Bright Soliton Solutions in Degenerate Femi Gas near Feshbach Resonance

Abstract

For molecular and standard Bose-Einstein condensates and Fermi gases near Feshbach resonances, the general polytropic equation of states is 𝑃 ∝ 𝑛 𝛾+1 . According to the effective power 𝛾 ≈ 0.5 ∼ 1.3, we resolve the timedependent nonlinear Schrodinger equation and find series bright solitons. The analysis could help in the search for matter-wave soliton trains in degenerate Femi gas.

Exact soliton solutions of the generalized Gross-Pitaevskii equation based on expansion method

“…Exact solutions of such equation in specific form have been found, and are shown to be of the type of a variety of solitons, as demonstrated in the works done by several groups. [5][6][7][8][9][10] Recently, with the amount of achievements in cold atomic Fermi gases attracting growing interests, the generalized Gross-Pitaevskii equation (GGPE) has been proposed in order to extract analytical solutions for dynamical behaviors; however, soliton solutions of such GGPE have not been formally investigated in generalized analytical format. The work presented in this paper will focus on this broadened category of GPE.…”

“…The work presented in this paper will focus on this broadened category of GPE. While previous works mainly focus on the original case of GPE, where the nonlinear interaction term involves integer power of the wavefunction (|ψ| 2 ψ) or the variable coefficients of the equation terms are restricted by certain constraint formula, 5,6 or external potential is not considered; 7 we try to investigate the more general case where the nonlinear interaction term is of arbitrary real value power of the wavefuction (|ψ| 2γ ψ) (γ is called polytropic index) with arbitrary variable coefficients of equation terms, which is of particular interest in the investigation of ultracold Fermi gases in the BCS-BEC crossover, 2-4 the dimer BEC superfluid and Cooper-paring BCS superfluid are two limits of this crossover while the strongly interaction unitarity regime intermediates them. It is known that γ = 1 corresponding to BEC limit while γ = 2/3 corresponding to BCS and unitarity limits where the scattering length diverges to infinity (+∞ from BEC side and −∞ from BCS side), [2][3][4] for BEC, BCS, and unitarity regimes, the behaviors of the system vary smoothly and express superfluid properties although the value of γ is not the limit values listed above.…”