Abstract
The dispersive regime of circuit QED is the main workhorse for todays quantum computing prototypes based on superconducting qubits. Analytic descriptions of this model typically rely on the rotating wave approximation of the interaction between the qubits and resonators, using the Jaynes-Cummings model as starting point for the dispersive transformation. Here we present analytic results on the dispersive regime of the dissipative Rabi model, without taking the rotating wave approximation of the underlying Hamiltonian. Using a recently developed hybrid perturbation theory based on the expansion of the time evolution on the Keldysh contour [Phys. Rev. A 95, 013847 (2017)], we derive simple analytic expressions for all experimentally relevant dynamical parameters like dispersive shift and resonator induced Purcell decay rate, focussing our analysis on a generic multi-level qubit. The analytical equations are easily tractable and reduce to the known Jaynes-Cummings results in the relevant limit. They however show qualitative differences at intermediate and large detuning, allowing for more accurate modelling of the interaction between superconducting qubits and resonators. In the limit of strong resonator driving, our results additionally predict new types of drive induced qubit dissipation and dephasing, not present in previous theories.
Highlights
Quantum optics and the related fields of quantum computation are at their heart concerned with the interactions between atoms and light, i.e., light as in coherent modes of electromagnetic radiation and atoms as in well-controlled, engineered quantum few-level systems [1]
This interaction is described in the so-called Jaynes-Cummings model [2,3], which is based on an approximation of the more fundamental Rabi model [4], describing the interaction between the light and dipole-allowed transitions in the atom
We show analytic expressions for Hamiltonian corrections and dominant dissipative dynamical contributions arising in the dispersive regime of the Rabi model directly, without making the rotating-wave approximation underlying the Jaynes-Cummings interaction
Summary
Quantum optics and the related fields of quantum computation are at their heart concerned with the interactions between atoms and light, i.e., light as in coherent modes of electromagnetic radiation and atoms as in well-controlled, engineered quantum few-level systems [1]. The so-called dispersive regime of the atom-light interaction [3], where the atomic transitions are detuned from the mode energies of the light field by more than the strength of their coupling It is in this regime that the successful early quantum computing prototypes based on superconducting artificial atoms and microwave resonators are operated [7,8,9,10]. Our treatment is based on a Keldysh diagrammatic perturbation approach [17], and delivers well-behaved and simple analytic expressions for all relevant parameters without requiring additional approximation These results are relevant for more accurate analytical modeling of any quantum hardware in the dispersive regime, like superconducting and spin qubits.
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