We study the decay of two repulsively interacting bosons tunnelling through a delta potential barrier by a direct numerical solution of the time-dependent Schrödinger equation. The solutions are analysed according to the regions of particle presence: both particles inside the trap (in–in), one particle in and one particle out (in–out) and both particles outside (out–out). It is shown that the in–in probability is dominated by the exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength, the decay of in–out probability is dominated by the single-particle decay mode. The decay mechanisms are adequately described by simple models.
We study the decay of two repulsively interacting bosons tunnelling through a delta potential barrier by a direct numerical solution of the time-dependent Schrödinger equation. The solutions are analysed according to the regions of particle presence: both particles inside the trap (in–in), one particle in and one particle out (in–out) and both particles outside (out–out). It is shown that the in–in probability is dominated by the exponential decay, and its decay rate is predicted very well from outgoing boundary conditions. Up to a certain range of interaction strength, the decay of in–out probability is dominated by the single-particle decay mode. The decay mechanisms are adequately described by simple models.
A dressed-state approach to mixing of bosonic matter waves is presented. Two cases are studied using this formalism. In the first, two macroscopically populated modes of atoms (two-wave mixing) are coupled through the presence of light. In the second case, three modes of Bogoliubov quasiparticles (three-wave mixing) are coupled through
s-wave interaction. In both cases, wave mixing induces oscillations in the population of the different modes that decay due to interactions. Analytic expressions for the dressed basis spectrum and the evolution of the mode populations in time are derived both for resonant mixing and nonresonant mixing. Oscillations in the population of a given mode are shown to lead to a splitting in the decay spectrum of that mode, in analogy with the optical Autler-Townes splitting in the decay spectrum of a strongly driven atom. These effects cannot be described by a mean-field approximation.