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arXiv:quant-ph/0203097 · Physical Review A

Optimized quantum nondemolition measurement of a field quadrature

Matteo G. A. Paris

Published Dec 14, 2001• 9 citations

Abstract

We suggest an interferometric scheme assisted by squeezing and linear feedback to realize the whole class of field-quadrature quantum nondemolition measurements, from Von Neumann projective measurement to a fully nondestructive noninformative one. In our setup, the signal under investigation is mixed with a squeezed probe in an interferometer and, at the output, one of the two modes is revealed through homodyne detection. The second beam is then amplitude-modulated according to the outcome of the measurement, and finally squeezed according to the transmittivity of the interferometer. Using strongly squeezed or antisqueezed probes respectively, one achieves either a projective measurement, i.e., homodyne statistics arbitrarily close to the intrinsic quadrature distribution of the signal, and conditional outputs approaching the corresponding eigenstates, or a fully nondestructive one, characterized by an almost uniform homodyne statistics, and by an output state arbitrarily close to the input signal. By varying the squeezing between these two extremes, or simply by tuning the internal phase shift of the interferometer, the whole set of intermediate cases may also be obtained. In particular, an optimal quantum nondemolition measurement of quadrature may be achieved, which minimizes the information gain versus state disturbance tradeoff.

DOI: 10.1103/physreva.65.012110

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The quantum effects on a cavity mode of the electromagnetic field caused by measuring one of its quadrature components is analyzed. We consider three measurement schemes: an intracavity quantum-nondemolition coupling to another mode, simple homodyne detection, and balanced homodyne detection. It is shown that, for suitable initial conditions, the first scheme has an effect which approaches that of a projective collapse of the state vector for long measurement times. However, the two homodyne schemes (which are shown to be equivalent for large local-oscillator amplitudes) do not approximate a projective measurement in any limit. In particular, it is shown that homodyne measurement cannot produce a squeezed state from a classical initial state. All three schemes are analyzed in terms of ``quantum trajectories'' which link measurement theory with stochastic quantum-jump processes.

We present the quantum theory of optical cavity feedback mediated by homodyne detection, with an arbitrary time delay. We apply this theory to a system with nonclassical dynamics, a sub-Poissonian pumped laser. By using the feedback to phase lock the laser it is possible to produce output light which exhibits perfect quadrature squeezing on resonance, rather than just sub-Poissonian intensity statistics. However, we also show that feedback mediated by homodyne detection (or any other extracavity measurement) cannot produce nonclassical light unless the cavity dynamics can do so without feedback. Furthermore, in systems which already exhibit squeezing, such feedback can only degrade the squeezing in the output. With feedback mediated by an intracavity measurement, these theorems do not apply. We show that an (admittedly unrealistic) intracavity quantum nondemolition quadrature measurement allows arbitrary squeezing to be produced by controlling the amplitude of a coherent driving field.