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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Quantum noise and quantum nondemolition measurements

Mark S. Hillery, Marlan O. Scully

Published Jun 15, 1982• 7 citations
Publisher

Abstract

We examine the effects of quantum noise in the readout of a proposed quantum non-demolition (QND) system. The equations of motion of the system are solved approximately both with and without noise. The effect of the noise upon the measurement accuracy of the system is determined and it is found that, in principle, the presence of quantum noise in the readout should not prevent one from measuring the amplitude of the oscillator to better than the standard quantum limit.

DOI
10.1103/physrevd.25.3137

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We examine the effects of quantum noise in the readout of a proposed quantum non-demolition (QND) system. The equations of motion of the system are solved approximately both with and without noise. The effect of the noise upon the measurement accuracy of the system is determined and it is found that, in principle, the presence of quantum noise in the readout should not prevent one from measuring the amplitude of the oscillator to better than the standard quantum limit.
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According to the Heisenberg uncertainty principle, if we measure one variable describing a physical system, we inevitably introduce noise into some other variable describing the same system. In practice, the situation is worse than that: measuring one variable usually introduces random noise into the very quantity we are measuring. It is possible in principle to make measurements, known as quantum non-demolition (or QND) measurements, which do not have this latter effect. A QND measurement may approach the ideal quantum measurement commonly encountered in quantum mechanics textbooks. Philippe Grangier and his co-workers at the Université Paris-Sud, at Orsay in France, have recently attempted to measure the intensity of a beam of light in this way (Phys. Rev. Len. (1991) 66 1418). Their experiment has shown that it is indeed possible to make a measurement which at least partially preserves the quantum mechanical state of the detected beam.
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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
Preface List of Illustrations Open Fundamental Questions of Limits to Information in the Quantum Measurement of a Single System Impossibility of Determining the Unknown Quantum Wavefunction of a Single System Quantum Nondemolition (QND) Measurements of a Single System Measurements without Entanglement of a Single Quantum System Adiabatic Measurements of a Single Quantum System Quantum Zeno Effect of a Single System Fundamental Quantum Limit to External Force Detection via Monitoring a Single Harmonic Oscillator (or Free Mass) Established Limits to Information in the Quantum Measurement of a Single System Bibliography Index.