Quantum Dynamics of Kerr Optical Frequency Combs below and above Threshold: Spontaneous Four-Wave-Mixing, Entanglement and Squeezed States of Light

摘要

In this article, we use quantum Langevin equations to provide a theoreticalunderstanding of the non-classical behavior of Kerr optical frequency combswhen pumped below and above threshold. In the configuration where the system isunder threshold, the pump field is the unique oscillating mode inside theresonator, and triggers the phenomenon of spontaneous four-wave mixing, wheretwo photons from the pump are symmetrically up- and down-converted in theFourier domain. This phenomenon can only be understood and analyzed from afully quantum perspective as a consequence of the coupling between the field ofthe central (pumped) mode and the vacuum fluctuations of the various sidemodes.We analytically calculate the power spectra of the spontaneous emission noise,and we show that these spectra can be either single- or double peaked dependingon the parameters of the system. We also calculate as well the overallspontaneous noise power per sidemode, and propose simplified analyticalexpressions for some particular cases. In the configuration where the system ispumped above threshold, we investigate the phenomena of quantum correlationsand multimode squeezed states of light that can occur in the Kerr frequencycombs originating from stimulated four-wave mixing. We show that for allstationary spatio-temporal patterns, the side-modes that are symmetricalrelatively to the pumped mode in the frequency domain display quantumcorrelations that can lead to squeezed states of light. We also explicitlydetermine the phase quadratures leading to photon entanglement, andanalytically calculate their quantum noise spectra. We finally discuss therelevance of Kerr combs for quantum information systems at opticaltelecommunication wavelengths, below and above threshold.