High-frequency suppression of inductive coupling between flux qubit and transmission line resonator

TL;DR

This paper provides a detailed theoretical analysis of the high-frequency cutoff in a flux qubit coupled to a transmission line resonator, revealing a natural decoupling at high frequencies and a resonance effect near qubit oscillation frequencies.

Contribution

It introduces a more accurate theoretical model that avoids certain approximations, capturing effects like resonance shifts and spectrum features not seen in previous studies.

Findings

Coupling strength varies as √ω at low frequencies and decreases as 1/√ω at high frequencies.

Resonance effects shift TLR mode frequencies near qubit oscillation frequencies.

Derived expressions for TLR frequencies, coupling strengths, and qubit Lamb shift.

Abstract

We perform theoretical calculations to investigate the naturally occurring high-frequency cutoff in a circuit comprising a flux qubit coupled inductively to a transmission line resonator (TLR). Specifically, a decoupling occurs between the qubit and the high-frequency modes. The coupling strength between the qubit and resonator modes increases with mode frequency $\omega$ as $\sqrt{\omega}$ at low frequencies and decreases as $1/\sqrt{\omega}$ at high frequencies. This result is similar to those of past studies that considered somewhat similar circuit designs. By avoiding the approximation of ignoring the qubit-TLR coupling in certain steps in the analysis, we obtain effects not captured in previous studies. In particular, we obtain a resonance effect that shifts the TLR mode frequencies close to qubit oscillation frequencies. We derive expressions for the TLR mode frequencies, qubit-TLR coupling strengths and qubit Lamb shift. We identify features in the spectrum of the system that can be used in future experiments to test and validate the theoretical model.