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Quantum Nondemolition Schemes using Second Order Nonlinearities

Robert M. Shelby, M. D. Levenson

Published Jul 18, 1988• 0 citations
OpenAlex

Abstract

Conventional devices for measuring the amplitude of a light wave absorb the light, thus destroying it. Recently, quantum nondemolition (QND) methods based on the optical Kerr effect have been shown capable of measuring optical amplitude fluctuations with near quantum-limited sensitivity.1 In these experiments, amplitude fluctuations of a signal beam are transferred to the phase fluctuation quadrature of a probe beam which co-propagates with the signal beam, by the intensity-dependent refractive index, without absorption of the signal beam. A pure Kerr nonlinearity can cause only phase modulation of the light wave, and the amplitude of the signal wave is preserved. Such methods should more properly be called back-action evading measurement schemes since the quantity being measured is not perturbed by the back-action that quantum mechanics requires for any measurement. The signal-to-noise ratio achieved in these experiments was limited by the small magnitude of the Kerr nonlinearity relative to the excess phase noise imposed on the probe beam by thermal light scattering processes in the glass fibers that were employed.

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Conventional devices for measuring the amplitude of a light wave absorb the light, thus destroying it. Recently, quantum nondemolition (QND) methods based on the optical Kerr effect have been shown capable of measuring optical amplitude fluctuations with near quantum-limited sensitivity.1 In these experiments, amplitude fluctuations of a signal beam are transferred to the phase fluctuation quadrature of a probe beam which co-propagates with the signal beam, by the intensity-dependent refractive index, without absorption of the signal beam. A pure Kerr nonlinearity can cause only phase modulation of the light wave, and the amplitude of the signal wave is preserved. Such methods should more properly be called back-action evading measurement schemes since the quantity being measured is not perturbed by the back-action that quantum mechanics requires for any measurement. The signal-to-noise ratio achieved in these experiments was limited by the small magnitude of the Kerr nonlinearity relative to the excess phase noise imposed on the probe beam by thermal light scattering processes in the glass fibers that were employed.
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.
To try to demonstrate a quantum nondemolition (QND) measurement of photon number,1 we built a nonlinear interferometer system with a 10-km polarization-maintaining fiber. (In theory, this fiber length is nearly optimum for 1.5-μm operation.) The optical Kerr effect allows a signal beam intensity to change a probe beam phase, which can then be read out by the interferometer. A modified ring interferometer structure and feedback stabilization enabled the 1,32-μm probe to read the intensity of the 1.06-μm signal beam. We measured a χ(3) value in this fiber of3.6× 10-33(1.4×10-33)MKS when the polarization of the signal beam is coincident with (perpendicular to) that of the probe beam. The interferometer output spectrum displayed large noise peaks due to guided acoustic-wave Brillouin scattering (GAWBS)2 in the fiber. GAWBS was also observed in 5-km conventional single-mode fibers in various interferometer configurations. The coexistence of two different kinds of GAWBS (polarized and depolarized) makes it particularly difficult to obtain QND measurements. We conclude that a QND measurement system free from GAWBS noise requires differential phase detection of two pulses having the same polarization state.
Quantum non-demolition (QND) measurements are of great interest in recent years as a method to increase the information capacity of communication systems. Common implementations of QND measurements in optical fiber are based on the Kerr effect: a probe beam acquires phase modulation which mimics the amplitude modulation of a signal beam. This phase is typically small and needs to be measured at high frequencies for practical fiber-optic communication systems. Here we present a self reflexive interferometer scheme adequate for this kind of measurements and describe its performance. Using this system we achieved fairly open eye-diagrams at 140 Mbit/sec.
This paper proposes a quantum nondemolition measurement scheme for the photon number. The signal and probe optical waves interact via the optical Kerr effect. The optical phase of the probe wave is selected as the readout observable for the measurement of the photon number of the signal wave. The measurement accuracy \ensuremath{\Delta}n and the imposed phase noise \ensuremath{\Delta}\ensuremath{\varphi} of the signal wave satisfy Heisenberg's uncertainty principle with an equality sign, 〈(\ensuremath{\Delta}n)2{)}^{2})2〉〈(\ensuremath{\Delta}\ensuremath{\varphi})2{)}^{2})2〉=(1/4). .AE