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Physical Review A

Quantum nondemolition measurements using a fully quantized parametric interaction

M. J. Gagen, Gerard J Milburn

Published Jun 1, 1991• 5 citations
Publisher

Abstract

A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.

DOI
10.1103/physreva.43.6177

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AIP conference proceedings•Jan 1, 1989•0 citations
A quantum nondemolition measurement based on a three-mode interaction mediated by a second-order nonlinear susceptibility is discussed. All three modes are treated quantum mechanically. The signal field is taken as one of the three modes and the probe field is the combined field in the other two modes. If the probe system is initially in a number state, the interaction between the signal and probe is equivalent to that between a harmonic oscillator and an angular momentum system. Photon counting on the probe field realizes a quantum nondemolition measurement of the square of a quadrature phase amplitude of the signal, and thus provides a direct measurement of second-order squeezing.
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.
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.
The quantum nondemolition (QND) measurement is one of the most studied quantum measurement procedures. Usually, such a process involves the coupling of a single system of interest, called signal, with a single probe system, so that the relevant information in the signal system is indirectly measured by observing the probe system. Here we extend the concept of quantum nondemolition interaction to the cases in which the signal and the probe systems are each one multipartite continuous-variable system. Specifically, we propose a general scheme that performs the multipartite QND interactions, relying on beam-splitter couplings between the signal and probe modes with only two ancillary modes prepared offline in squeezed states. The scheme is also composed of homodyne detection and feedforward modulation. The ancillary modes are detected in the process, providing photocurrents for postmodulation of the output systems, as well as sufficient information to calculate genuine multipartite entanglement conditions of the input systems and to monitor similar conditions of the output systems.
A fully quantum-mechanical Heisenberg description of the quantum-nondemolition measurements via soliton collision in an optical fiber is provided. Solutions to the equations of motion for meaningful soliton collective operators such as photon number, phase, position, and frequency (momentum) are applied to quantifying the error of inference of photon number and frequency of the signal soliton by performing a measurement on the probe soliton. A detection method based on measuring a four-component quadrature amplitude is proposed and proved to give the best accuracy.