Cirac graduated from the Complutense University of Madrid in 1988 and moved to the United States in 1991 to work as a postdoctoral scientist with Peter Zoller in the Joint Institute for Laboratory Astrophysics in University of Colorado at Boulder. Between 1991 and 1996, he was teaching physics in the Ciudad Real Faculty of Chemistry, University of Castilla-La Mancha.
In 1996, Cirac became professor in the Institut für Theoretische Physik in Innsbruck, Austria, and in 2001 he became a director of the Max Planck Institute of Quantum Optics in Garching, Germany, where he heads the Theory Division. At the same time, he was appointed Honorary Professor at the Technical University of Munich. He is a Distinguished Visiting Professor and Research Advisor at ICFO - the Institute of Photonic Sciences in Barcelona since its foundation in 2002. He has been a member of research teams at the universities of Harvard, Technical University of Munich, Hamburg, UCSB, Hannover, Bristol, Paris, CEA/Saclay, École Normale Supérieure, Massachusetts Institute of Technology.
His research is focused on quantum optics, the quantum theory of information and quantum many-body physics. According to his theories, quantum computing will revolutionize the information society and lead to much more efficient and secure communication of information. His joint work with Peter Zoller on ion trap quantum computation opened up the possibility of experimental quantum computation, and his joint work on optical lattices jumpstarted the field of quantum simulation. He has also made seminal contributions in the fields of quantum information theory, degenerated quantum gases, quantum optics, and renormalization group methods. As of 2017 Juan Ignacio Cirac has published more than 440 articles in the most prestigious journals and is one of the most cited authors in his fields of research.