Basic Properties of Coherent-Squeezed States Revisited
arXiv:1312.3016
Abstract
In this paper we treat coherent-squeezed states of Fock space once more and study some basic properties of them from a geometrical point of view. Since the set of coherent-squeezed states $\{\ket{α, β}\ |\ α, β\in \fukuso\}$ makes a real 4-dimensional surface in the Fock space (which is of course not flat), we can calculate its metric. On the other hand, we know that coherent-squeezed states satisfy the minimal uncertainty of Heisenberg under some condition imposed on the parameter space , so that we can study the metric from the view point of uncertainty principle. Then we obtain a surprising simple form (at least to us). We also make a brief review on Holonomic Quantum Computation by use of a simple model based on nonlinear Kerr effect and coherent-squeezed operators.
Latex ; 19 pages ; 2 figures ; minor changes. To appear in International Journal of Geometric Methods in Modern Physics