Quantum measurements of spatial conjugate variables: Displacement and tilt of a Gaussian beam

Australian Research Council Centre of Excellence for Quantum-Atom Optics, The Australian National University, Canberra, Australia.
Optics Letters (Impact Factor: 3.29). 06/2006; 31(10):1537-9. DOI: 10.1364/OL.31.001537
Source: PubMed


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.

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    • "The TEM 00 waist size was w 0 =106 μmin the PZT plane, beam power 170 μW, RBW=100 kHz, and VBW=100 Hz, corresponding to a minimum resolvable displacement QNL of d QNL =0.6 nm. Figures (b) and (c) were reproduced from Delaubert et al. (2006), with permission. the strength of the spatial homodyne detector is that it can also measure beam tilt, which is not accessible in the plane of a split detector, simply by adjusting the relative phase between the LO and the input beams. "
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    ABSTRACT: We have presented a quantum formalism for the measurement of the spatial properties of an optical field. It was shown that the spatial homodyne technique is optimal and outperforms split detection for the detection of spatial parameter p. Applications of this measurement scheme in enhancing the sensitivities of atomic force microscopes and optical tweezers measurements have been discussed.
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    • "The use of DSI can thus make possible to conduct ultra precise measurements that might be difficult to achieve by other means [34]. In this context, note that the proper use of a multimodal expansion of a displaced Gaussian beam has recently afforded sub-shot-noise measurements of small beam displacement [35] "
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