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Acta Physica Sinica

QUANTUM NONDEMOLITION MEASUREMENTS IN DEGENERATE OPTICAL PARAMETRIC OSCILLATOR

WANG DAN-LING, GONG QI-HUANG, WANG KAI-GE, YANG GUO-JIAN, (1)北京大学物理系，人工微结构和介观物理国家重点实验室，北京 100871; (2)北京师范大学物理系，北京 100875

Published Jan 1, 2000• 0 citations
Publisher

Abstract

The knowledge about nonlinear quantum optics is applied to the study of the degenerate optical parametric oscillator as a quantum non-demolition (QND) measurement device. We find that the model can perform a perfect QND measurement at the threshold in the resonant case, and the optimum QND measurement occurs at the nonlinear double resonances in the detuning case.

DOI
10.7498/aps.49.1484

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The knowledge about nonlinear quantum optics is applied to the study of the degenerate optical parametric oscillator as a quantum non-demolition (QND) measurement device. We find that the model can perform a perfect QND measurement at the threshold in the resonant case, and the optimum QND measurement occurs at the nonlinear double resonances in the detuning case.
A quantum-nondemolition (QND) measurement is one which does not disturb the quantity it measures. Any measurement can be regarded as a QND measurement followed by an additional back-action which may disturb that quantity. By feeding back the measurement result to control the system dynamics, this back-action can always be eliminated in principle. A practical device based on homodyne measurement of the x quadrature of a cavity mode is investigated. First, a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ crystal is inserted in the cavity so that it becomes a degenerate parametric oscillator at threshold. Then the photocurrent is used to control coherent driving of the cavity, so as to give positive feedback with unit gain. This feedback, combined with the nonlinearity, turns the homodyne measurement into a QND measurement of x. The device can also be used to measure the x quadrature of a traveling wave, and gives near-perfect QND correlations over a large bandwidth. However, the quality of the measurement is badly degraded by even slightly inefficient photodetectors.
Unlike classical systems, the very act of observing quantum systems perturbs their behaviour. This introduces noise, which imposes limits on the knowledge that can be obtained through measurement. Certain measurement techniques, known generally as quantum non-demolition (QND) measurements, exist to circumvent this noise. An alternative method to evade backaction noise is to amplify the observable of interest above the noise. However, this generally leaves the system in a different state, and is therefore not considered a QND measurement. In this thesis, I examine the benefits of amplification for various kinds of measurement of mechanical harmonic oscillators which, at the micrometre and nanometre scale, comprise an emerging quantum technology. For this prototypical case, modulation of the spring constant, also known as parametric amplification, is a well-studied noiseless amplification technique. Using the theory of trajectories developed in the field of quantum optics, I show that a weak measurement combined with a detuned parametric drive achieves the same ends as strong QND measurement. Namely, it allows backaction-free observation of one quadrature of mechanical motion, and through this, quantum squeezing below the quantum zero-point motion. This equivalence is experimentally confirmed in the classical limit using an optically detected, electrically modulated cantilever. In addition, I analyse similar amplification enhanced techniques for quantum entanglement and quantum tomography. These results are applicable to research in quantum optomechanics and electromechanics, and can be translated to other kinds of quantum harmonic oscillators, such as microwave cavities.
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.
Many theoretical and experimental approaches to quantum entanglement in Optical Parametric Oscillators (OPO) concern the degenerate or the slightly non-degenerate cases where a single local oscillator can be used to measure quadrature correlations for the characterization of fluctuations below the Standard Quantum Limit (SQL) in the frequency domain. In the strongly non-degenerate case, alternative characterizations of quantum entanglement are needed. We provide evidence that correlation functions corresponding to coincidence measurements of the intensity difference between signal and idler fields should be able to assess quantum entanglement and at the same time be experimentally viable in the case of strongly non-degenerate OPO.