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In this paper we give a theoretical description of resonant coupling betweentwo collective excitations of a Bose condensed gas (BEC) on, or close, to asecond harmonic resonance. Using analytic expressions for the quasi-particlewavefunctions we show that the coupling between quadrupole modes is strong,leading to a coupling time of a few milliseconds (for a TOP trap with radialfrequency 100 Hz and 10^4 atoms). Using the hydrodynamic approximation, wederive analytic expression for the coupling matrix element. These can be usedwith an effective Hamiltonian (that we also derive) to describe the dynamics ofthe coupling process and the associated squeezing effects.Comment: 12 pages, 3 figure

Calculation of mode coupling for quadrupole excitations in a Bose-Einstein condenstate