On the quantum instability of attractive Bose systems (Q604840)

We have considered the case of an atom-molecule condensate in which the interactions were attractive yet the effective scattering length was positive. This situation raised the question of whether the condensate collapsed due to the mutual attractions or remained stable in accordance with the positive scattering length. Starting with a two-body analysis, a separable potential was used to realistically model the interparticle interaction. Due to its success, this separable form was implemented in the many-body Hamiltonian. Equations of state were then obtained from the application of a variational principle that utilized a Gaussian trial wave functional for the many-body state. Despite the positive scattering length, a collapsing solution was obtained, consisting of a relatively low-density piece having only a molecular component to its condensate. At higher density, there occurred a quantum phase transition after which the solution comprised both atomic and molecular condensate components. Only by allowing the chemical potential to assume complex values could the experimentally observed case be obtained. As the phase of the order parameter, the chemical potential has an imaginary part quantifying a decay, rate, assigned a physical meaning through a small oscillation analysis about the equilibrium solutions. Expanding around the stationary points revealed two discrete eigenfrequencies associated with the low-density molecular condensate solution. Moreover, the experimentally observed energy per particle lay within an excitation continuum of the collapsing two-piece lower state. From energy conservation, the decay was interpreted as a coherent process corresponding to the evolution of the observed case into the excitations of the lower solution.