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European Quantum Electronics Conference (EQEC)

Homodyne detection as an optimal small displacement measurement

V. Delaubert, Nicolas Treps, Magnus T. L. Hsu, Warwick P. Bowen, C. C. Harb, Ping Koy Lam, Hans‐A. Bachor

Published Jan 18, 2006• 0 citations
Publisher

Abstract

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.
DOI
10.1109/eqec.2005.1567426

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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.
A methodology is introduced that enables an absolute, quantum-limited measurement of sub-wavelength interferometric displacements. The technique utilizes a high-frequency optical path modulation within an interferometer operated in a homodyne configuration. All of the information necessary to fully characterize the resultant path displacement is contained within the relative strengths of the various harmonics of the phase modulation. The method, which is straightforward and readily implementable, allows a direct measurement of the theoretical Cramér-Rao limit of detection without any assumptions on the nature of the light source.
The homodyne detection is one of the most basic tools for identifying the quantum state of light. It has been used to detect useful non-local properties, such as entanglement for the quantum teleportation and distillability of a secret key in quantum key distribution. In so doing, the detection scheme employs a bright optical pulse, called the local oscillator (LO) pulse, and the LO pulse is usually transmitted along with the signal pulses. The LO pulse is presumed to be a coherent state with an infinite intensity. However, it is difficult in practice to hold this presumption owing to noise in the optical transmission channels or an intervention by a malicious third party. As a result, the implementation may no longer be the homodyne detection, and those outcomes may merely disguise successful detection of entanglement or a secret key. Here, we present an alternative scheme that works as the homodyne detection to detect the non-local properties of light in a verifiable manner, without any presumption for the LO pulses. This scheme is essentially based on the same setup as the conventional implementation for the homodyne detection. This result contributes to close any possible loophole in the homodyne detection caused by the deviation from the ideal LO pulses.
Homodyne tomography - i. e. homodyning while scanning the local oscillator phase - is now a well assessed method for ``measuring'' the quantum state. In this paper I will show how it can be used as a kind of universal detection, for measuring generic field operators, however at expense of some additional noise. The general class of field operators that can be measured in this way is presented, and includes also operators that are inaccessible to heterodyne detection. The noise from tomographical homodyning is compared to that from heterodyning, for those operators that can be measured in both ways. It turns out that for some operators homodyning is better than heterodyning when the mean photon number is sufficiently small. Finally, the robustness of the method to additive phase-insensitive noise is analyzed. It is shown that just half photon of thermal noise would spoil the measurement completely.
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.