Linear dependence of deformed two-photon quadrature operators on spatial noncommutative parameter

By deriving useful formulas on the variances of the deformed two-photon quadrature operators in noncommutative space, we show that the variances in general have a linear dependence on the spatial noncommutative parameter θ, significantly different from the previous θ2-dependence results. The θ-dependence instead of θ2-dependence results make the scheme of testing the space noncommutativity via measuring such variances much easier to realize experimentally, well within the reach of nowadays technology.