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What $g^{(2)}(0)<1/2$ tells you - and what it does not

P. Grünwald

Published Nov 16, 2017• 0 citations
OpenAlex

Abstract

Quantum-optical research on semiconductor quantum dots puts special emphasis on the measurement of the second-order correlation function $g^{(2)}(\tau)$, arguing that $g^{(2)}(0)<1/2$ implies the source field represents a good single-photon light source. We analyze this claim theoretically. A quantum state of light having no projection on the single-photon Fock state can not give a value of $g^{(2)}(0)<1/2$. However, with solely the value of $g^{(2)}(0)$, the amplitude of this single-photon projection can be arbitrarily small, owing to vacuum contributions. Yet, one can determine a lower bound on the ratio of single-to-multi-photon emission from $g^{(2)}(0)$. For a fixed ratio of single-to-multi-photon emission, $g^{(2)}(0)$ is artificially enhanced by the vacuum contributions. We derive an effective second-order correlation function, which corrects this enhancement, substantially improving the lower bound. The results are applied to theoretical and realized experimental setups and indicate that the quality of solid-state single-photon sources, at least with respect to this criterion, is often underestimated.

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What g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2 tells you - and what it does not
Quantum-optical research on semiconductor quantum dots puts special emphasis on the measurement of the second-order correlation function g(2)(τ)g^{(2)}(\tau)g(2)(τ), arguing that g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2 implies the source field represents a good single-photon light source. We analyze this claim theoretically. A quantum state of light having no projection on the single-photon Fock state can not give a value of g(2)(0)<1/2g^{(2)}(0)<1/2g(2)(0)<1/2. However, with solely the value of g(2)(0)g^{(2)}(0)g(2)(0), the amplitude of this single-photon projection can be arbitrarily small, owing to vacuum contributions. Yet, one can determine a lower bound on the ratio of single-to-multi-photon emission from g(2)(0)g^{(2)}(0)g(2)(0). For a fixed ratio of single-to-multi-photon emission, g(2)(0)g^{(2)}(0)g(2)(0) is artificially enhanced by the vacuum contributions. We derive an effective second-order correlation function, which corrects this enhancement, substantially improving the lower bound. The results are applied to theoretical and realized experimental setups and indicate that the quality of solid-state single-photon sources, at least with respect to this criterion, is often underestimated.
Abstract Quantum-optical research on semiconductor single-photon sources puts special emphasis on the measurement of the second-order correlation function g (2) ( τ ), arguing that g (2) (0) < 1/2 implies the source field represents a good single-photon light source. We analyze the gain of information from g (2) (0) with respect to single photons. Any quantum state, for which the second-order correlation function falls below 1/2, has a nonzero projection on the single-photon Fock state. The amplitude p of this projection is arbitrary, independent of g (2) (0). However, one can extract a lower bound on the single-to-multi-photon-projection ratio. A vacuum contribution in the quantum state of light artificially increases the value of g (2) (0), cloaking actual single-photon projection. Thus, we propose an effective second-order correlation function g ˜ ( 2 ) ( 0 ) , which takes the influence of vacuum into account and also yields lower and upper bounds on p . We consider the single-photon purity as a standard figure of merit in experiments, reinterpret it within our results and provide an effective version of that physical quantity. Besides comparing different experimental and theoretical results, we also provide a possible measurement scheme for determining g ˜ ( 2 ) ( 0 ) .
Estimating the quality of a single-photon source is crucial for its use in quantum technologies. The standard test for semiconductor sources is a value of the second-order correlation function of the emitted field below 1/21/21/2 at zero time delay. This criterion alone provides no information regarding the amplitude of the single-photon contribution for general quantum states. Addressing this question requires the knowledge of additional observables. We derive an effective second-order correlation function, strongly connected to the Mandel-QQQ parameter and given in terms of both the second-order correlation and the average photon number, that provides a lower bound on the single-to-multiphoton projection ratio. Using both observables individually allows for lower and upper bounds for the single-photon projection. Comparing the tightness of our bounds with those in the literature, we find that relative bounds may be better described using the average photon number, while absolute bounds for low excitation states are tighter using the vacuum projection. Our results show that estimating the quality of a single-photon source based on additional information is very much dependent on what aspect of the quantum state of light one is interested in.
A variety of quantum emitters compete in the quest for the best single-photon source for photonic quantum technologies. Consequently, only a consistent approach to analyze the second-order auto correlation function allows comparison of the multi-photon contribution (g(2)(0)g^{(2)}(0)g(2)(0)) of different sources. However, the community employs different and inconsistent methods for blinking sources, leading to incomparable benchmarks of source quality. Here, we use the emission of an inherently non-blinking quantum dot (QD) and apply artificial blinking through two different mechanisms: masking the recorded raw data in post-processing and emulation of a blinking system by gating the laser excitation pulses. We then compare the g(2)(0)g^{(2)}(0)g(2)(0) values with the non-blinking result. For the analysis, we investigate five estimators of g(2)(0)g^{(2)}(0)g(2)(0) actively used in the literature. While fitting the envelope of the correlations on long-time scales with the correct blinking model is the best choice, normalizing to the Poisson level gives by far the worst proximity. Furthermore, we test our predictive model to identify the underlying blinking mechanism of a QD in a circular Bragg grating cavity.
A Quantum Non-Gaussianity Criterion Based on Photon Correlations g(2)g^{(2)}g(2) and g(3)g^{(3)}g(3)
Quantum non-Gaussian states, which cannot be written as mixtures of Gaussian states, are necessary to achieve a quantum advantage in continuous variable systems. They represent an important benchmark for the realization of an advanced quantum light source, as they cannot be made by simple means such as displacement and squeezing. We introduce an attenuation-resistant sufficient criterion for quantum non-Gaussian states based on the second- and third-order correlation functions, g(2)g^{(2)}g(2) and g(3)g^{(3)}g(3). The general non-linear bound for classical mixtures of Gaussian states is g(3)+3g(2)≥2\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} \geq 2g(3)​+3g(2)​≥2. Any mixture of Gaussian states must fulfill this inequality, thus, the violation of it represents a direct confirmation of quantum non-Gaussianity. We experimentally show the non-Gaussianity of the state produced by a quantum dot single-photon source, where we obtain g(3)+3g(2)=0.174(13)\sqrt{g^{(3)}} + 3 \sqrt{g^{(2)}} = 0.174 (13)g(3)​+3g(2)​=0.174(13), which represents a statistical significance of more than 100100100 standard deviations.
We investigate the intensity correlation properties of single photons emitted from an optically excited single semiconductor quantum dot. The second order temporal coherence function of the photons emitted at various wavelengths is measured as a function of the excitation power. We show experimentally and theoretically that a quantum dot is not only a source of nonclassically correlated monochromatic photons but is also a source of multicolor photons with tunable correlation properties. We found that the emitted photon statistics can be varied by the excitation rate from a sub-Poissonian one, where the photons are temporally antibunched, to super-Poissonian, where they are temporally bunched.
The development of linear quantum computing within integrated circuits demands high quality semiconductor single photon sources. In particular, for a reliable single photon source it is not sufficient to have a low multi-photon component, but also to possess high efficiency. We investigate the photon statistics of the emission from a single quantum dot with a method that is able to sensitively detect the trade-off between the efficiency and the multi-photon contribution. Our measurements show, that the light emitted from the quantum dot when it is resonantly excited possess a very low multi-photon content. Additionally, we demonstrated, for the first time, the non-Gaussian nature of the quantum state emitted from a single quantum dot.