Inversion of Qubit Energy Levels in Qubit-Oscillator Circuits in the Deep-Strong-Coupling Regime

Understand

We report on experimentally measured light shifts of superconducting flux qubits deep-strongly coupled to LC oscillators, where the coupling constants are comparable to the qubit and oscillator resonance frequencies.

• By using two-tone spectroscopy, the energies of the six lowest levels of each circuit are determined.
• We find huge Lamb shifts that exceed 90% of the bare qubit frequencies and inversions of the qubits' ground and excited states when there are a finite number of photons in the oscillator.
• Our experimental results agree with theoretical predictions based on the quantum Rabi model.