Superpositions of coherent states determined by Gauss sums
Quantum Physics
2022-09-29 v3 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
We describe a family of quantum states of the Schr\"odinger cat type as superpositions of the harmonic oscillator coherent states with coefficients defined by the quadratic Gauss sums. These states emerge as eigenfunctions of the lowering operators obtained after canonical transformations of the Heisenberg-Weyl algebra associated with the ordinary and fractional Fourier transformation. The first member of this family is given by the well known Yurke-Stoler coherent state.
Keywords
Cite
@article{arxiv.2112.07613,
title = {Superpositions of coherent states determined by Gauss sums},
author = {Vyacheslav P. Spiridonov},
journal= {arXiv preprint arXiv:2112.07613},
year = {2022}
}
Comments
11 pp