Two-resonator circuit QED: Dissipative Theory

TL;DR

This paper develops a theoretical framework for a dissipative two-resonator circuit QED system, analyzing how a superconducting qubit mediates switchable coupling and influences the system's dynamics, with implications for quantum information processing.

Contribution

It derives an effective Hamiltonian beyond the rotating wave approximation and analyzes dissipative dynamics, providing analytical and numerical insights into the quantum switch behavior.

Findings

Analytical expression for qubit influence on the quantum switch

Numerical results on resonator oscillations and entanglement decay

Protocol for measuring damping constants via quadrature measurements

Abstract

We present a theoretical treatment for the dissipative two-resonator circuit quantum electrodynamics setup referred to as quantum switch. There, switchable coupling between two superconducting resonators is mediated by a superconducting qubit operating in the dispersive regime, where the qubit transition frequency is far detuned from those of the resonators. We derive an effective Hamiltonian for the quantum switch beyond the rotating wave approximation and study the dissipative dynamics within a Bloch-Redfield quantum master equation approach. We derive analytically how the qubit affects the quantum switch even if the qubit has no dynamics, and we estimate the strength of this influence. The analytical results are corroborated by numerical calculations, where coherent oscillations between the resonators, the decay of coherent and Fock states, and the decay of resonator-resonator entanglement are studied. Finally, we suggest an experimental protocol for extracting the damping constants of qubit and resonators by measuring the quadratures of the resonator fields.