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arXiv:1809.00818 · New Journal of Physics

Quantum tomography of light states by photon-number-resolving detectors

Stefano Olivares, Alessia Allevi, Giovanni Caiazzo, Matteo G. A. Paris, Maria Bondani

Published Oct 1, 2019• 26 citations
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Abstract

Abstract We address state reconstruction by photon-number-resolving detectors, and demonstrate that they may be effectively exploited to perform quantum tomography of states of light. In particular, we find that the pattern function technique, originally developed for optical homodyne tomography, may be also applied to discrete data. Our results open new perspectives for quantum-state reconstruction in the mesoscopic regime, and pave the way to the use of photon-number-resolving-based detection schemes in Quantum Information science.

DOI
10.1088/1367-2630/ab4afb

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Abstract We address state reconstruction by photon-number-resolving detectors, and demonstrate that they may be effectively exploited to perform quantum tomography of states of light. In particular, we find that the pattern function technique, originally developed for optical homodyne tomography, may be also applied to discrete data. Our results open new perspectives for quantum-state reconstruction in the mesoscopic regime, and pave the way to the use of photon-number-resolving-based detection schemes in Quantum Information science.
Generation and measurement of quantum states of light represent a hot and widely discussed topic in the physical community for their possible applications to quantum optics and quantum information. To this aim, it is desirable that optical states are robust with respect to losses and can be produced and addressed at high rates. In fact, mesoscopic pulsed optical states containing few photons per pulse seem to be the ideal candidates for applications to quantum communication protocols. For all these reasons, during the last two decades many efforts have been devoted to the development of new kinds of detectors that can operate in such a photon-number-resolving domain.
Quantum state tomography and the reconstruction of the photon number distribution are techniques to extract the properties of a light field from measurements of its mean and fluctuations. These techniques are particularly useful when dealing with macroscopic or mesoscopic systems, where a description limited to the second order autocorrelation soon becomes inadequate. In particular, the emission of nonclassical light is expected from mesoscopic quantum dot systems strongly coupled to a cavity or in systems with large optical nonlinearities. We analyze the emission of a quantum dot-semiconductor optical amplifier system by quantifying the modifications of a femtosecond laser pulse propagating through the device. Using a balanced detection scheme in a self-heterodyning setup, we achieve precise measurements of the quadrature components and their fluctuations at the quantum noise limit1. We resolve the photon number distribution and the thermal-to-coherent evolution in the photon statistics of the emission. The interferometric detection achieves a high sensitivity in the few photon limit. From our data, we can also reconstruct the second order autocorrelation function with higher precision and time resolution compared with classical Hanbury Brown-Twiss experiments.
The measurement of quantum states of light is fundamental for the investigations of Quantum Optics and for the applications of Quantum Information. Here we present the implementation of a novel detection apparatus, that is a homodyne-like detection scheme based on photon-number-resolving detectors. Thanks to its hybrid nature, the apparatus is useful to investigate both the particle-like and wave-like properties of light. We tested the scheme in the measurement of the quadratures of different optical states, namely coherent states and mixtures of coherent states. In particular, we investigate the performance of our scheme compared to that of a standard homodyne detector.
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.