Inversion of qubit energy levels in qubit-oscillator circuits in the deep-strong-coupling regime

摘要

We report on experimentally measured light shifts of superconducting fluxqubits deep-strongly-coupled to an LC oscillator, where the coupling constantis comparable to the qubit's transition frequency and the oscillator'sresonance frequency. By using two-tone spectroscopy, the energies of thesix-lowest levels of the coupled circuits are determined. We find a huge Lambshift that exceeds 90% of the bare qubit frequencies and inversion of thequbits' ground and excited states when there is a finite number of photons inthe oscillator. Our experimental results agree with theoretical predictionsbased on the quantum Rabi model.