M. Porter, M. Chugunova, and D. Pelinovsky

Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices

Physical Review E 74, 036610 (2006)

We analyze gap solitons in trapped Bose-Einstein condensates (BECs) in optical lattice potentials under Feshbach resonance management. Starting with a Hamiltonian-averaged Gross-Pitaevsky (GP) equation with a periodic potential, we employ an envelope wave approximation to derive coupled-mode equations describing the slow BEC dynamics in the first spectral gap of the optical lattice. We construct exact analytical formulas describing gap soliton solutions and examine their spectral stability using the Chebyshev interpolation method. We show numerically that these gap solitons are unstable far from the threshold of local bifurcation and that the instability results in beating dynamics.

Bose-Einstein condensates, Optical lattices, Feshbach resonances, Hamiltonian coupled-mode systems, gap solitons, spectral stability, eigenvalues, time evolution