The critical number of atoms in an attractive Bose-Einstein condensate on optical plus harmonic traps

The stability of an attractive Bose-Einstein condensate on a joint one-dimensional optical lattice and an axially symmetrical harmonic trap is studied using the numerical solution of the time-dependent mean-field Gross-Pitaevskii equation and the critical number of atoms for a stable condensate is calculated. We also calculate this critical number of atoms in a double-well potential which is always greater than that in an axially symmetrical harmonic trap. The critical number of atoms in an optical trap can be made smaller or larger than the corresponding number in the absence of the optical trap by moving a node of the optical lattice potential in the axial direction of the harmonic trap. This variation of the critical number of atoms can be observed experimentally and compared with the present calculations.

Bound states of attractive Bose-Einstein condensates in shallow traps in two and three dimensions

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation for attractive interaction (with cubic or Kerr nonlinearity), we show that a stable bound state can appear in a Bose-Einstein condensate (BEC) in a localized exponentially screened radially symmetric harmonic potential well in two and three dimensions. We also consider an axially symmetric configuration with zero axial trap and a exponentially screened radial trap so that the resulting bound state can freely move along the axial direction like a soliton. The binding of the present states in shallow wells is mostly due to the nonlinear interaction with the trap playing a minor role. Hence, these BEC states are more suitable to study the effect of the nonlinear force on the dynamics. We illustrate the highly nonlinear nature of breathing oscillations of these states. Such bound states could be created in BECs and studied in the laboratory with present knowhow.

Josephson oscillation and induced collapse in an attractive Bose-Einstein condensate

Using the axially symmetric time-dependent Gross-Pitaevskii equation we study the Josephson oscillation of an attractive Bose-Einstein condensate (BEC) in a one-dimensional periodic optical-lattice potential. We find that the Josephson frequency is virtually independent of the number of atoms in the BEC and of the interatomic interaction (attractive or repulsive). We study the dependence of the Josephson frequency on the laser wave length and the strength of the optical-lattice potential. For a fixed laser wave length (795 nm), the Josephson frequency decreases with increasing strength as found in the experiment of Cataliotti [Science 293, 843 (2001)]. For a fixed strength, the Josephson frequency remains essentially unchanged for a reasonable variation of laser wave length around 800 nm. However, the Josephson oscillation is disrupted with the increase of laser wave length beyond 2000 nm leading to a collapse of a sufficiently attractive BEC. These features of a Josephson oscillation can be tested experimentally with present setups.

Dissipation-managed soliton in a quasi-one-dimensional Bose-Einstein condensate

We use the time-dependent mean-field Cross-Pitaevskii equation to study the formation of a dynamically-stabilized dissipation managed bright soliton in a quasi-one dimensional Bose-Einstein condensate (BEC). Because of three-body recombination of bosonic atoms to molecules, atoms are lost (dissipated) from a BEC. Such dissipation leads to the decay of a BEC soliton. We demonstrate by a perturbation procedure that an alimentation of atoms from an external source to the BEC may compensate for the dissipation loss and lead to a dynamically-stabilized soliton. The result of the analytical perturbation method is in excellent agreement with mean-field numerics. It seems possible to obtain such a dynamically stabilized BEC soliton without dissipation in laboratory.

Finite-well potential in the 3D nonlinear Schrodinger equation: application to Bose-Einstein condensation

Using variational and numerical solutions we show that stationary negative-energy localized (normalizable) bound states can appear in the three-dimensional nonlinear Schrodinger equation with a finite square-well potential for a range of nonlinearity parameters. Below a critical attractive nonlinearity, the system becomes unstable and experiences collapse. Above a limiting repulsive nonlinearity, the system becomes highly repulsive and cannot be bound. The system also allows nonnormalizable states of infinite norm at positive energies in the continuum. The normalizable negative-energy bound states could be created in BECs and studied in the laboratory with present knowhow.

Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is investigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevskii equation.

Evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries

Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.

Stability and collapse of a coupled Bose-Einstein condensate

The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other. We find interesting oscillation of the number of atoms in each of the states. For all repulsive interactions, stable condensates are formed. When some of the atomic interactions are attractive, the possibility of collapse is studied by including an absorptive contact interaction and a quartic three-body recombination term. One or both components of the condensate may undergo collapse when one or more of the nonlinear terms are attractive in nature. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Gap solitons in Bose-Einstein condensates in linear and nonlinear optical lattices

Properties of localized states on array of BEC confined to a potential, representing superposition of linear and nonlinear optical lattices are investigated. For a shallow lattice case the coupled mode system has been derived. We revealed new types of gap solitons and studied their stability. For the first time a moving soliton solution has been found. Analytical predictions are confirmed by numerical simulations of the Gross-Pitaevskii equation with jointly acting linear and nonlinear periodic potentials. (c) 2007 Elsevier B.V. All rights reserved.

Superconductivity as a Bose-Einstein condensation?

Bose-Einstein condensation (BEC) in two dimensions (2D) (e.g., to describe the quasi-2D cuprates) is suggested as the possible mechanism widely believed to underlie superconductivity in general. A crucial role is played by nonzero center-of-mass momentum Cooper pairs (CPs) usually neglected in BCS theory. Also vital is the unique linear dispersion relation appropriate to weakly-coupled bosonic CPs moving in the Fermi sea-rather than in vacuum where the dispersion would be quadratic but only for very strong coupling, and for which BEC is known to be impossible in 2D.

Effect of an impulsive force on vortices in a rotating Bose-Einstein condensate

The effects of a sudden increase and decrease of the interatomic interaction and harmonic-oscillator trapping potential on vortices in a quasi two-dimensional rotating Bose-Einstein condensate are investigated using the mean-field Gross-Pitaevskii equation. We also study the decay of vortices when the rotation of the condensate is suddenly stopped. Upon a free expansion of a rotating BEC with vortices the radius of the vortex core increases more rapidly than the radius of the condensate. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Dynamics of collapsing and exploding Bose-Einstein condensate

Recently, Donley et al. performed an experiment on the dynamics of collapsing and exploding Bose-Einstein condensates by suddenly changing the scattering length of atomic interaction to a large negative value on a preformed repulsive condensate of Rb-85 atoms in an axially symmetric trap. Consequently, the condensate collapses and ejects atoms via explosions, We show that the accurate numerical solution of the time-dependent Gross-Pitaevskii equation with axial symmetry can explain some aspects of the dynamics of the collapsing condensate. (C) 2002 Published by Elsevier B.V. B.V.

Bose-Einstein condensation and free DKP field

The thermodynamical partition function of the Duffin-Kemmer-Petiau theory is evaluated using the imaginary-time formalism of quantum field theory at finite temperature and path integral methods. The DKP partition function displays two features: (i) full equivalence with the partition function for charged scalar particles and charged massive spin 1 particles; and (ii) the zero mode sector which is essential to reproduce the well-known relativistic Bose-Einstein condensation for both theories. (C) 2003 Published by Elsevier B.V.

Bose-Einstein condensates in 2D with time-periodic scattering length

We discuss two-dimensional Bose-Einstein Condensates (BEC) under time-periodic variation of the scattering length. In particular we argue that for high-frequency variation there exist stable self-confined condensates without an external trap, when the do component of the scattering length is negative. Our results are based on a variational approximation, on direct averaging of the Gross-Pitaevskii equation and on numerical simulations.

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.