Factorization with a logarithmic energy spectrum of a central potential

We propose a method to factor numbers based on two interacting bosonic atoms in a central potential where the single-particle spectrum depends logarithmically on the radial quantum numbers of the zero angular momentum states. The bosons initially prepared in the ground state are excited by a sinusoidally time-dependent interaction into a state characterized by the quantum numbers which represent the factors of a number encoded in the frequency of the perturbation. We also discuss the full single-particle spectrum and limitations of our method caused by decoherence.