Raman-noise-induced quantum limits for χ⁽³⁾ nondegenerate phase-sensitive amplification and quadrature squeezing

We present a quantum theory of nondegenerate phase-sensitive parametric amplification in a χ⁽³⁾ nonlinear medium. The nonzero response time of the Kerr (χ⁽³⁾) nonlinearity determines the quantum-limited. noise figure of the χ⁽³⁾ parametric amplification, as well as the limit on quadrature squeezing. This nonzero response time of the nonlinearity requires coupling of the parametric process to a molecular vibration phonon bath, causing the addition of excess noise through spontaneous Raman scattering. We present analytical expressions for the quantum-limited noise figure of frequency nondegenerate and frequency degenerate χ⁽³⁾ parametric amplifiers operated as phase-sensitive amplifiers. We also present results for frequency nondegenerate quadrature squeezing. We show that our nondegenerate squeezing theory agrees with the degenerate squeezing theory of Boivin and Shapiro as degeneracy is approached. We have also included the effect of linear loss on the phase-sensitive process.