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 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.

LATEX2e, 21 pages , 7 eps figures

References in corpus (3)

• Observation of ultracold atomic bubbles in orbital microgravity
• A space-based quantum gas laboratory at picokelvin energy scales
• The Quantum Mellin transform

Cited by in corpus (1)

• Achieving quantum advantage in a search for a violations of the Goldbach conjecture, with driven atoms in tailored potentials