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Physical Review A

Quantum-nondemolition schemes to measure quadrature phases using intracavity harmonic generation

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

Published Aug 1, 1993• 13 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.48.1532

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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.
We analyze schemes for performing quantum nondemolition (QND) measurements in optical cavities. We consider three schemes: (1) measurement of a quadrature phase amplitude using a parametric process, (2) measurement of a quadrature phase amplitude using the optical Kerr effect in a nonlinear fiber, and (3) measurement of the photon number also using the Kerr effect in a fiber. We show that in the second scheme an enhancement of the QND effect may be obtained by making the cavity finesse for the signal larger than that for the probe.
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.
A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.
We consider a scheme for quantum nondemoliton (QND) measurements involving a cavity containing a Faraday rotator and a nonlinear crystal for (frequency degenerate) parametric downconversion into orthogonal polarizations. For the case of nondepletion of the pump field we analyze the coupled equations for the quadrature amplitudes of the fields using both semiclassical and quantum mechanical approaches. We show that when the magnitudes of the coupling coefficients κ of the crystal and σ of the Faraday rotator are appropriately chosen, the Hamiltonian of the system is of an ideal QND form for the intracavity field in the absence of dissipation. With the inclusion of cavity damping in the form of a single mirror of finite transmissivity, we demonstrate that information in the quadrature amplitude X1 of one polarization of the incident field can be measured (in a QND sense) by monitoring the quadrature amplitude Y2 of the orthogonal polarization.