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arXiv:quant-ph/9801053 · Physical Review A

Transverse-mode coupling in a Kerr medium

Jean-Michel Courty, Astrid Lambrecht

Published Dec 1, 1996• 3 citations
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Abstract

We analyze nonlinear transverse mode coupling in a Kerr medium placed in an optical cavity and its influence on bistability and different kinds of quantum noise reduction. Even for an input beam that is perfectly matched to a cavity mode, the nonlinear coupling produces an excess noise in the fluctuations of the output beam. Intensity squeezing seems to be particularly robust with respect to mode coupling, while quadrature squeezing is more sensitive. However, it is possible to find a mode whose quadrature squeezing is not affected by the coupling. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physreva.54.5243

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Annual Meeting Optical Society of America•Jan 1, 1985•1 citation
We analyze nonlinear transverse mode coupling in a Kerr medium placed in an optical cavity and its influence on bistability and different kinds of quantum noise reduction. Even for an input beam that is perfectly matched to a cavity mode, the nonlinear coupling produces an excess noise in the fluctuations of the output beam. Intensity squeezing seems to be particularly robust with respect to mode coupling, while quadrature squeezing is more sensitive. However, it is possible to find a mode whose quadrature squeezing is not affected by the coupling. \textcopyright{} 1996 The American Physical Society.
When a light beam interacts with Kerr medium inside an optical cavity, its quantum fluctuations are squeezed.1 One can show that perfect squeezing can be obtained close to the turning points of the bistability curve. In order to implement such a scheme, one needs perfect Kerr media (with no losses, infinite frequency bandwidth and no excess noise) that are not available to date.2 We study here a new kind of Kerr medium, in which the nonlinearity has a mechanical origin: if a mirror is free to move, the radiation pressure will induce a coupling between its position and the intensity of the light beam, thus modifying the optical path in an intensity-dependent way.
We investigate theoretically an optomechanical system composed of an optical mode and a mechanical mode interacting through first-order coupling and second-order coupling in the presence of a Kerr nonlinear medium. We study how the nonlinearities (second-order optomechanical coupling and Kerr nonlinearity) alter the optical output spectrum, optical quadrature squeezing and optomechanical entanglement. It is shown that the intensity of the output optical spectrum decreases drastically with an increase in second-order optomechanical coupling while it increases significantly with an increase in Kerr nonlinear parameter. More interestingly, by choosing suitable second-order optomechanical coupling and detuning of the optical cavity field, one can achieve strong squeezing of the cavity light field. Further, these nonlinearities play an important role in creating robust optomechanical entanglement between optical and mechanical modes. Hence, the presence of various nonlinearities in the system can be a good platform for achieving the squeezing of light and robust optomechanical entanglement which can be used in realizing better quantum optomechanical devices.
We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic ${\ensuremath{\chi}}^{(3)}$ medium in which self-phase- and cross-phase-modulation, as well as four-wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output-field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the orthogonally polarized vacuum mode, and show how this produces polarization squeezing.
Polarization squeezing [1] is attracting much attention in the last few years because of its potential applications in quantum information. We reconsider here the analysis of quantum fluctuations in dispersive optical bistability by generalizing the standard model in order to take into account fluctuations in the two orthogonal polarization components of the intracavity field, and not only in the pumped one as it is customary. In other words, we consider a relatively simple model for a vectorial Kerr cavity: The Kerr nonlinearity is the responsible for dispersive bistability, and two extra nonlinear terms, describing cross-phase modulation and four-wave mixing, couple the intense (pumped) intracavity field (with polarization parallel to that of the field injected in the cavity) with the orthogonally polarized mode. The weight of the new nonlinearities is controlled by the Maker-Terhune coefficients, which verily A + B!2 = 1 for an isotropic material, which we consider. This system exhibits a very rich variety of bifurcations [2], In this communication we describe the simplest results.
In this paper, we investigate the nonlinear optical properties and photon correlations in a cavity containing quantum wells and interacting with a third-order nonlinear medium. More precisely, we study the interaction of the photonic Kerr nonlinearity with polariton and dipolariton quasiparticles in thermal environments. The optical bistability, the intensity spectrum, and the squeezing spectrum of the transmitted radiation are analyzed. It is shown that the regime of the bistability is reached in the dipolariton cavity faster than attained by the polariton system. Furthermore, the increase of the coupling with the wells reduces the squeezing. More interestingly, it turns out that the additional interactions arising in the dipolariton cavity, between direct and indirect excitons, slow down the variation of the squeezing. As a consequence, dipolaritons offer a greater margin of squeezed light than polaritons, and also than the ${\ensuremath{\chi}}^{(3)}$ medium in the absence of quantum wells. Moreover, the dipolariton system is found to be much more robust against the bath temperature in the weak-coupling regime.
In optical fibers, nonlinear dispersion due to the same third-order susceptibility as that responsible for parametric mixing significantly alters the squeezing behavior in a traveling wave geometry, giving the squeezed quadrature an intensity dependent phase and reducing the overall squeezing. Phase noise is not squeezed at all. In the case of a fiber ring resonator, the nonlinear susceptibility will also lead to dispersive optical bistability and the squeezing will be strongly dependent on pump and sideband detuning. Yurke1 has analyzed squeezing due to backward four-wave mixing in a cavity, but the pump wave did not circulate in the cavity, and bistability was not dealt with. We have developed a theory of the resonant fiber ring interferometer, where the pump wave is near resonance with an interferometer mode and the circulating power is thereby enhanced. For perfect pump resonance and for frequencies corresponding to sideband resonance, the overall enhancement of the squeezing in the output mode compared to the traveling wave case is proportional to the square of the resonator finesse. The best squeezing in the output mode is always found for this condition of sideband resonance. The phase of the minimum noise quadrature is quite sensitive to both pump and sideband detuning. This feature may provide a means for avoiding excess thermal phase noise due to guided acoustic wave Brillouin scattering in the fiber itself. At the critical points for dispersive optical bistability in such a resonator and for sideband resonance (i.e., noise frequencies which are multiples of the resonator free spectral range), perfect squeezing of the output light is predicted. This result was also obtained previously for the case of degenerate mixing in a resonant cavity by Collett and Walls.2 Our current theory does not account for the reduction in squeezing due to the loss present in such a resonator.2 Since the loss is also enhanced by a factor of the resonator finesse, this is of some concern and will limit the maximum useful finesse for quantum noise squeezing. The major source of loss is the single-mode directional coupler, which for currently available technology is of the order of a few percent.