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Optics Letters

Nonunity gain quantum nondemolition measurements based on measurement and repreparation

Jessica Schneider, O. Glöckl, Gerd Leuchs, Ulrik L. Andersen

Published Aug 9, 2006• 1 citation
Publisher

Abstract

We demonstrate experimentally a nonunity gain quantum nondemolition measurement based on a simple homodyne measurement and recreation strategy. Although the output state is an amplified version of the input state, the device meets standard criteria for QND measurements: the transfer coefficient was measured to 1.78, and the conditional variance was measured to 0.66.

DOI
10.1364/ol.31.002628

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We demonstrate experimentally a nonunity gain quantum nondemolition measurement based on a simple homodyne measurement and recreation strategy. Although the output state is an amplified version of the input state, the device meets standard criteria for QND measurements: the transfer coefficient was measured to 1.78, and the conditional variance was measured to 0.66.
A quantum-nondemolition (QND) measurement is one which does not disturb the quantity it measures. Any measurement can be regarded as a QND measurement followed by an additional back-action which may disturb that quantity. By feeding back the measurement result to control the system dynamics, this back-action can always be eliminated in principle. A practical device based on homodyne measurement of the x quadrature of a cavity mode is investigated. First, a ${\mathrm{\ensuremath{\chi}}}^{(2)}$ crystal is inserted in the cavity so that it becomes a degenerate parametric oscillator at threshold. Then the photocurrent is used to control coherent driving of the cavity, so as to give positive feedback with unit gain. This feedback, combined with the nonlinearity, turns the homodyne measurement into a QND measurement of x. The device can also be used to measure the x quadrature of a traveling wave, and gives near-perfect QND correlations over a large bandwidth. However, the quality of the measurement is badly degraded by even slightly inefficient photodetectors.
A new quantum measurement scheme of intensity difference fluctuation between two light beams of equal mean intensity is presented. In this system a beam splitter is used as the coupling device and the twin beams with high quantum correlation are injected into its dark port as the input meter wave instead of the usual vacuum field. A measurement satisfying all the quantum nondemolition criteria is experimentally achieved. The measured sum of the transfer coefficients and the conditional variance are, respectively, Ts+Tm=1.31{T}_{s}{+T}_{m}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.31Ts​+Tm​=1.31 and ${V}_{s/m}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\ensuremath{-}2.1\mathrm{dB}$.
Optical quantum nondemolition measurements are performed using a beamsplitter with a nonclassical meter input and a electro-optic feedforward loop. The nonclassical meter input is provided by a stable 4.5 dB amplitude squeezed source generated by an optical parametric amplifier. We show that the implementation of a feedforward loop gives a substantial improvement in the signal transfer efficiency. With a 92% reflective beamsplitter we measure a transfer coefficient of Ts+m = 1.81. The quantum state preparation ability of our system is evaluated using two-dimensional correlation plots. This technique allows the direct visualization of the quantum correlations between the outputs of the QND system.
We analyze a quantum nondemolition measurement scheme similar to that advocated by Song, Caves, and Yurke [Phys. Rev. A 41, 5261 (1990)] for generating superpositions of macroscopically distinct quantum states, but with the parametric amplifier and the back-action evader interchanged. We determine the asymptotic behavior of the output and obtain the conditions under which a superposition of two coherent states is approached. By presqueezing the signal port input, we find that gain requirements of the back-action evader are much less demanding.