Qubit-photon interactions in a cavity: Measurement induced dephasing and number splitting

TL;DR

This paper theoretically analyzes measurement-induced dephasing in a superconducting qubit within circuit QED, demonstrating how photon number fluctuations cause dephasing and predicting a spectrum splitting into multiple peaks in the strong dispersive regime.

Contribution

It provides a theoretical framework that explains experimental observations of dephasing and predicts photon number splitting in the qubit spectrum under strong dispersive coupling.

Findings

Good agreement between theory and experiment on qubit spectrum line shape

Prediction of qubit spectrum splitting into multiple peaks in strong dispersive limit

Identification of photon number fluctuations as a key source of dephasing

Abstract

We theoretically study measurement induced-dephasing of a superconducting qubit in the circuit QED architecture and compare the results to those obtained experimentally by Schuster {\it et al.}, [Phys. Rev. Lett. 94, 123602 (2005)]. Strong coupling of the qubit to the resonator leads to a significant ac-Stark shift of the qubit transition frequency. As a result, quantum fluctuations in the photon number populating the resonator cause dephasing of the qubit. We find good agreement between the predicted line shape of the qubit spectrum and the experimental results. Furthermore, in the strong dispersive limit, where the Stark shift per photon is large compared to the cavity decay rate and the qubit linewidth, we predict that the qubit spectrum will be split into multiple peaks, with each peak corresponding to a different number of photons in the cavity.