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The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting

Super-Resolving Quantum Radar: Coherent-State Sources with Homodyne Detection Suffice to Beat the Diffraction Limit

Kebei Jiang, Hwang Lee, Christopher C. Gerry, Jonathan P. Dowling

Published Jan 1, 2013• 4 citations
Publisher

Abstract

We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at the shot-noise limit.
DOI
10.1364/cqo.2013.m6.49

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There has been much recent interest in quantum metrology for applications to sub-Raleigh ranging and remote sensing such as in quantum radar. For quantum radar, atmospheric absorption and diffraction rapidly degrades any actively transmitted quantum states of light, such as N00N states, so that for this high-loss regime the optimal strategy is to transmit coherent states of light, which suffer no worse loss than the linear Beer's law for classical radar attenuation, and which provide sensitivity at the shot-noise limit in the returned power. We show that coherent radar radiation sources, coupled with a quantum homodyne detection scheme, provide both longitudinal and angular super-resolution much below the Rayleigh diffraction limit, with sensitivity at shot-noise in terms of the detected photon power. Our approach provides a template for the development of a complete super-resolving quantum radar system with currently available technology.
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We have derived a quantum LADAR scheme which exploits even coherent states of light, is shot noise limit in sensitivity and can resolve features much below Rayleigh diffraction limit. For a return power of n = 100, the resolution of our proposed scheme can reach 120 times higher than the classical diffraction limit in the sense of the well-define narrow feature. More importantly, our scheme has the super-resolving characteristics in the usual sense of word as there are multiple narrow peaks as would be the case in a N00N-states scheme.
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect alignment with the centroid of the object. Both inhibit the practical application of these methods, as uniform motion and/or relative jitter destroy their assumptions. Here, we show that measuring intensity in the Fourier plane enables super-resolution without any of the issues of image-based methods. We start with the shift-invariance of the Fourier transform and the observation that the two-point position problem x1,x2{x_1,x_2}x1​,x2​ in the near field corresponds to the single-point wavenumber problem k =2π/(x2−x1)k\ =2π/(x_2-x_1)k =2π/(x2​−x1​) in the far field. We consider the full range of mutual coherence and show that for fully coherent sources, the Fourier method saturates the quantum limit, i.e. it gives the best possible measurement. Similar results hold for sub-Rayleigh constellations of NNN sources, which can act collectively as a spatially averaged metasurface and/or individually as elements of a phased-array antenna. The theory paves the way to merge Fourier optics with super-resolution techniques, enabling experimental devices that are both simpler and more robust than previous designs.