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Physical Review Letters

Quantum-nondemolition measurements via second-harmonic generation

M.J. Dance, Matthew J. Collett, Daniel F. Walls

Published Mar 4, 1991• 23 citations
Publisher

Abstract

In this Letter, we present a theoretical investigation into the quantum-nondemolition properties of a system which utilizes intracavity second-harmonic generation. The results show a significant improvement over the quantum-nondemolition properties of other systems studied previously, and should be accessible to experiment.
DOI
10.1103/physrevlett.66.1115

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In this paper, we present a theoretical investigation into the quantum-nondemolition (QND) properties of a system which utilizes intracavity harmonic generation. It is found that a nearly ideal QND measurement of the amplitude of a signal can be performed using second-harmonic generation, while subharmonic generation can be utilized to give a nearly ideal QND measurement of a phase. The results show a significant improvement over the QND properties of other systems studied previously and should be accessible to experiment.
Using the full nonlinear equations of motion, we calculate the quantum-nondemolition (QND) correlations for the traveling-wave second-harmonic generation. We find that, after a short interaction length, these are qualitatively different from results calculated previously using a linearized fluctuation analysis. We demonstrate that, although individual QND criteria can be very good in certain regions, there is no region where all three of the standard criteria are perfect, as has previously been claimed. We also show that only the amplitude quadrature of the output field can be considered as a QND quantity, with the phase quadrature not satisfying all the criteria.
Second-harmonic generation (SHG) in doubly resonant optical resonators (resonant for the pump and for the harmonic wave) is a subject rich in outstanding challenges: the demonstration of self-pulsing, in which the intracavity field amplitudes undergo a Hopf bifurcation to a stable limit cycle,1 and chaos; the generation of near-perfect squeezing near but below the self-pulsing threshold; the generation of squeezed radiation in the self-pulsing regime; and the demonstration of quantum nondemolition measurements.