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Quantum Optics Journal of the European Optical Society Part B

Squeezing and quantum noise correlations in dispersive two-photon optical bistability

Philippe Grangier, Jean-François Roch

Published Sep 1, 1989• 19 citations
Publisher

Abstract

Presents an analysis of a two-photon double-beam bistable device, in the dispersive and high-finesse limits. The expressions for the mean fields inside the cavity are given above the destabilization thresholds, and quantum fluctuations of the outcoming fields are analyzed below these thresholds. It appears that this device yields several new quantum noise reduction schemes, which are closely related to the mean fields behaviour.

DOI
10.1088/0954-8998/1/1/003

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Presents an analysis of a two-photon double-beam bistable device, in the dispersive and high-finesse limits. The expressions for the mean fields inside the cavity are given above the destabilization thresholds, and quantum fluctuations of the outcoming fields are analyzed below these thresholds. It appears that this device yields several new quantum noise reduction schemes, which are closely related to the mean fields behaviour.
A Bose-Einstein condensate of ultracold atoms inside the field of a laser-driven optical cavity exhibits dispersive optical bistability. We describe this system by using mean-field approximation and by analyzing the correlation functions of the linearized quantum fluctuations around the mean-field solution. The entanglement and the statistics of the atom-field quadratures are given in the stationary state. It is shown that the mean-field solution, that is, the Bose-Einstein condensate, is robust against entanglement generation for most of the phase diagram.
The dynamics of the quantum-statistical properties of the radiation of an atom in a cavity interacting with an external coherent field is investigated. A high level of quantum fluctuations of the field in the cavity is shown to destroy optical bistability in the multiatom case. Photon-number fluctuations and the spectral dispersion of the canonically conjugate quadratures of the field inside and outside a cavity are calculated. It is found that in contrast to the multiatom case quadrature squeezing and squeezing of the radiation intensity of a single atom are negligible inside and outside the cavity.
It is shown that a laser with a two-photon saturable absorber exhibits a phase instability similar to that of two-photon optical bistability. The authors calculate the spectrum of the intensity fluctuations in the output field under conditions of exact resonance between the amplifier and the absorber. In the bad-cavity limit the relevant part of the spectrum assumes a simple Lorentzian form; as the phase-instability threshold is approached, the reduction of quantum noise becomes perfect for small frequencies.
We report the observation and theoretical interpretation of two-photon double-beam optical bistability, where the nonlinearity is obtained in a two-photon transition in a sodium atomic beam. The experimental results, obtained in the dispersive regime, are compared with a simple crossed-phase-modulation model, and also with a numerical solution of the interaction between the cavity fields and three-level atoms, using the optical Bloch equations. For a wide range of parameters, both models agree with the experimental results. Oscillatory regimes may also appear, in agreement with the predictions of the complete model.