Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime

Abstract

We derive the Hamiltonian of a superconducting circuit that comprises a single-Josephson-junction flux qubit inductively coupled to an LC oscillator, and we compare the derived circuit Hamiltonian with the quantum Rabi Hamiltonian, which describes a two-level system coupled to a harmonic oscillator. We show that there is a simple, intuitive correspondence between the circuit Hamiltonian and the quantum Rabi Hamiltonian. While there is an overall shift of the entire spectrum, the energy level structure of the circuit Hamiltonian up to the seventh excited states can still be fitted well by the quantum Rabi Hamiltonian even in the case where the coupling strength is larger than the frequencies of the qubit and the oscillator, i.e., when the qubit-oscillator circuit is in the deep-strong-coupling regime. We also show that although the circuit Hamiltonian can be transformed via a unitary transformation to a Hamiltonian containing a capacitive coupling term, the resulting circuit Hamiltonian cannot be approximated by the variant of the quantum Rabi Hamiltonian that is obtained using an analogous procedure for mapping the circuit variables onto Pauli and harmonic oscillator operators, even for relatively weak coupling. This difference between the flux and charge gauges follows from the properties of the qubit Hamiltonian eigenstates.

7 figures in the main text + 4 figures in Supplementary Information

References in corpus (7)

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Cited by in corpus (7)

• Extremely large Lamb shift in a deep-strongly coupled circuit QED system with a multimode resonator
• Kondo QED: The Kondo effect and photon trapping in a two-impurity Anderson model ultra-strongly coupled to light
• Relaxation breakdown and resonant tunneling in ultrastrong-coupling cavity QED
• Flux qubit-based detector of microwave photons
• Circuit QED Spectra in the Ultrastrong Coupling Regime: How They Differ from Cavity QED
• High-frequency suppression of inductive coupling between flux qubit and transmission line resonator
• Optimal Dynamical Gauge in the Quantum Rabi Model