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Chua, Vivien P.; Porter, Mason A.

Spatial resonance overlap in Bose–Einstein condensates in superlattice potentials. (English) Zbl 1115.82304

Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 4, 945-959 (2006).
Summary: We employ Chirikov’s overlap criterion to investigate interactions between subharmonic resonances of coherent structure solutions of the Gross–Pitaveskii (GP) equation governing the mean-field dynamics of cigar-shaped Bose–Einstein condensates in optical superlattices. We apply a standing wave ansatz to the GP equation to obtain a parametrically forced Duffing equation describing the BEC’s spatial dynamics. We then investigate analytically the dependence of spatial resonances on the depth of the superlattice potential, deriving an order-of-magnitude estimate for the critical depth at which spatial resonances with respect to different lattice harmonics first overlap. We also derive a formula for the size of resonance zones and examine changes in our estimates as the relative superlattice amplitudes corresponding to the different harmonics are adjusted. We investigate the onset of global chaos and support our analytical work with numerical simulations.

Cited in 2 Documents

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
81V45 Atomic physics
37K60 Lattice dynamics; integrable lattice equations

Keywords:

Bose–Einstein condensates; Hamiltonian systems; Chirikov’s overlap criterion
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\textit{V. P. Chua} and \textit{M. A. Porter}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 4, 945--959 (2006; Zbl 1115.82304)
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