Galilean covariant Lagrangian models

We construct non-relativistic Lagrangian field models by enforcing Galilean covariance with a (4, 1) Minkowski manifold followed by a projection onto the (3, 1) Newtonian spacetime. We discuss scalar, Fermi and gauge fields, as well as interactions between these fields, preparing the stage for their quantization. We show that the Galilean covariant formalism provides an elegant construction of the Lagrangians which describe the electric and magnetic limits of Galilean electromagnetism. Similarly we obtain non-relativistic limits for the Proca field. Then we study Dirac Lagrangians and retrieve the Levy-Leblond wave equations when the Fermi field interacts with an Abelian gauge field.

Black soliton in a quasi-one-dimensional trapped fermion-fermion mixture

Employing a time dependent mean-field-hydrodynamic model we study the generation of black solitons in a degenerate fermion-fermion mixture in a cigar-shaped geometry using variational and numerical solutions. The black soliton is found to be the first stationary vibrational excitation of the system and is considered to be a nonlinear continuation of the vibrational excitation of the harmonic oscillator state. We illustrate the stationary nature of the black soliton, by studying different perturbations on it after its formation.

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.

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.

Formation of bright solitons and soliton trains in a fermion-fermion mixture by modulational instability

We employ a time- dependent mean- field- hydrodynamic model to study the generation of bright solitons in a degenerate fermion - fermion mixture in a cigar- shaped geometry using variational and numerical methods. Due to a strong Pauli- blocking repulsion among identical spin- polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean-field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions, where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.

Fermionic bright soliton in a boson-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to study the formation of fermionic bright solitons in a trapped degenerate Fermi gas mixed with a Bose-Einstein condensate in a quasi-one-dimensional cigar-shaped geometry. Due to a strong Pauli-blocking repulsion among spin-polarized fermions at short distances there cannot be bright fermionic solitons in the case of repulsive boson-fermion interactions. However, we demonstrate that stable bright fermionic solitons can be formed for a sufficiently attractive boson-fermion interaction in a boson-fermion mixture. We also consider the formation of fermionic solitons in the presence of a periodic axial optical-lattice potential. These solitons can be formed and studied in the laboratory with present technology.

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.

Bright solitons in coupled defocusing NLS equation supported by coupling: Application to Bose-Einstein condensation

We demonstrate the formation of bright solitons in coupled self-defocusing nonlinear Schrodinger (NLS) equation supported by attractive coupling. As an application we use a time-dependent dynamical mean-field model to study the formation of stable bright solitons in two-component repulsive Bose-Einstein condensates (BECs) supported by interspecies attraction in a quasi one-dimensional geometry. When all interactions are repulsive, there cannot be bright solitons. However, bright solitons can be formed in two-component repulsive BECs for a sufficiently attractive interspecies interaction, which induces an attractive effective interaction among bosons of same type. (c) 2005 Elsevier B.V. All rights reserved.

Tightly bound gap solitons in a Fermi gas

Within the framework of the mean-field hydrodynamic model of a degenerate Fermi gas ( DFG), we study, by means of numerical methods and variational approximation ( VA), the formation of fundamental gap solitons ( FGSs) in a DFG ( or in a BCS superfluid generated by weak interaction between spin- up and spin- down fermions), which is trapped in a periodic optical- lattice ( OL) potential. An effectively one- dimensional ( 1D) con. guration is considered, assuming strong transverse confinement; in parallel, a proper 1D model of the DFG ( which amounts to the known quintic equation for the Tonks- Girardeau gas in the OL) is considered too. The FGSs found in the first two bandgaps of the OL- induced spectrum ( unless they are very close to edges of the gaps) feature a ( tightly bound) shape, being essentially confined to a single cell of the OL. In the second bandgap, we also find antisymmetric tightly bound subfundamental solitons ( SFSs), with zero at the midpoint. The SFSs are also confined to a single cell of the OL, but, unlike the FGSs, they are unstable. The predicted solitons, consisting of similar to 10(4) - 10(5) atoms, can be created by available experimental techniques in the DFG of Li-6 atoms.

Expansion of a Bose-Einstein condensate formed on a joint harmonic and one-dimensional optical-lattice potential

We study the expansion of a Bose-Einstein condensate trapped in a combined optical-lattice and axially-symmetric harmonic potential using the numerical solution of the mean-field Gross-Pitaevskii equation. First, we consider the expansion of such a condensate under the action of the optical-lattice potential alone. In this case the result of numerical simulation for the axial and radial sizes during expansion is in agreement with two experiments by Morsch et al (2002 Phys. Rev. A 66 021601(R) and 2003 Laser Phys. 13 594). Finally, we consider the expansion under the action of the harmonic potential alone. In this case the oscillation, and the disappearance and revival of the resultant interference pattern is in agreement with the experiment by Muller et al (2003 J. Opt. B: Quantum Semiclass. Opt. 5 S38).

Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length

Using variational and numerical solutions of the mean-field Gross-Pitaevskii equation we show that a bright soliton can be stabilized in a trapless three-dimensional attractive Bose-Einstein condensate (BEC) by a rapid periodic temporal modulation of scattering length alone by using a Feshbach resonance. This scheme also stabilizes a rotating vortex soliton in two dimensions. Apart from possible experimental application in BEC, the present study suggests that the spatiotemporal solitons of nonlinear optics in three dimensions can also be stabilized in a layered Kerr medium with sign-changing nonlinearity along the propagation direction.

Bright solitons and soliton trains in a fermion-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to predict and study bright solitons in a degenerate fermion-fermion mixture in a quasi-one-dimensional cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies fermion-fermion interactions. However, stable bright solitons can be formed for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains. These fermionic solitons can be formed and studied in laboratory with present technology.