Deep strong coupling in a circuit QED system - huge Lamb shift -

Among a variety of cavity/circuit-QED systems, circuits employing superconducting flux qubits as artificial atoms can achieve large coupling strengths because of the flux qubit's huge magnetic moment [1-3]. Using a flux qubit and a compact superconducting LC oscillator, we have realized so-called deep strong coupling between the qubit and the oscillator, where $g / \omega_o/ 2\pi = 1.3$ ($g$: coupling strength, $\omega_o/ 2\pi $: bare oscillator frequency) [1]. The measured spectra of the coupled system are well described with the Hamiltonian of Rabi model. The bare qubit frequency $\Delta / 2\pi $ is found to be ~3.8 GHz, and the theoretical model predicts that the frequency of the qubit, $\omega_{01}$, will be suppressed to ~0.5 GHz, indicating an extraordinary large Lamb shift of about 0.85$\Delta $. Recently, we have measured the spectrum of $\omega_{01}/ 2\pi $, by driving $\omega_{01}/ 2\pi $ and probing $\omega_{03}/ 2\pi $. In this presentation, the measured spectroscopy data will be shown. [1] F. Yoshihara, T. Fuse, et al., Nature Physics (2016) doi:10.1038/nphys3906. [2] P. Forn-Diaz, et al., Nature Physics (2016) doi:10.1038/nphys3905. [3] S. Ashhab and F. Nori, PRA 81, 042311 (2010).