Cold antihydrogen atoms are a powerful tool to probe the validity of fundamental physics laws, and it's clear that colder atoms, generally speaking, allow an increased level of precision. After the first production of cold antihydrogen (H in 2002 [1], experimental efforts have progressed continuously (trapping [2], beam formation [3], spectroscopy [4, 5]), with competitive results already achieved by adapting to cold antiatoms techniques previously well developed for ordinary atoms. Unfortunately, the number of H atoms that can be produced in dedicated experiments is many orders of magnitude smaller than available hydrogen atoms, which are at hand in large amount, so the development of novel techniques that allow the production of H with well defined conditions (and possibly control its formation time and energy levels) is essential to improve the sensitivity of the methods applied by the different experiments. We present here the first experimental results concerning the production of H in a pulsed mode where the time when 90% of the atoms are produced is known with an uncertainty of around 250 ns [6]. The pulsed H source is generated by the charge-exchange reaction between Rydberg positronium atoms (Ps) and trapped antiprotons (p), cooled and manipulated in an electromagnetic trap: p + Ps∗ → H∗ + e− where Rydberg positronium atoms, in turn, are produced through the implantation of a pulsed positron beam into a mesoporous silica target, and are excited by two subsequent laser pulses, the first to n = 3, the second to the needed Rydberg level (n ≃ 17). The pulsed production allows the control of the antihydrogen temperature, and facilitates the tunability of the Rydberg states, their de-excitation by pulsed lasers and the manipulation through electric field gradients. In fact, the production of pulsed antihydrogen is a major milestone in the AEgIS experiment to perform direct measurements of the validity of the Weak Equivalence Principle for antimatter.