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Physical Review Letters

High-Accuracy Optical Homodyne Detection with Low-Efficiency Detectors: "Preamplification" from Antisqueezing

Ulf Leonhardt, Henryk Paul

Published Jun 27, 1994• 80 citations
Publisher

Abstract

A novel experimental scheme is proposed that allows us to avoid the deterioration of homodyne detection measurements due to nonideal detectors. The basic idea is to "preamplify" the signal by means of antisqueezing. Experimentally, we would employ a squeezer, e.g., a degenerate optical parametric amplifier, that squeezes just the nonobserved quadrature component of the electric field while antisqueezing the conjugate component which is measured. It is shown that for sufficiently strong antisqueezing one achieves the same measurement accuracy as with perfectly efficient detectors. In particular, in this way the actual Wigner function can be reconstructed in cptical homodyne tomography.

DOI
10.1103/physrevlett.72.4086

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A novel experimental scheme is proposed that allows us to avoid the deterioration of homodyne detection measurements due to nonideal detectors. The basic idea is to "preamplify" the signal by means of antisqueezing. Experimentally, we would employ a squeezer, e.g., a degenerate optical parametric amplifier, that squeezes just the nonobserved quadrature component of the electric field while antisqueezing the conjugate component which is measured. It is shown that for sufficiently strong antisqueezing one achieves the same measurement accuracy as with perfectly efficient detectors. In particular, in this way the actual Wigner function can be reconstructed in cptical homodyne tomography.
The operational theory of homodyne detection by nonideal detectors, used in quantum tomography, was recently modified in order to incorporate the preamplification (before homodyne detection) of the input signal, thus enabling one to beat the handicap of the lower than 0.5 detector efficiency. In the present work we set expressions for the Mandel QQQ parameter and the signal-to-noise ratio in terms of the operational (measured) moments of the preamplified homodyne detection formalism. These quantities furnish important information on the statistical properties of the input signal field and the photocounts at the output. We illustrate the theory by considering several kinds of fields (for the input signal) and determine the effects of the preamplification on the output signal-to-noise ratios. Here we essentially verify that (i) the preamplification shifts the statistics towards the super-Poissonian limit, without jeopardizing the capacity of reconstructing a sub-Poissionan input signal, and (ii) the preamplification is more effective, i.e., the rate of increase of the signal-to-noise ratio of the output photocount is larger for low-efficiency detectors than for ideal ones.
Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, obtaining an improved method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by a distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to OPA-assisted homodyne detection.
Optical homodyne tomography consists in reconstructing the quantum state of an optical field from repeated measurements of its amplitude at different field phases (homodyne data). The experimental noise, which unavoidably affects the homodyne data, leads to a detection efficiency η<1\eta<1η<1 . The problem of reconstructing quantum states from noisy homodyne data sets prompted an intense scientific debate about the presence or absence of a lower homodyne efficiency bound ( η>0.5\eta> 0.5η>0.5 ) below which quantum features, like quantum interferences, cannot be retrieved. Here, by numerical experiments, we demonstrate that quantum interferences can be effectively reconstructed also for low homodyne detection efficiency. In particular, we address the challenging case of a Schrödinger cat state and test the minimax and adaptive Wigner function reconstruction technique by processing homodyne data distributed according to the chosen state but with an efficiency η<0.5\eta< 0.5η<0.5 . By numerically reproducing the Schrödinger’s cat interference pattern, we give evidence that quantum state reconstruction is actually possible in these conditions, and provide a guideline for handling optical tomography based on homodyne data collected by low efficiency detectors.
Abstract Current advances in nonlinear optics have made it possible to perform a homodyne-like tomography of an unknown state without highly efficient detectors or a strong local oscillator. Thereby, a new experimental direction has been opened into multimode and large-bandwidth quantum optics. An optical parametric amplifier (OPA) allows us to reconstruct the quadrature distribution of an unknown state directly from the measured intensity distribution with high precision. We propose adding a controllable displacement to the standard scheme, thus, obtaining a method applicable even to asymmetric and non-Gaussian states while significantly increasing estimation accuracy and lowering the OPA amplification requirement. To demonstrate the power of our method, we accurately detect the sub-Planck phase-space structure by obtaining distillable squeezing from the OPA estimates of various non-Gaussian states. With the improvements, OPA tomography became a generally applicable loss-tolerant and efficient alternative to homodyne detection.
Homodyne measurement is a corner-stone of quantum optics. It measures the fundamental variables of quantum electrodynamics - the quadratures of light, which represent the cosine-wave and sine-wave components of an optical field and constitute the quantum optical analog of position and momentum. Yet, standard homodyne, which is used to measure the quadrature information, suffers from a severe bandwidth limitation: While the bandwidth of optical states can easily span many THz, standard homodyne detection is inherently limited to the electrically accessible, MHz to GHz range, leaving a dramatic gap between the relevant optical phenomena and the measurement capability. We demonstrate a fully parallel optical homodyne measurement across an arbitrary optical bandwidth, effectively lifting this bandwidth limitation completely. Using optical parametric amplification, which amplifies one quadrature while attenuating the other, we measure two-mode quadrature squeezing of 1.7dB below the vacuum level simultaneously across a bandwidth of 55THz, using just one local-oscillator - the pump. As opposed to standard homodyne, our measurement is highly robust to detection inefficiency, and was obtained with >50%>50\%>50% loss in the detection channel. This broadband parametric homodyne measurement opens a wide window for parallel processing of quantum information.