Resilience of the quantum Rabi model in circuit QED

Abstract

In circuit quantum electrodynamics (circuit QED), an artificial "circuit atom" can couple to a quantized microwave radiation much stronger than its real atomic counterpart. The celebrated quantum Rabi model describes the simplest interaction of a two-level system with a single-mode boson field. When the coupling is large enough, the bare multilevel structure of a realistic circuit atom cannot be ignored even if the circuit is strongly anharmonic. We explored this situation theoretically for flux (fluxonium) and charge (Cooper pair box) type multi-level circuits tuned to their respective flux/charge degeneracy points. We identified which spectral features of the quantum Rabi model survive and which are renormalized for large coupling. Despite significant renormalization of the low-energy spectrum in the fluxonium case, the key quantum Rabi feature -- nearly-degenerate vacuum consisting of an atomic state entangled with a multi-photon field -- appears in both types of circuits when the coupling is sufficiently large. Like in the quantum Rabi model, for very large couplings the entanglement spectrum is dominated by only two, nearly equal eigenvalues, in spite of the fact that a large number of bare atomic states are actually involved in the atom-resonator ground state. We interpret the emergence of the two-fold degeneracy of the vacuum of both circuits as an environmental suppression of flux/charge tunneling due to their dressing by virtual low-/high-impedance photons in the resonator. For flux tunneling, the dressing is nothing else than the shunting of a Josephson atom with a large capacitance of the resonator. Suppression of charge tunneling is a manifestation of the dynamical Coulomb blockade of transport in tunnel junctions connected to resistive leads.

Invited manuscript (in press) for the Special Issue "Semi-classical and quantum Rabi models", Journal of Physics A

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• Universal spectral features of ultrastrongly coupled systems
• Realizing the two-dimensional hard-core Bose-Hubbard model with superconducting qubits
• Nonperturbative cavity quantum electrodynamics: is the Jaynes-Cummings model still relevant?
• Optimal gauge for the multimode Rabi model in circuit QED
• Hamiltonian of a flux qubit-LC oscillator circuit in the deep-strong-coupling regime
• Non-Gaussian superradiant transition via three-body ultrastrong coupling
• Asymptotic behavior of observables in the asymmetric quantum Rabi model
• Unified linear response theory of quantum electronic circuits
• Radiative Properties of an Artificial Atom coupled to a Josephson Junction Array
• Circuit QED Spectra in the Ultrastrong Coupling Regime: How They Differ from Cavity QED
• GHZ-like states in the Qubit-Qudit Rabi Model