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Journal of Modern Optics

Spatial quantum effects with continuous-wave laser beams

Hans‐A. Bachor, V. Delaubert, C. C. Harb, Magnus T. L. Hsu, Ping Koy Lam, Claude Fabre, Nicolas Treps

Published Oct 6, 2005• 3 citations
Publisher

Abstract

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.

DOI
10.1080/09500340500167628

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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.
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.
Spatial multi-mode quantum optics, also termed « quantum imaging », allows a study of the detection of any physical parameter within an optical image. The parameter considered here can for instance be the transverse displacement or the tilt of a laser beam, or even the bit sequence of an optical disc encoded onto the beam. Such measurements are ultimately limited by the quantum nature of optical images. We show that the use of non classical beams allows a reduction of the measurement fluctuations below the latter fundamental limit. Using this theoretical result, we have performed optimal measurements of laser beam nano-displacement, as well as entanglement between this quantity and its conjugate variable : beam tilt. The implementation of these experiments has led us to demonstrate all the key elements required for quantum imaging experiments. We have also investigated the possibility of using multi-mode light as parallel communication channels for quantum information.
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.
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.
This thesis presents the first experimental demonstration of two-dimensional spatial squeezing. A dual squeezer was used to produce two beams of temporally squeezed light. Specially designed wave-plates were required to generate the necessary spatially orthogonal modes. These modes were mixed on an optical cavity to form a multi-mode superposition that converted the original temporal correlations into the desired spatial correlations. We used this light to improve the sensitivity of a two-dimensional beam displacement measurement to below the quantum noise limit. Our setup was also configured to generate a one-dimensional spatially squeezed state of light that did not require either of the two input modes to suffer substantial loss. This was the first experimental demonstration of a proper spatial squeezing measurement.