Raman-effect induced noise limits on χ⁽³⁾ parametric amplifiers and wavelength converters

The non-zero response time of the Kerr (χ⁽³⁾) nonlinearity determines the quantum-limited noise figure of χ⁽³⁾ parametric amplifiers and wavelength converters. This non-zero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss. The effect of this excess noise on the noise figure of the amplifier can be significant. We derive analytical expressions for this quantum-limited noise figure in the case of non-degenerate phase-insensitive operation of a χ⁽³⁾ parametric amplifier and show excellent agreement with experiment without any fitting parameter. We also derive analytical expressions for the quantum limited noise figure for χ⁽³⁾-based wavelength converters.