Indefinite-mean Pareto photon distribution from amplified quantum noise

Mathieu Manceau, Kirill Yu. Spasibko, Gerd Leuchs, Radim Filip, Maria V. Chekhova

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Mar 22, 2019
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Recieved date: 3rd March 19

The existence of extreme events is a fascinating phenomenon in natural and social sciences. They appear whenever the probability distribution has a `heavy tail', differing very much from the equilibrium one. Examples are `rogue waves' in the ocean and their analogues in nonlinear optics, Lévy flights, and other numerous examples in physics, biology, Earth science, etc. Most famous are the statistics of income and wealth with a power-law (Pareto) probability distribution describing social inequality and responsible for the renowned `80/20 rule'. The power laws can be however very different; for some outstanding cases the power exponents are less than 2 leading to indefinite mean values, to say nothing of higher moments. Here we present the first evidence of such probability distributions of photon numbers using nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.3 when BSV pumps supercontinuum generation, and other heavy-tailed distributions for the optical harmonics generated from BSV. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. Besides photonic applications such as ghost imaging, this extremely fluctuating light is also interesting for quantum thermodynamics as a resource to produce more efficiently non-equlibrium states by single-photon subtraction, which we demonstrate in experiment.


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This is an abstract of a preprint hosted on an independent third party site. It has not been peer reviewed but is currently under consideration at Nature Communications.


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