Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/0407209 · Journal of Optics B Quantum and Semiclassical Optics

Optimal optical measurement of small displacements

Magnus T. L. Hsu, V. Delaubert, Ping Koy Lam, Warwick P. Bowen

Published Oct 16, 2004• 82 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1464-4266/6/12/003

Related papers

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

V. Delaubert, Nicolas Treps, Mikael Lassen +4 more

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.

arXiv:quant-ph/0607142•Physical Review A•Nov 30, 2006•60 citations

Homodyne detection as an optimal small displacement measurement

V. Delaubert, Nicolas Treps, Magnus T. L. Hsu +4 more

We demonstrate a scheme based on homodyne detection with a TEM/sub 10/ local oscillator for optimum small displacement measurements beyond the quantum noise limit. It is demonstrated to be directly extendable to optimum tilt measurement.

European Quantum Electronics Conference (EQEC)•Jan 18, 2006•0 citations

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

Nicolas Treps, Ulrik L. Andersen, B. C. Buchler +4 more

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.

arXiv:quant-ph/0204017•Physical Review Letters•May 3, 2002•240 citations

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

V. Delaubert, Nicolas Treps, C. C. Harb +2 more

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.

arXiv:quant-ph/0512151•Optics Letters•Apr 28, 2006•45 citations

Crossing the standard quantum limit for high sensitivity measurements in optical images using non classical light

Nicolas Treps, Ulrik L. Andersen, B. C. Buchler +4 more

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.

•Jan 1, 2002•1 citation

Nano-displacement measurements using spatially multimode squeezed light

Nicolas Treps, Nicolai B. Grosse, Warwick P. Bowen +5 more

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.

arXiv:quant-ph/0311122•Journal of Optics B Quantum and Semiclassical Optics•Jul 28, 2004•47 citations
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 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.
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.
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.
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.
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.