Describing qubit dissipation in circuit QED beyond black-box quantization

A standard approach for describing weakly anharmonic superconducting qubits coupled to cavities is “black-box quantization” [1], where the nonlinearity is written using the eigenmodes of the linear problem. This approach (as typically used) misses dissipative effects that are higher-order in the nonlinearity. In this work, we develop analytic methods based on the Keldysh technique and Lindblad perturbation theory that systematically describe such higher-order dissipative effects. These approaches offer advantages over traditional Schrieffer-Wolff methods and provide simple analytic descriptions of qubit dephasing and relaxation. Our work provides new theoretical tools that could be useful in a variety of different settings. They could also help shed light on the somewhat surprising photon number dependence of qubit relaxation seen in many experiments.

[1] S. Nigg, et al., Phys. Rev. Lett. 108, 240502 (2012).