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The European Physical Journal D

Ultimate quantum limits for resolution of beam displacements

Stephen Mark Barnett, Claude Fabre, Agnès Maître

Published Mar 1, 2003• 81 citations
Publisher
DOI
10.1140/epjd/e2003-00003-3

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Abstract We present a general method to find the ultimate limits on the resolution of optical image on a surface perpendicular to the light beam propagation. We prove that the optimal sensitivity always obeys the standard quantum limit for a single mode light. In the absence of photon losses, we find the possibility to achieve the Heisenberg limit by using two-mode or multi-mode lights. We also use the variational approach to obtain the lower bound on the sensitivity considering the effects of photon losses.
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Quantum imaging can be defined as an area of quantum optics that investigates the ultimate performance limits of optical imaging allowed by the quantum nature of light. Quantum Imaging techniques possess a high potential for improving the performance in recording, storage, and readout of optical images beyond the limits set by the standard quantum level of fluctuations known as the shot noise. This talk aims at giving an overview of the fundamentals of Quantum Imaging as well as its most important directions. We shall discuss generation of the spatially multimode squeezed states of light be means of a travelling-wave optical parametric amplifier. We shall demonstrate that this kind of light allows us to reduce the spatial fluctuations of the photocurrent in a properly chosen homodyne detection scheme with a highly efficient CCD camera. It will be shown that using the amplified quadrature of the light wave in a travelling-wave optical parametric amplifier, one can perform noiseless amplification of optical images. We shall provide recent experimental results demonstrating a single-shot noiseless image amplification by a pulsed optical parametric amplifier. One of important experimental achievements of Quantum Imaging, coined in the literature as quantum laser pointer, is a precise measurement of position and transverse displacement of a laser beam with resolution beyond the limit imposed by the shot noise. We shall describe briefly the idea of the experiment in which the transverse displacement of a laser beam was measured with resolution of the order of Angstrom. The problem of precise measurement of transverse displacement of a light beam brings us to a more general question about the quantum limits of optical resolution. The classical resolution criterion, derived in the nineteen century by Abbe and Rayleigh, states that the resolution of an optical instrument is limited by diffraction and is related to the wavelength of the light used in the imaging scheme. However, it was for a long time recognised in the literature that in some cases when one has some a priori information about the object, one can improve the resolution beyond the Rayleigh limit using the so-called super-resolution techniques. As a final topic in this talk, we shall discuss the quantum limits of optical super-resolution. In particular, we shall formulate the standard quantum limit of super-resolution and demonstrate how one can go beyond this limit using specially designed multimode squeezed light.