Quantum noise in parametric amplification under phase-mismatched conditions

Kyo Inoue

Phase-sensitive amplification (PSA) is a particular type of optical parametric amplification (OPA) that features a low-noise property such that the quantum-limited noise figure is 0 dB. The PSA operation is typically achieved when the signal and idler spectra are degenerate in optical parametric interactions, i.e., the degenerate OPA condition. However, for a spectrally broadened incident light, these two spectra can be partially degenerate. The present work investigates the noise property of OPA in such conditions in terms of quantum mechanics. The results quantitatively indicate the intermediate properties between PSA and phase-insensitive amplification.

Izo I. Abram, Juan Ariel Levenson

Kyo Inoue

Wavelength dependence of quantum noise in nondegenerate phase-sensitive amplification in an optical fiber, where signal and its phase-conjugated idler lights are incident into a fiber together with pump light, is theoretically investigated. An analytical formula of the quantum-limited noise figure, that takes Raman scattering into account as well as parametric amplification, is derived based on full quantum mechanical treatment. Using the obtained formula, a calculation example of the noise figure spectrum is also presented, where the pump light phase is adjusted so that the signal gain is maximum at a phase-matched wavelength, supposing multichannel amplification.

B. Schr�der

David D. Crouch

This thesis is primarily a theoretical study of degenerate parametric amplification as a means of generating squeezed-state light. i) A wideband traveling-wave formalism is developed for analyzing quantum mechanically a degenerate parametric amplifier. The formalism is based on spatial differential equations — spatial Langevin equations — that propagate temporal Fourier components of the field through the nonlinear medium. In addition to the parametric nonlinearity, the Langevin equations include absorption and associated fluctuations, dispersion, and pump quantum fluctuations. The dominant effects of dispersion and pump quantum fluctuations on the squeezing produced by a degenerate parametric amplifier are analyzed. ii) The wideband formalism of i) is used to carry out a more detailed analysis of the effects of phase mismatching. With the assumption of a lossless medium and a classical pump, we find that parametric amplification is capable of generating squeezed-state light over a wide band if materials with large χ(2) nonlinearities can be found, and that the squeezing bandwidth can be enhanced by phase mismatching away from degeneracy. iii) We consider again the effect of pump quantum fluctuations on the squeezing produced by parametric amplification. We perform discrete-mode calculations for a parametric amplifier with a quantum pump, and discuss some of the limitations of calculations of this sort in quantum optics. We derive stochastic differential equations (SDEs) for one- and two-mode parametric amplifiers, and from them obtain an iterative solution showing that pump quantum fluctuations impose a limitation on the degree of squeezing obtainable from a parametric amplifier. iv) A possible application of squeezing is considered; in particular, we study the effects of squeezing the intracavity noise in a laser oscillator. We solve the classical noise problem of a realistic laser model by making a bold — and possibly unrealizable — assumption, that the in-phase and quadrature Langevin sources which are responsible for the "noisiness" of the laser can be squeezed. We show that the effect of squeezing the in-phase quadrature is to reduce the phase noise, including the linewidth, of the laser but, due to amplitude-phase coupling, not to eliminate them altogether.

Éric Lantz, F. Devaux, A. Mosset