Black-box superconducting circuit quantization

Phys Rev Lett. 2012 Jun 15;108(24):240502. doi: 10.1103/PhysRevLett.108.240502. Epub 2012 Jun 12.

Abstract

We present a semiclassical method for determining the effective low-energy quantum Hamiltonian of weakly anharmonic superconducting circuits containing mesoscopic Josephson junctions coupled to electromagnetic environments made of an arbitrary combination of distributed and lumped elements. A convenient basis, capturing the multimode physics, is given by the quantized eigenmodes of the linearized circuit and is fully determined by a classical linear response function. The method is used to calculate numerically the low-energy spectrum of a 3D transmon system, and quantitative agreement with measurements is found.