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Physical Review A

State reduction in quantum-counting quantum nondemolition measurements

Gerard J Milburn, Daniel F. Walls

Published Jul 1, 1984• 76 citations
Publisher

Abstract

We show how quantum-counting quantum nondemolition measurements may be made using standard demolition counting techniques (e.g., photoelectron counting) for two oscillators coupled via a four-wave-mixing interaction. The analysis reveals how the state of one oscillator is reduced to a number eigenstate during the irreversible demolition counting process occurring in another coupled oscillator.

DOI
10.1103/physreva.30.56

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We show how quantum-counting quantum nondemolition measurements may be made using standard demolition counting techniques (e.g., photoelectron counting) for two oscillators coupled via a four-wave-mixing interaction. The analysis reveals how the state of one oscillator is reduced to a number eigenstate during the irreversible demolition counting process occurring in another coupled oscillator.
A specific measurement model based on quantum nondemolition monitoring of oscillator quanta is used to illustrate the essential elements of the quantum theory of measurement, viz., state reduction and existence of a ``pointer basis,'' recently discussed by Zurek. The form of the interaction between the meter and its environment determines the system observable recorded by the meter. In our model this quantity is the square of the oscillator's quanta. The corresponding pointer basis states are the meter coherent states. The more accurate the measurement the more excited (and classical) these states become. We show explicitly that the state reduction of the system during measurement is due to nonunitary evolution resulting from the meter-environment coupling. A particular realization of the environment as a photoelectron counter is discussed.
We consider making quantum nondemolition measurements on a harmonic oscillator by coupling it to an oscillator readout system using a four-wave-mixing interaction. The quantum nondemolition variable of interest appears as a nonlinear function of the number operator. It has the form ${\stackrel{^}{D}}_{1}(t)=cos(\ensuremath{\chi}{a}^{\ifmmode\dagger\else\textdagger\fi{}}at)$. A sequence of measurements of this operator may be made with completely predictable results. The possible use of this system to detect gravitational radiation is suggested.