Quantum entanglement of angular momentum states with quantum numbers up to 10,010

Significance Challenging quantum mechanical predictions is an important task to better understand the underlying principles of nature and possibly develop novel applications. Quantum entanglement as one of the key features is often investigated in optical experiments to push the known limits from smaller to larger scales, for example by increasing the number of entangled systems, their separation, or dimensionality. In the present study we pursue another route and investigate photons with large quantum numbers. We demonstrate entanglement between a photon with orbital angular momentum quantum numbers up to 10,010 and its partner encoded in polarization. The results show how complex the structure of entangled photons can be and hint at the large information content a single quantum system is able to carry. Photons with a twisted phase front carry a quantized amount of orbital angular momentum (OAM) and have become important in various fields of optics, such as quantum and classical information science or optical tweezers. Because no upper limit on the OAM content per photon is known, they are also interesting systems to experimentally challenge quantum mechanical prediction for high quantum numbers. Here, we take advantage of a recently developed technique to imprint unprecedented high values of OAM, namely spiral phase mirrors, to generate photons with more than 10,000 quanta of OAM. Moreover, we demonstrate quantum entanglement between these large OAM quanta of one photon and the polarization of its partner photon. To our knowledge, this corresponds to entanglement with the largest quantum number that has been demonstrated in an experiment. The results may also open novel ways to couple single photons to massive objects, enhance angular resolution, and highlight OAM as a promising way to increase the information capacity of a single photon.