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arXiv:quant-ph/0204017 · Physical Review Letters

Surpassing the Standard Quantum Limit for Optical Imaging Using Nonclassical Multimode Light

Nicolas Treps, Ulrik L. Andersen, B. C. Buchler, Ping Koy Lam, Agnès Maître, Hans‐A. Bachor, Claude Fabre

Published May 3, 2002• 240 citations
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Abstract

Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.

DOI
10.1103/physrevlett.88.203601

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Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.
Using continuous wave superposition of spatial modes, we demonstrate experimentally displacement measurement of a light beam below the standard quantum limit. Multimode squeezed light is obtained by mixing a vacuum squeezed beam and a coherent beam that are spatially orthogonal. Although the resultant beam is not squeezed, it is shown to have strong internal spatial correlations. We show that the position of such a light beam can be measured using a split detector with an increased precision compared to a classical beam. This method can be used to improve the sensitivity of small displacement measurements.
Abstract A scheme is proposed to realize high‐precision spatial measurement of laser beams beyond quantum limit using a novel quantum state called the order spatially squeezed state, which is the combination of a bright mode coherent state and squeezed vacuum mode state. An effective technique for the generation of a rectangular shape higher‐order mode squeezed light with a maximum mode order of 5 is experimentally demonstrated using a doubling resonated optical parametric amplifier. Furthermore, the fourth order tilt‐ and displacement‐squeezed beams are constructed and used to perform spatial tilt and displacement measurements, thereby improving the signal‐to‐noise ratio by 10 and 8.6 dB compared to the mode. The results indicate that high‐order spatially squeezed states enhance measurement precision beyond the shot noise limit and are more prominent in back‐action noise reduction. High‐precision spatial measurement has potential practical applications in high‐sensitivity atomic force microscope and super‐resolution quantum imaging.
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 demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x - and y -displacement fluctuations of 2.2 and 3.1 dB below the quantum noise limit.
We consider the problem of the measurement of very small displacements in the transverse plane of an optical image with a split photodetector. We show that the standard quantum limit for such a measurement, which is equal to the diffraction limit divided by the square root of the number of photons used in the measurement, cannot be overcome by use of ordinary single-mode squeezed light. We give the form of possible multimode nonclassical states of light, enabling us to enhance by orders of magnitude the resolution of such a measurement beyond the standard quantum limit.
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.