Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

We introduce the coordinate-dependent one- and two-mode squeezingtransformations and discuss the properties of the corresponding one-andtwo-mode squeezed states. We show that the coordinate-dependentone-and two-mode squeezing transformations can be constructed by the combination of two transformations, a coordinate-dependent displacementfollowed by the standard squeezed transformation. Such a decomposition turns a nonlinear problem into a linear one because all the calculationsinvolving the nonlinear one- and two-mode squeezed transformation have beenshown to be able to reduce to those only concerning the standard one-and two-mode squeezed states.