Factorization with a Logarithmic Energy Spectrum of a Central Potential

Abstract

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 states corresponding to zero angular momentum. Bosons initially prepared in the ground state are excited by a sinusoidally time-dependent interaction into a state characterized by quantum numbers, which represent the factors of the number encoded in the frequency of the perturbation. We also discuss the complete single-particle spectrum as well as the limitations of our method caused by decoherence.