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The quasiparticle excitations and dynamical stability of an atomicBose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms atzero temperature is studied. The Fermi gas is assumed to be either in thenormal state or to have undergone a phase transition to a superfluid state byforming Cooper pairs. The quasiparticle excitations of the Bose-Einsteincondensate exhibit a dynamical instability due to a resonant exchange of energyand momentum with quasiparticle excitations of the Fermi gas. The stabilityregime for the bosons depends on whether the Fermi gas is in the normal stateor in the superfluid state. We show that the energy gap in the quasiparticlespectrum for the superfluid state stabilizes the low energy energy excitationsof the condensate. In the stable regime, we calculate the boson quasiparticlespectrum, which is modified by the fluctuations in the density of the Fermigas.Comment: 12 pages, 3 figure

Quasiparticle spectrum and dynamical stability of an atomic Bose-Einstein condensate coupled to a degenerate Fermi gas