Bright solitons and soliton trains in a fermion-fermion mixture

Adhikari, Sadhan K.

doi:10.1140/epjd/e2006-00203-3

Cited by 11 publications

(4 citation statements)

References 29 publications

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“…Nevertheless, the dynamical equation, if it is treated as a phenomenologically postulated one, may yield reasonable predictions for stability of static MFHD states in the DFG [12,18,20].…”

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confidence: 99%

“…Currently, 6 Li-7 Li [13], 6 Li- 23 Na [14], and 40 K-87 Rb [15] mixtures of boson and fermion atoms are available, as well as binary DFGs, such as mixtures of two different spin states in 40 K [16] and 6 Li [17] gases. Accordingly, solitons in a binary fermion gas with attraction between the two species have been predicted [18].…”

mentioning

confidence: 99%

“…with ψ(r, t) = e −iµt/ Ψ(r), although this generalization is formal, as the above-mentioned derivation does not define the phase of the fermion wave function. Nevertheless, the dynamical equation, if it is treated as a phenomenologically postulated one, may yield reasonable predictions for stability of static MFHD states in the DFG [12,18,20].…”

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confidence: 99%

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Tightly bound gap solitons in a Fermi gas

Adhikari

Malomed

2007

Europhys. Lett.

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Abstract. -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 opticallattice (OL) potential. An effectively one-dimensional (1D) configuration 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 ∼ 10 4 − 10 5 atoms, can be created by available experimental techniques in the DFG of 6 Li atoms.Introduction: Matter-wave solitons were created as localized nonlinear excitations in Bose-Einstein condensates (BECs) of attractively interacting 7 Li [1] and 85 Rb [2] atoms loaded in a cigar-shaped trap. In both cases, the interaction was switched from repulsion to attraction by applying magnetic field near the Feshbach resonance [3,4]). In the absence of axial confinement, the solitons can propagate freely in the axial direction. This was followed by the creation of gap solitons, GSs (formed by a few hundred atoms of 87 Rb) in a self-repulsive BEC loaded in a cigar-shaped trapped combined with an optical lattice (OL) [5], which was created as the interference pattern by counter-propagating laser beams (see also review [6]). Theoretical description of the dilute BEC relies upon the Gross-Pitaevskii equation (GPE), which provides for a remarkably accurate description of various matter-wave patterns, including solitons [7]. In particular, GSs exist at values of the chemical potential that fall in finite gaps of the band spectrum of the linear problem, induced by the periodic OL potential. In that case, the system possesses a negative effective mass, which allows the formation of solitons in balance with the repulsive nonlinearity [8].

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“…Nevertheless, the dynamical equation, if it is treated as a phenomenologically postulated one, may yield reasonable predictions for stability of static MFHD states in the DFG [12,18,20].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Tightly bound gap solitons in a Fermi gas

Adhikari

Malomed

2007

Europhys. Lett.

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“…Moreover, a similar perspective was discussed in the context of Bose-Fermi mixtures, where the interaction between bosons is repulsive, but the bosons and fermions attract each other [17]. Similarly, solitons in a binary degenerate Fermi gas, supported by the attraction between the fermion species, were predicted [18]. It was also proposed to use the attraction between fermions and bosons for making bosonic quantum dots that can trap fermion atoms (in particular, gap solitons in the BEC trapped in the OL may play the role of such dots) [19].…”

Section: Introduction and The Modelmentioning

confidence: 86%

Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice

2007

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We consider effects of inter-species attraction on two-component gap solitons (GSs) in the binary BEC with intra-species repulsion, trapped in the one-dimensional optical lattice (OL). Systematic simulations of the coupled Gross-Pitaevskii equations (GPEs) corroborate an assumption that, because the effective mass of GSs is negative, the inter-species attraction may split the two-component soliton. Two critical values, κ1 and κ2, of the OL strength (κ) are identified. Two-species GSs with fully overlapping wave functions are stable in strong lattices (κ > κ1). In an intermediate region, κ1 > κ > κ2, the soliton splits into a double-humped state with separated components. Finally, in weak lattices (κ < κ2), the splitting generates a pair of freely moving single-species GSs. We present and explain the dependence of κ1 and κ2 on thenumber of atoms (total norm), and on the relative strength of the competing inter-species attraction and intra-species repulsion. The splitting of asymmetric solitons, with unequal norms of the two species, is briefly considered too. It is found and explained that the splitting threshold grows with the increase of the asymmetry.

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Multi-Component Bose-Einstein Condensates: Theory

Malomed

Atomic, Optical, and Plasma Physics

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Bright solitons and soliton trains in a fermion-fermion mixture

Cited by 11 publications

References 29 publications

Tightly bound gap solitons in a Fermi gas

Tightly bound gap solitons in a Fermi gas

Competition between attractive and repulsive interactions in two-component Bose-Einstein condensates trapped in an optical lattice

Multi-Component Bose-Einstein Condensates: Theory

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