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We investigate classical thermal activation (TA) and macroscopic quantumtunneling (MQT) for a YBa$_2$Cu$_3$O$_{7-\delta}$ (YBCO) Josephson junctioncoupled to an LC circuit theoretically. Due to the coupling between thejunction and the LC circuit, the macroscopic phase dynamics can be described asthe escape process of a fictitious particle with an anisotropic mass moving ina two-dimensional potential. We analytically calculate the escape rateincluding both the TA and MQT regime by taking into account the peculiardynamical nature of the system. In addtion to large suppression of the MQT rateat zero temperature, we study details of the temperature dependece of theescape rate across a crossover region. These results are in an excellentagreement with recent experimental data for the MQT and TA rate in a YBCObiepitaxial Josephson junction. Therefore the coupling to the LC circuit isessential in understanding the macroscopic quantum dynamics and the qubitoperation based on the YBCO biepitaxial Josephson junctions.

Theory of two-dimensional macroscopic quantum tunneling in YBa$_2$ Cu$_3$ O$_{7-\delta}$ Josephson junctions coupled to an LC circuit