Nonlinearity refers to behaviour that deviates from a simple, proportional relationship and cannot be accurately described by linear equations. This concept is fundamental to understanding complex systems across various scientific disciplines, including meteorology, epidemiology, chemistry, and quantum mechanics. 

In the field of quantum optics, achieving nonlinearity at the single-photon level is essential for the development of advanced quantum information protocols. Such nonlinearity enables more precise control over information transmission, facilitates faster and more scalable quantum networks, and enhances the security of quantum communication. 

Rydberg atoms, which are atoms in highly excited states, exhibit strong long-range interactions. These interactions, particularly the Rydberg blockade effect, make them promising candidates for inducing strong nonlinear interactions between photons. However, a key challenge lies in achieving this nonlinearity in a controllable and efficient manner, rather than relying on probabilistic or inefficient methods. 

In this work, the authors introduce a novel approach for precisely engineering Rydberg states to enable continuous tuning of single-photon nonlinearity. This tunability represents a significant advancement, with potential applications spanning fundamental physics and the development of next-generation quantum technologies. 

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Probing quantum correlations in many-body systems: a review of scalable methods by Irénée Frérot, Matteo Fadel and Maciej Lewenstein (2023)

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