Quantum theory of the low-frequency linear susceptibility of interferometer-type superconducting qubits

TL;DR

This paper develops a quantum theoretical framework to analyze the low-frequency linear susceptibility of interferometer-type superconducting qubits interacting with a tank circuit, including spectroscopy and continuous state monitoring.

Contribution

It introduces a density matrix approach to model qubit-tank interactions and explores spectroscopy and measurement techniques using dressed states and a DC SQUID.

Findings

Derived expressions for qubit susceptibility in the low-frequency regime.

Analyzed qubit spectroscopy under microwave irradiation.

Proposed methods for continuous qubit state monitoring.

Abstract

We use the density matrix formalism to analyze the interaction of interferometer-type superconducting qubits with a high quality tank circuit, which frequency is well below the gap frequency of a qubit. We start with the ground state characterization of the superconducting flux and charge qubits. Then, by making use of a dressed state approach we describe the qubits' spectroscopy when the qubit is irradiated by a microwave field which is tuned to the gap frequency. The last section of the paper is devoted to continuous monitoring of qubit states by using a DC SQUID in the inductive mode.