This paper investigates the accuracy of the standard current-phase relation (CPR) in describing the energy spectra of transmon artificial atoms. The authors find that the standard sinusoidal CPR is insufficient and demonstrate that a mesoscopic model incorporating higher Josephson harmonics provides significantly better agreement with experimental data. The presence and impact of these harmonics have important implications for the development of AlOx-based quantum technologies.

Dennis Willsch, Dennis Rieger, Patrick Winkel, Madita Willsch, Christian Dickel, Jonas Krause, Yoichi Ando, Raphaël Lescanne, Zaki Leghtas, Nicholas T. Bronn, Pratiti Deb, Olivia Lanes, Zlatko K. Minev, Benedikt Dennig, Simon Geisert, Simon Günzler, Sören Ihssen, Patrick Paluch, Thomas Reisinger, Roudy Hanna, Jin Hee Bae, Peter Schüffelgen, Detlev Grützmacher, Luiza Buimaga-larinca, Cristian Morari, Wolfgang Wernsdorfer, David P. DiVincenzo, Kristel Michielsen, Gianluigi Catelani, loan M. Pop