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arXiv:1109.5627 · Physical Review A

Critical Kerr nonlinear optical cavity in the presence of internal loss and driving noise

A. Thüring, Roman Schnabel

Published Sep 20, 2011• 7 citations
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Abstract

We theoretically analyze the noise transformation of a high-power continuous-wave light field that is reflected off a critical Kerr nonlinear cavity (KNLC). Our investigations are based on a rigorous treatment in the time domain. Thereby, realistic conditions of a specific experimental environment including optical intracavity loss and strong classical driving noise can be modeled for any KNLC. We show that, even in the presence of optical loss and driving noise, considerable squeezing levels can be achieved. We find that the achievable squeezing levels are not limited by the driving noise but solely by the amount of optical loss. Amplitude-quadrature squeezing of the reflected mean field is obtained if the KNLC's operating point is chosen properly. Consistently, a KNLC can provide a passive purely optical reduction of laser-power noise as experimentally demonstrated in Khalaidovski et al. [Phys. Rev. A 80, 053801 (2009)]. We apply our model to this experiment and find good agreement with measured noise spectra.

DOI
10.1103/physreva.84.033839

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We theoretically analyze the noise transformation of a high-power continuous-wave light field that is reflected off a critical Kerr nonlinear cavity (KNLC). Our investigations are based on a rigorous treatment in the time domain. Thereby, realistic conditions of a specific experimental environment including optical intracavity loss and strong classical driving noise can be modeled for any KNLC. We show that, even in the presence of optical loss and driving noise, considerable squeezing levels can be achieved. We find that the achievable squeezing levels are not limited by the driving noise but solely by the amount of optical loss. Amplitude-quadrature squeezing of the reflected mean field is obtained if the KNLC's operating point is chosen properly. Consistently, a KNLC can provide a passive purely optical reduction of laser-power noise as experimentally demonstrated in Khalaidovski et al. [Phys. Rev. A 80, 053801 (2009)]. We apply our model to this experiment and find good agreement with measured noise spectra.
Quantum-noise reduction to levels nearly 1 dB below the standard quantum limit are reported for light frequencies near an atomic-sodium resonance. This squeezed light is generated in an optical confocal cavity using four-wave mixing due to the atomic-sodium resonance nonlinearity. Squeezed light exits the cavity through a partially reflecting mirror and is detected outside the cavity with a balanced homodyne detector. Experimental details are described for minimizing losses in the atomic beam and detection apparatus. Frequency jitter due to the pump laser also plays a key role in the limits for noise reduction. A wideband phenomenological model is used to analyse the results. Good agreement between this model and the experimental results is obtained. A full quantum model also agrees with the results and predicts even larger squeezing at higher pump intensities. Prospects for achieving this larger-noise-reduction regime are good.
We introduce a model of squeezing and noise reduction in the Kerr effect that accounts for noise in all quadratures of the driving field. Consequently we show that Kerr squeezing is much more sensitive to driving noise than squeezing produced by second harmonic generation (SHG). We experimentally demonstrate this sensitivity using a nonlinear system that tunes between strong classical SHG and Kerr behaviours. Whilst the system experiences strong squeezing in the SHG limit, it experiences no squeezing in the Kerr limit, although it does experience strong classical noise reduction, or `classical squeezing'.
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Quantum noise in a model of singly resonant frequency doubling including phase mismatch and driving in the harmonic mode is analyzed. The general formulae about the fixed points and their stability as well as the squeezing spectra calculated linearizing around such points are given. The use of a nonlinear normalization allows to disentangle in the spectra the dynamic response of the system from the contributions of the various noisy inputs. A general ``reference'' model for one-mode systems is developed in which the dynamic aspects of the problem are not contaminated by static contributions from the noisy inputs. The physical insight gained permits the elaboration of general criteria to optimize the noise suppression performance. With respect to the squeezing in the fundamental mode the optimum working point is located near the first turning point of the dispersive bistability induced by cascading of the second order nonlinear response. The nonlinearities induced by conventional crystals appear enough to reach it being the squeezing ultimately limited by the escape efficiency of the cavity. In the case of the harmonic mode both, finite phase mismatch and/or harmonic mode driving allow for an optimum dynamic response of the system something not possible in the standard phase matched Second Harmonic Generation. The squeezing is then limited by the losses in the harmonic mode, allowing for very high degrees of squeezing because of the non-resonant nature of the mode. This opens the possibility of very high performances using artificial materials with resonantly enhanced nonlinearities. It is also shown how it is possible to substantially increase the noise reduction and at the same time to more than double the output power for parameters corresponding to reported experiments.
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We discuss different approaches to the generation of bright amplitude-squeezed light using second-order nonlinear effects in optical cavities. A 0.2 mW beam at 1064 nm exhibiting 4 dB squeezing has been generated using a phase-sensitive type-I parametric amplifier pumped by a frequency-doubled Nd:YAG laser. In applying frequency-doubling processes to the generation of amplitude-squeezed light, the appearance of parasitic parametric oscillation must be considered. This effect has been observed in a singly-resonant frequency doubler. We also describe recent developments in optical cavity design for doubly-resonant frequency-doubling. Finally, we show theoretically that phase-mismatched second-harmonic generation in an optical cavity can be employed to generate a strong effective Kerr nonlinearity. This system appears promising for achieving optical bistability and for generating squeezed light of high power. Keywords: Non-classical light, squeezed light, amplitude squeezing, nonlinear op...