Factorization with a logarithmic energy spectrum

Abstract

We propose a method to factor numbers based on the quantum dynamics of two interacting bosonic atoms where the single-particle energy spectrum depends logarithmically on the quantum number. We show that two atoms initially prepared in the ground state are preferentially excited by a time-dependent interaction into a two-particle energy state characterized by the factors. Hence, a measurement of the energy of one of the two atoms yields the factors. The number to be factored is encoded in the frequency of a sinusoidally modulated interaction. We also discuss the influence of off-resonant transitions and the limitation of the number to be factored imposed by experimental conditions.