Basic properties of coherent-squeezed states revisited

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 {|α, β〉|α, β ∈ C} makes a real four-dimensional surface in the Fock space ℱ (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 {α, β}, so that we can study the metric from the viewpoint 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.