The statistics of strongly interacting, ultracold Rydberg gases are governed by the interplay of two factors: geometrical restrictions induced by blockade effects and quantum mechanical effects. To shed light on their relative roles in the statistics of Rydberg gases, we compare three models in this paper: a quantum mechanical model describing the excitation dynamics within a Rydberg gas, a random sequential adsorption (RSA) process on a random geometric graph (RGG), and a RSA process on a decomposed random intersection graph (DRIG). The last model refers to choosing a particular subgraph of a mixture of two other random graphs. Contrary to the first two models, it lends itself for a rigorous mathematical analysis, and it is built specifically to have particular structural properties of a RGG. We establish for it a fluid limit describing the time evolution of the number of Rydberg atoms and show numerically that the expression remains accurate across a wider range of particle densities than an earlier approach based on an RSA process on an Erdős-Rényi random graph (ERRG). Finally, we also develop a heuristic using random graphs that gives a recursion to describe a normalized pair-correlation function of a Rydberg gas. Our results suggest that even without dissipation, on long timescales the statistics are affected most by the geometrical restrictions induced by blockade effects, while on short timescales the statistics are affected most by quantum mechanical effects.

中文翻译：

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使用随机图上的随机顺序吸附对Rydberg气体进行建模

强相互作用的超冷Rydberg气体的统计数据受两个因素的相互作用支配：封锁效应引起的几何限制和量子力学效应。为了阐明它们在Rydberg气体统计中的相对作用，我们比较了三种模型：描述Rydberg气体内激发动力学的量子力学模型，随机几何图（RGG）上的随机顺序吸附（RSA）过程），以及对分解后的随机相交图（DRIG）进行RSA处理。最后一个模型是指选择其他两个随机图的混合物的特定子图。与前两个模型相反，它适合进行严格的数学分析，并且专门为具有RGG的特定结构特性而构建。我们为此建立了描述Rydberg原子数的时间演化的流体极限，并从数字上表明，与在Erdős-Rényi随机图（ERRG）上基于RSA过程的早期方法相比，该表达式在更宽的粒子密度范围内仍保持准确的状态。 ）。最后，我们还开发了一种使用随机图的启发式方法，该方法给出了递归来描述Rydberg气体的归一化对相关函数。我们的结果表明，即使没有耗散，在较长的时间尺度上，统计数据受阻塞效应引起的几何限制的影响最大，而在较短的时间尺度上，统计数据受量子力学效应的影响最大。