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Conference on Lasers and Electro-Optics

Quantum limits for resolution of beam displacements

Stephen Mark Barnett, Claude Fabre, Agnès Maître

Published Aug 29, 2005• 0 citations
Publisher

Abstract

Summary form only given. It has long been recognised that the resolution of optical interferometers is determined by the quantum nature of light. Interferometers are sensitive to phase shifts arising from changes in optical path length. In this paper we are concerned with the quantum factors limiting the detection of displacements perpendicular to the direction of beam propagation.

DOI
10.1109/iqec.2000.907772

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Summary form only given. It has long been recognised that the resolution of optical interferometers is determined by the quantum nature of light. Interferometers are sensitive to phase shifts arising from changes in optical path length. In this paper we are concerned with the quantum factors limiting the detection of displacements perpendicular to the direction of beam propagation.
A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramér-Rao limit of detection without any assumptions on the nature of the light source.
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.
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.
Tracking small transverse displacements of an optical beam with ultra-high accuracy is a fundamental problem underlying numerous important applications ranging from pointing, acquisition and tracking for establishing a lasercom link, to atomic force microscopy for imaging with atomic-scale resolution. Determining what is the optimal quantum-optical probe and the best achievable sensitivity of measuring a small transverse optical beam displacement, is the fundamental question central to these sensing schemes. By mapping this problem to an array of nested Mach-Zehnder interferometers, we explicitly construct the optimal probe state. It is entangled across the spatial modes allowed within the Fresnel number product of the propagation geometry, and entangled across the temporal modes within the time-bandwidth product of the optical probe. We show that the optimal sensitivity of measuring the beam displacement achieves a Heisenberg limited scaling over both the number of temporal modes and the average number of photons transmitted per mode. Surprisingly, we discover a sub-Heisenberg limited scaling over the number of available spatial modes. To qualify the quantum enhancement, we also establish the optimal sensitivity of a classical-light probe, which gives shot-noise limit over both the number of temporal modes and the number of photons per mode, and Heisenberg limited scaling over the number of spatial modes. Finally, we construct an explicit design for quantum-enhanced beam tracking, which uses a Gaussian (multi-mode-entangled squeezed-state) probe and a Gaussian (multi-mode homodyne) receiver.