Induced instability for boson-fermion mixed condensates of alkali-metal atoms due to the attractive boson-fermion interaction

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Abstract
Instabilities for boson-fermion mixed condensates of trapped alkali-metal atoms due to the boson-fermion attractive interaction are studied using a variational method. A stable, metastable, and unstable region as a function of the boson-fermion interaction exists. The stability condition is obtained analytically from the asymptotic expansion of the variational total energy. The lifetime of metastable states is discussed for tunneling decay and is estimated to be very long. It suggests that, except near the instability border, metastable mixed condensate should be almost stable against tunneling decay. The critical border between metastable and unstable phases is calculated numerically and is shown to be consistent with the Mølmer scaling condition.