QUANTUM PROPAGATION IN A KERR MEDIUM - LOSSLESS, DISPERSIONLESS FIBER

Intense light beams propagating in a lossless, dispersionless, single- mode optical fiber are subject to the Kerr effect, i.e., to the intens ity-dependent refractive index of the fiber's fused-silica core. Class ically, Kerr-effect-induced self-phase modulation (SPM) can be used fo r spectral broadening of a picosecond pulse for grating-pair pulse com pression down to femtosecond duration. Quantum mechanically, Kerr-effe ct-induced four-wave mixing (FWM) has been used to produce squeezed-st ate light. We present a quantum propagation theory for a lossless, dis persionless fiber with the Kerr nonlinearity. The theory includes clas sical SPM and quantum FWM within their regions of validity. It introdu ces a material time constant for the Kerr interaction, limiting the qu antum phase shifts caused by the broadband zero-point fluctuations tha t accompany any input field, to develop a coarse-grained time multitem poral mode field analysis. Explicit expressions are obtained for the f irst and the second output-field moments when the fiber's input field is in an arbitrary Gaussian state. These results are used to obtain ho modyne-detection noise spectra, which are employed, in turn, to seek e xperimentally accessible manifestations of the Kerr time constant.