Circuit Quantization in the Presence of Time-Dependent External Sources

Circuit quantization serves as a link between physical circuits and quantum Hamiltonians. The standard procedure [1] established decades ago implicitly assumes the external magnetic flux threading a circuit loop to be static. However, time-dependence arises inevitably when flux modulation or noise are considered. Naïve application of the existing circuit-quantization procedure can then lead to inconsistencies in predictions of qubit relaxation times. In this talk, we present a generalized approach to circuit quantization valid in the presence of time-dependent external sources. Our results uncover the reason for the inconsistency and resolve it, and are applicable to a wide range of circuits utilizing time-varying external fields.

[1] M. H. Devoret, Les Houches, Session LXIII 7 (1995)