features of the potential by the addition of a second incommensurate component appears to remove the IBI regions, stabilizing a continuous BG phase over an extended parameter range. Moreover, we discuss the validity of the local-density approximation in the presence of a parabolic trap, clarifying the notion of a local BG phase in a trapped system; we investigate the behavior of first- and second-order coherence upon increasing the strength of the quasiperiodic potential; and we discuss the ab initio derivation of the Bose-Hubbard Hamiltonian with quasiperiodic potential starting from the microscopic Hamiltonian of bosons in an incommensurate superlattice.

Hysteresis and reentrant melting of a self-organized system of classical particles confined in a parabolic trap

The melting of a self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and a long-range repulsive potential is studied. Different behaviors of the melting temperature are found depending on the strength (B) of the attractive part of the interparticle potential. The melting of a system consisting of small bubbles takes place through a two-step melting process. A reentrant behavior and a thermally induced structural phase transition are observed in a small region of the (B,kappa) space. A hysteresis effect in the configuration of the particles is observed as a function of temperature. This is a consequence of the presence of a potential barrier between different configurations of the system.

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 $\omega $, 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 $\omega/ \sqrt{2}$ 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.

Two-dimensional multisolitons and azimuthons in Bose-Einstein condensates

We present numerical solutions in the form of spatially localized nonrotating and rotating (azimuthon) multisolitons in the two-dimensional (``pancake-shaped configuration'') Bose-Einstein condensate (BEC) confined by a parabolic trap. The numerical relaxation procedure with a stabilizing factor is used.

Mixture of bosonic and spin-polarized fermionic atoms in an optical lattice

We investigate the properties of trapped Bose-Fermi mixtures for experimentally relevant parameters in one dimension. The effect of the attractive Bose-Fermi interaction onto the bosons is to deepen the parabolic trapping potential, and to reduce the bosonic repulsion in higher order. This leads for many situations to an increase in bosonic coherence. The opposite effect was observed in {sup 87}Rb-{sup 40}K experiments, most likely due to a sharp rise in temperature. We also discuss low-temperature features, such as a bosonic Mott insulator transition driven by the fermion concentration, and the formation of composite particles such as polarons and molecules.

Effects of the range of the potential on the structure and dynamics of two-dimensional Coulomb clusters

The structure, dynamics, and thermodynamics of finite systems of two-dimensional particles interacting mutually through a shielded Coulomb potential, V(r) = e (−κr)/r, and bound together by an isotropic parabolic trap, are investigated by means of global optimization and simulation methods. As the range of the potential decreases, or as κ increases, the number of distinct minima rapidly increases for a given size and the cluster generally shrinks. Looking more specifically at selected sizes below 50, non- monotonic cluster size effects seem to dominate the energetics, chaotic dynamics, and thermodynamics, even though the melting point is weakly affected by the range of the potential.

Structural and dynamical aspects of small three-dimensional spherical Coulomb clusters

An analysis of the structural and dynamical properties of small size three-dimensional clusters of classical charged particles confined in a spherical parabolic trap is presented. The ground state and the lowest metastable configurations are identified for Coulomb clusters consisting of N=4–100 particles. The eigenmode frequencies are investigated both for clusters with Coulomb and screened Coulomb interparticle interaction. The breathing mode frequency is analytically determined and is found to be the highest energy eigenmode and independent of the number of particles for the case of Coulomb inter-particle interaction.

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 {alpha} 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 {alpha}.

Crystallization in Mass‐Asymmetric Electron‐Hole Bilayers

AbstractWe consider a mass‐asymmetric electron and hole bilayer. Electron and hole Coulomb correlations and electron and hole quantum effects are treated on first principles by path integral Monte Carlo methods. For a fixed layer separation we vary the mass ratio M of holes and electrons between 1 and 100 and analyze the structural changes in the system. While, for the chosen density, the electrons are in a nearly homogeneous state, the hole arrangement changes from homogeneous to localized, with increasing M, which is verified for both, mesoscopic bilayers in a parabolic trap and for a macroscopic system. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Rayleigh scattering from a trapped bose condensate and the corresponding recoil atom velocity distribution

An approach has been developed that allows the Rayleigh scattering cross section to be calculated with allowance for the quantum character of motion of the center of mass of the trapped scattering particles. The shape of the line of light scattering from a Bose condensate in a parabolic trap has been studied. A shift of the scattering line center is equal to the recoil shift, while the line width depends on the chemical potential of the Bose gas and on the relaxation time of the velocity of the above-condensate recoil particles. A velocity distribution function in the beam of recoil atoms formed in the course of induced Rayleigh scattering is determined. It is shown that, under the typical experimental conditions, the characteristic width Δv/v of the recoil velocity distribution in this beam is on the order of 10−3 at a velocity v on the order of several centimeters per second.

Luther-Emery Phase and Atomic-Density Waves in a Trapped Fermion Gas

The Luther-Emery liquid is a state of matter that is predicted to occur in one-dimensional systems of interacting fermions and is characterized by a gapless charge spectrum and a gapped spin spectrum. In this Letter we discuss a realization of the Luther-Emery phase in a trapped cold-atom gas. We study by means of the density-matrix renormalization-group technique a two-component atomic Fermi gas with attractive interactions subject to parabolic trapping inside an optical lattice. We demonstrate how this system exhibits compound phases characterized by the coexistence of spin pairing and atomic-density waves. A smooth crossover occurs with increasing magnitude of the atom-atom attraction to a state in which tightly bound spin-singlet dimers occupy the center of the trap. The existence of atomic-density waves could be detected in the elastic contribution to the light-scattering diffraction pattern.

Melting of a two-dimensional binary cluster of charged particles confined in a parabolictrap

Melting of a finite size binary system consisting of two types of particles having differentcharges and/or masses, confined in a two-dimensional (2D) parabolic trap, is studied. Themelting temperature is obtained for different values of the ratio between the charges and/ormasses of the two types of particles. The two types of particles melt at differenttemperatures; e.g., particles with smaller charge melt first. The importance of thecommensurate/incommensurate configurations and the different normal modes to themelting phenomenon is studied. When the ground state consists of a nonsymmetricarrangement of particles new thermally induced structural phase transitions are found. Inaddition, a remarkable temperature induced spatial separation of the two types of particlesis found.