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arXiv:1611.07737 · Optics Express

Quantum non-Gaussianity from a large ensemble of single photon emitters

Lukáš Lachman, Radim Filip

Published Nov 15, 2016• 11 citations
arXivHTMLPDF

Abstract

Quantum attributes of light have been related to non-classicality so far, i. e. to incompatibility with mixtures of coherent states. The progress in quantum optics indicates that this feature does not suffice to witness exotic behavior of light. Contrary, quantum non-Gaussianity is starting to appear as a promising and applicable property reflecting interesting states of light that are suitable for quantum protocols. We investigate a newly introduced hierarchy of criteria of quantum non-Gaussianity and predict this attribute can be observed on light emitted from many single photon emitters, even if the light undergoes realistic optical losses. It contrasts negativity of Wigner function, that is unreachable in experimental platforms with losses above fifty percent.

DOI
10.1364/oe.24.027352

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Quantum attributes of light have been related to non-classicality so far, i. e. to incompatibility with mixtures of coherent states. The progress in quantum optics indicates that this feature does not suffice to witness exotic behavior of light. Contrary, quantum non-Gaussianity is starting to appear as a promising and applicable property reflecting interesting states of light that are suitable for quantum protocols. We investigate a newly introduced hierarchy of criteria of quantum non-Gaussianity and predict this attribute can be observed on light emitted from many single photon emitters, even if the light undergoes realistic optical losses. It contrasts negativity of Wigner function, that is unreachable in experimental platforms with losses above fifty percent.
Nonclassical quantum effects gradually reach domains of physics of large systems previously considered as purely classical. We derive a hierarchy of operational criteria suitable for a reliable detection of nonclassicality of light from an arbitrarily large ensemble of independent single-photon emitters. We show, that such large ensemble can always emit nonclassical light without any phase reference and under realistic experimental conditions including incoherent background noise. The nonclassical light from the large ensemble of the emitters can be witnessed much better than light coming from a single or a few emitters.
We introduce and experimentally explore the concept of the non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly witnessed quantum non-Gaussianity withstands significant attenuation, exhibiting a depth of 18 dB, while the nonclassicality remains unchanged. Quantum non-Gaussian depth is an experimentally approachable quantity that is much more robust than the negativity of the Wigner function. Furthermore, we use it to reveal significant differences between otherwise strongly nonclassical single-photon sources.
Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.
Quantum non-classicality is not only a fundamental feature which shows the solely quantum character of an emitted photon, but is also necessary for modern applications based on the quantum character of light like quantum information processing [1]. The usual way to show that a light source is non-classical is to measure its auto-correlation [2]. In our work instead we used a different criterion developed in [3] which puts a bound on states that cannot be expressed as a mixture of coherent states. With the same measurement technique we have already proven the non-Gaussianity of the photon [4] using a similar criterion [5,6].
Quantum non-Gaussian states of photons and phonons are conclusive and direct witnesses of higher-than-quadratic nonlinearities in optical and mechanical processes. Moreover, they are proven resources for quantum sensing, communication and error correction with diverse continuous-variable systems. This review introduces theoretical analyses of nonclassical and quantum non-Gaussian states of photons and phonons. It recapitulates approaches used to derive operational criteria for photons tolerant to optical losses, their application in experiments and their nowadays extension to quantum non-Gaussian photon coincidences. It extends to a recent comparison of quantum non-Gaussianity, including robustness to thermal noise, and sensing capability for high-quality phononic Fock states of single trapped cooled ions. The review can stimulate further development in the criteria of quantum non-Gaussian states and experimental effort to prepare and detect such useful features, navigating the community to advanced quantum physics and technology.
Many applications in quantum communication, sensing and computation need provable quantum non-Gaussian light. Recently, such light witnessed by a negative Wigner function has been estimated using homodyne tomography from a single atom dispersively coupled to a high-finesse cavity \cite{Hacker2019}. It opens an investigation of quantum non-Gaussian light for many experiments with atoms and solid-state emitters. However, at their early stage, an atom or emitter in a cavity system with different channels to the environment and additional noise are insufficient to produce the negative Wigner function. Moreover, the homodyne detection is frequently challenging for such experiments. We analyse those issues and prove such cavities can be used to emit quantum non-Gaussian light employing single-photon detection in the Hanbury-Brown and Twiss configuration and quantum non-Gaussianity criteria suitable for this measurement. We investigate in details the cases of considerable cavity leakage when the negativity of Wigner function disappears completely. Advantageously, quantum non-Gaussian light can be still conclusively proven for a large set of the cavity parameters at the cost of overall measurement time, even if noise is present.