M. Porter, M. Chugunova, and D. Pelinovsky
Feshbach Resonance Management of Bose-Einstein Condensates in Optical Lattices
Physical Review E 74, 036610 (2006)
Abstract:
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.
Keywords:
Bose-Einstein condensates, Optical lattices, Feshbach resonances,
Hamiltonian coupled-mode systems, gap solitons, spectral
stability, eigenvalues, time evolution