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On ultrastrong coupling in quantum Rabi theory

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Abstract

We develop an effective Hamiltonian model to study resonance properties of multi-photon processes in c-QED. This proposal predicts an effective H eff having the structure 𝒜 + 𝒫𝒟-1𝒫† where 𝒟-1 is the propagator of the intermediate states and 𝒜, 𝒫  two operators given by Rabi hamiltonian H R . The adiabatic elimination of Ken et al. [Phys Rev. A 92, 023842 (2015)] is recovered as time independent limit where 𝒟-1 is approached by the inverse of a constant matrix ℬ which is also determined from H R . A new limit, named as linear approximation, is also obtained; it corresponds to approximating 𝒟-1 like ℬ-1 − ℬ-2 (i∂/∂t) and leads to a refined expression of the effective H eff . Others features are also studied.

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Authors and Affiliations

  1. Equipe de Recherche en Energie Electrique et Commande, Ecole Mohammadia d’Ingénieurs, Université Mohamed V, Rabat, Morocco

    Sarah Saidi & Mohamed Maaroufi

  2. LPHE-Modélisation et Simulation, Faculté des Sciences, Université Mohamed V, Rabat, Morocco

    Lalla Btissam Drissi

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  1. Sarah Saidi
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  2. Mohamed Maaroufi
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Correspondence to Sarah Saidi.

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Saidi, S., Maaroufi, M. & Drissi, L.B. On ultrastrong coupling in quantum Rabi theory. Eur. Phys. J. D 72, 22 (2018). https://doi.org/10.1140/epjd/e2017-80392-2

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