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Optics Letters

Noise in homodyne detection

Bonny L. Schumaker

Published May 1, 1984• 244 citations
Publisher

Abstract

A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50-50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.

DOI
10.1364/ol.9.000189

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A simple but rigorous analysis of the important sources of noise in homodyne detection is presented. Output noise and signal-to-noise ratios are compared for direct detection, conventional (one-port) homodyning, and two-port homodyning, in which one monitors both output ports of a 50-50 beam splitter. It is shown that two-port homodyning is insensitive to local-oscillator quadrature-phase noise and hence provides (1) a means of detecting reduced quadrature-phase fluctuations (squeezing) that is perhaps more practical than one-port homodyning and (2) an output signal-to-noise ratio that can be a modest to significant improvement over that of one-port homodyning and direct detection.
The fluctuations in the processes of one-port and balanced two-port homodyning are calculated in the operator picture for a weak signal and a strong local oscillator beam where the last is contaminated with Gaussian excess noise. For such a mixture of coherent and chaotic light, we construct a physical model with the help of a linear laser amplifier. To be able to measure phase-dependent quantum fluctuations like squeezing with one-port homodyning, demands a Poisson-like photon distribution of the local oscillator and stringent requirements on its intensity. The Poisson-like photon distribution can also be achieved by a very low reflectivity which is equivalent to strong attenuation. These conditions are relaxed for balanced two-port homodyning but certain less stringent consequences of the excess noise are derived to occur.
Quantum-mechanical calculations of the mean-square fluctuation spectra in optical homodyning and heterodyning are made for arbitrary input and local-oscillator quantum states. In addition to the unavoidable quantum fluctuations, it is shown that excess noise from the local oscillator always affects homodyning and, when it is broadband, also heterodyning. Both the quantum and the excess noise of the local oscillator can be eliminated by coherent subtraction of the two outputs of a 50-50 beam splitter. This result also demonstrates the fact that the basic quantum noise in homodyning and heterodyning is signal quantum fluctuation, not local-oscillator shot noise.
Abstract In the absence of a signal field, vacuum entering through the empty beam splitter port is considered to be the sole contributor to the output noise of conventional two-port homodyne detection. We study a modified configuration that alters the input coefficient of vacuum, predicting an output noise less than that of the conventional configuration. Measurements, however, reveal identical output noise profiles for both the configurations. We explain the observations in terms of the incident field noise alone, and suggest that vacuum does not contribute to homodyne noise or shot-noise. We extend our results to the measurement of squeezed light, with non-ideal detectors.
The eight-port homodyne detector is an optical circuit designed to perform the monitoring of two quadratures of an optical field: the signal. By using quantum Bose fields and quantum stochastic calculus, we give a complete quantum description of this apparatus, when used as quadrature detector in continuous time. We can treat either the traveling waves in the optical circuit or the observables involved in the detection part: two couples of photodiodes, postprocessing of the output currents\dots{}. The analysis includes imperfections, such as not perfectly balanced beam splitters, detector efficiency, electronic noise, phase and intensity noise in the laser acting as local oscillator; this last noise is modeled by using mixtures of field coherent states as statistical operator of the laser component. Due to the monitoring in continuous time, the output is a stochastic process and its full probability distribution is obtained. When the output process is sampled at discrete times, the quantum description can be reduced to discrete mode operators, but at the price of having random operators, which contain also the noise of the local oscillator. Consequently, the local oscillator noise has a very different effect on the detection results with respect to an additive noise, such as the noise in the electronic components. As an application, the problem of secure random-number generation is considered, based on the local oscillator shot noise. The rate of random bits that can be generated is quantified by the min-entropy; the possibility of classical and quantum side information is taken into account by suitable conditional min-entropies. The final rate depends on which parts of the apparatus are considered to be secure and on which ones are considered to be exposed to the intervention of an intruder. In some experimentally realistic situations, the entropy losses are computed, depending on the values of the parameters quantifying the imperfections.
Quantum noise in optical heterodyning and homodyning, usually analyzed under the assumption that the photodetector output is conditionally Poisson,1,2 is frequently supposed to arise from local oscillator (LO) shot noise. However, a fully quantum mechanical analysis from Yuen and Shapiro3 has shown that it actually arises from the signal quantum fluctuation; in particular homodyning and heterodyning are realizations of abstract quantum measurements of the field quadratures. We analyze the effect of LO noise, both quantum and excess noise, on homodyne and heterodyne detection. For conventional input light, i.e., fields in coherent states or their random superpositions, we demonstrate how a conditionally Poisson calculation would yield the correct answer but incorrect interpretation for the detection quantum noise.