Factorization with a Logarithmic Energy Spectrum of a Central Potential

F. Gleisberga, W.P. Schleicha, b aInstitut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQST), Universität Ulm, D–89069 Ulm, Germany bHagler Institute for Advanced Study at Texas A & M University, Texas A & M AgriLife Research, Institute for Quantum Studies and Engineering (IQSE) and Department of Physics and Astronomy, Texas A & M University, College Station, Texas 77843-4242, USA

Full Text PDF

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.

DOI:10.12693/APhysPolA.143.112 topics: factorization, logarithmic energy spectrum, central potential, cold atoms