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Acta Optica Sinica

The fluctuation spectra of signal mode in non-degenerate parametric down-conversion

Kunchi Peng

Published Jan 1, 1993• 0 citations
OpenAlex

Abstract

Using the linearized langevin equations and the spectral matrix, we discuss the fluctuation spectra of signal mode in the output field from a F-P cavity below or above threshold for the process of non-degenerate parametric down-conversion. It is indicated that the signal and idler modes usually are in minimum-uncertainty states.

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Using the linearized Langevin equations and spectral matrix, we calculated the squeezing spectra of the coupled mode in the output field for the process of parametric down-conversion with frequency degenerate but polarizations non-degenerate. The squeezing as a function of the driving field is obtained. We compare our results with that of the semiclassic and indicate that it is possible to generate a two-mode squeezed state with large amplitudes. The quantum correlation between the signal and the idler modes is also discussed.
A quantum analysis of the intensity fluctuations is given for the nondegenerate parametric oscillator both above and below threshold. Theoretical analysis and experiments by Heidmann, Horowicz, Reynaud, Giacobino, and Fabre [Phys. Rev. Lett. 59, 2555 (1987)] have shown that a noise suppression below the vacuum level is possible in the difference of the intensities of the signal and idler modes. The effect of nonequal cavity decay rates and intracavity losses is shown to modify significantly the fluctuation spectra for the difference in the intensity of the signal and idler beams. The results of exact nonlinear solutions for the internal cavity modes are discussed. We demonstrate that a very sensitive absorption detector may be made by operating the oscillator near threshold.
A full quantum treatment about the process of parametric down-conversion with frequency degenerate but polarization non-degenerate in an optical parametric oscillator (OPO) cavity is presented. Using the linearized Langevin equations and spectral matrix, we calculated the squeezing spectra of the coupled mode in the output field. The squeezing as a function of driving field and detection frequency is obtained. The results obtained, which are compared with those found semiclassically by Reynaud et al. , indicate that it is possible to generate a two-mode coherent squeezed state with large amplitude. The quantum correlation between the signal and the idler modes is also discussed. It is shown that there is an inseparable relationship between the two-mode squeezing and the intermode quantum correlation.
Using the quantum theory of a non-degenerate parametric amplifier, we discuss the phase correlations between signal and idler modes well above threshold. Particular attention is paid to the influence which fluctuation of the driving laser has on these correlations. We point out that the signal and idler mode phase correlation may be tuned by control of the driving laser field intensity and linewidth. For coherent driving, the mode phases are negatively cross-correlated. We stress the qualitative importance of these mode correlations for a class of two-photon resonant excitation experiments in atoms. In particular, the non-degenerate parametric oscillator represents a concrete model of a source with negatively cross-correlated phase fluctuations.
SUMMARY Parametric processes in the interaction of electromagnetic field with a medium in an optical cavity are well known to produce states of light with nonclassical properties. The quantum correlations between these states can be employed for a realization of an EinsteinPodolsky-Rosen (EPR) paradox [l], in the original formulation using continuous variables, as proposed [2] and experimentally demonstrated [3] in the case of Nondegenerate Parametric Amplification below threshold. In this paper we study EPR-like behaviour between the signal and idler fields emitted by a degenerate optical parametric oscillator (OPO) above threshold; these fields, generated by conversion of a pump photon of frequency 2w0 in two photons of frequency w. , are spatially separated in the far field, showing non-local quantum correlations. The system is described by the full Hamiltonian for the operators associated with the pump and signal fields; the optical cavity introduces proper damping constants and corresponding vacuum field operators [4,5]. Above the threshold for the generation of the signal field, we consider the fluctuations in the intensity difference and in the phase sum of the signal beams, which are related to their degree of mutual correlation. By linearizing around the stationary state, we calculate the spectral variances of these quantities (i.e. the Fourier transform of the two time correlation functions). The Heisenberg uncertainty principle sets a lower limit to the product of the spectral variances for the fluctuations in the intensity and in the phase of each individual signal field; by using the idler beam to infer results of measurements on the correlated signal beam, we have an EPR paradox if the product of the spectral variances for the fluctuations in the intensity difference and phase sum of the fields, is below the uncertainty limit. This feature is apparent for a wide interval around zero frequency in the far field of the active OPO system, depending on the parameter space; in particular there is maximum correlation between signal beams, and therefore maximum breaking of the uncertainty limit, if the damping constant of the signal field is larger than that of the pump field.