Max Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany.
Université Paris 13, Sorbonne Paris Cité, Laboratoire de Physique des Lasers, 93430 Villetaneuse, France.
Phys Rev Lett. 2019 Sep 20;123(12):123606. doi: 10.1103/PhysRevLett.123.123606.
Extreme events appear in many physics phenomena, whenever the probability distribution has a "heavy tail" differing very much from the equilibrium one. Most unusual are the cases of power-law (Pareto) probability distributions. Among their many manifestations in physics, from "rogue waves" in the ocean to Lévy flights in random walks, Pareto dependences can follow very different power laws. For some outstanding cases, the power exponents are less than 2, leading to indefinite values not only for higher moments but also for the mean. Here we present the first evidence of indefinite-mean Pareto distribution of photon numbers at the output of nonlinear effects pumped by parametrically amplified vacuum noise, known as bright squeezed vacuum (BSV). We observe a Pareto distribution with power exponent 1.31 when BSV is used as a pump for supercontinuum generation, and other heavy-tailed distributions (however, with definite moments) when it pumps optical harmonics generation. Unlike in other fields, we can flexibly control the Pareto exponent by changing the experimental parameters. This extremely fluctuating light is interesting for ghost imaging and for quantum thermodynamics as a resource to produce more efficiently nonequilibrium states by single-photon subtraction, the latter of which we demonstrate experimentally.
极端事件出现在许多物理现象中，每当概率分布具有与平衡状态非常不同的“重尾”时。最不寻常的是幂律（帕累托）概率分布的情况。在物理领域的众多表现中，从海洋中的“异常波”到随机游走中的 Lévy 飞行，帕累托依赖关系可能遵循非常不同的幂律。对于一些突出的情况，幂指数小于 2，这不仅导致更高阶矩而且还导致平均值不确定。在这里，我们首次在由参数放大真空噪声泵浦的非线性效应输出中观察到光子数的不确定均值帕累托分布，这种效应被称为亮压缩真空（BSV）。当 BSV 用作超连续产生的泵浦时，我们观察到幂指数为 1.31 的帕累托分布，而当它泵浦光学谐波产生时，则观察到其他重尾分布（但是，具有确定的矩）。与其他领域不同，我们可以通过改变实验参数来灵活控制帕累托指数。这种极端波动的光在幽灵成像和量子热力学中很有趣，因为它是通过单光子减法更有效地产生非平衡态的资源，我们通过实验证明了这一点。
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