Squeezing Effects in the Sum and Difference of the Field Amplitude in the Raman Process

Abstract

Sum and difference squeezing of the field amplitude are higher-order squeezing effects. These effects are studied in the Raman process under the short-time approximation based on a fully quantum mechanical approach. It is shown that for uncorrelated modes, the normal squeezing in the sum and difference-frequency field depends on the sum and difference squeezing of input field modes respectively, which can generate normal squeezing in the sum and difference-frequency field mode. All the possibilities for obtaining sum and difference squeezing in two modes and its dependence on squeezing of individual field modes are investigated. We have also shown that if the high-frequency mode is in a coherent state and the low-frequency mode is squeezed, the field state will be difference squeezed if the amplitude of the high-frequency mode is large enough; otherwise the state may or may not be difference squeezed. If both modes are squeezed, then the state may or may not be difference squeezed. These higher-order squeezing effects are useful in the production of squeezing in the Raman process.

Squeezing in the Difference of the Fields in Degenerate Four-and Five-wave Interaction Processes

“…Garcia Fernandez et al [38] and Mishra et al [39,40] have worked on higher-order nonclassical states in single-mode and their use in detecting nonclassical light. Further, another type of higher-order squeezing, called sum and difference squeezing was proposed by Hillery [41] for the two modes and generalized to include three modes [42] as well as an arbitrary number of modes for sum and difference squeezing [43][44][45]. Prakash et al [46] studied enhancement and generation of sum squeezing in two-mode light in mixing with coherent light using a beam splitter.…”

Sum Squeezing of the Field Amplitude in Frequency Upconversion Process

“…Another type of seminal paper on higher-order squeezing, called sum and difference squeezing, was proposed by Hillery [34] for the two modes which are in fact the simplest versions of multimode higher-order squeezing. ese concepts have been generalized to include three modes for sum and difference squeezing [35][36][37] as well as an arbitrary number of modes for sum and difference squeezing [38][39][40]. Furthermore, more recently, Prakash and Shukla [41], Mukherjee et al [42], and Mukherjee et al [43] have also studied and reported about sum and difference squeezing and their detections in some nonlinear optical processes.…”