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

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.

32 pages (preprint), 4 figures

References in corpus (7)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Coplanar Waveguide Resonators for Circuit Quantum Electrodynamics
• Beyond Strong Coupling in a Massively Multimode Cavity
• Finite sizes and smooth cutoffs in superconducting circuits
• Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator
• All-microwave Lamb shift engineering for a fixed frequency multi-level superconducting qubit

Cited by in corpus (1)

• Circuit QED theory of direct and dual Shapiro steps with finite-size transmission line resonators