Factorization with a logarithmic energy spectrum of a central potential

TL;DR

This paper introduces a novel factorization method using two bosonic atoms in a central potential with a logarithmic energy spectrum, encoding numbers in the excitation frequencies.

Contribution

It presents a new physical approach to factorization leveraging quantum states of bosonic atoms in a specific potential, with analysis of spectrum and decoherence effects.

Findings

Method encodes factors in quantum excitation frequencies.

Spectrum analysis reveals limitations due to decoherence.

Potential for quantum-based factorization demonstrated.

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 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.