Cardona was born in Barcelona, Spain in 1934. After obtaining a Masters in physics in 1955 from University of Barcelona Cardona was awarded a fellowship to work as a graduate student at Harvard University starting in 1956. At Harvard he began investigations of the dielectric properties of semiconductors, in particular germanium and silicon. With this work as a thesis he received a PhD in Applied Physics at Harvard. From 1959 till 1961 he continued similar work on III-V semiconductors at the RCA Laboratories in Zurich, Switzerland. In 1961 he moved to the RCA Labs in Princeton, NJ, where he continued work on the optical properties of semiconductors and started investigations of the microwave properties of superconductors. In 1964 he became a member of the Physics Faculty of Brown University (Providence, RI). In June–September 1965 he taught at the University of Buenos Aires under the auspices of the Ford Foundation. In 1971 he moved to Stuttgart, Germany as a founding director of the then-recently created Max Planck Institute for Solid State Research. Concomitantly he became scientific Member of the Max Planck Society, where he became emeritus in 2000.
From 1992 to 2004, Cardona served as chief editor of Solid State Communications.