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arXiv:quant-ph/0607142 · Physical Review A

TEM10 homodyne detection as an optimal small-displacement and tilt-measurement scheme

V. Delaubert, Nicolas Treps, Mikael Lassen, C. C. Harb, Claude Fabre, Ping Koy Lam, Hans‐A. Bachor

Published Nov 30, 2006• 60 citations
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Abstract

We present a detailed description of small displacement and tilt measurements of a Gaussian beam using split detectors and ${\mathrm{TEM}}_{10}$ homodyne detectors. Theoretical analysis and an experimental demonstration of measurements of these two conjugate variables are given. A comparison between the experimental efficiency of each scheme proves that the standard split detection is only 64% efficient relative to the ${\mathrm{TEM}}_{10}$ homodyne detection, which is optimal for beam displacement and tilt. We also demonstrate experimentally that squeezed light in the appropriate spatial modes allows measurements beyond the quantum noise limit for both types of detectors. Finally, we explain how to choose the detection scheme best adapted to a given application.

DOI
10.1103/physreva.74.053823

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We present a detailed description of small displacement and tilt measurements of a Gaussian beam using split detectors and TEM10{\mathrm{TEM}}_{10}TEM10​ homodyne detectors. Theoretical analysis and an experimental demonstration of measurements of these two conjugate variables are given. A comparison between the experimental efficiency of each scheme proves that the standard split detection is only 64% efficient relative to the TEM10{\mathrm{TEM}}_{10}TEM10​ homodyne detection, which is optimal for beam displacement and tilt. We also demonstrate experimentally that squeezed light in the appropriate spatial modes allows measurements beyond the quantum noise limit for both types of detectors. Finally, we explain how to choose the detection scheme best adapted to a given application.
We derive the quantum noise limit for the optical beam displacement of a TEM00 mode. Using a multimodal analysis, we show that the conventional split detection scheme for measuring beam displacement is non-optimal with 80% efficiency. We propose a new displacement measurement scheme that is optimal for small beam displacement. This scheme utilises a homodyne detection setup that has a TEM10 mode local oscillator. We show that although the quantum noise limit to displacement measurement can be surpassed using squeezed light in appropriate spatial modes for both schemes, the TEM10 homodyning scheme out-performs split detection for all values of squeezing.
We consider the problem of measurement of optical transverse profile parameters and their conjugate variable. Using multimode analysis, we introduce the concept of detection noise modes. For Gaussian beams, displacement and tilt are a pair of transverse-profile conjugate variables. We experimentally demonstrate the optimal encoding and detection of these variables with a spatial homodyning scheme. Using higher-order spatial mode squeezing, we show the sub-shot-noise measurements for the displacement and tilt of a Gaussian beam.
The application of quantum optics to spatial measurements with continuous-wave laser beams is discussed. In particular, we summarize the work on measuring small displacements and tilt. We present the required theoretical multi-mode model and discuss how it applies to split detectors and spatial homodyne detectors. We show how spatial measurements can be improved using squeezed light. Finally, we present a demonstration of improved spatial homodyne measurements using squeezed light in a higher order spatial mode.
We investigated the estimation of an unknown Gaussian process (containing displacement, squeezing and phase-shift) applied to a matter system. The state of the matter system is not directly measured; instead, we measure an optical mode which interacts with the system. We propose an interferometric setup exploiting a beam-splitter-type of light-matter interaction with homodyne detectors and two methods of estimation. We demonstrate the superiority of the interferometric setup over alternative non-interferometric schemes. Importantly, we show that even limited coupling strength and a noisy matter system are sufficient for very good estimation. Our work opens the way to many future investigations of light-matter interferometry for experimental platforms in quantum metrology of matter systems.