Investigating the convergence of the iteration scheme of operator method for description of eigenstates of the quantum Rabi model
Keywords:
Rabi model, operator method, two-level system, quantum field, resonanceAbstract
In the present paper we investigate the rate of convergence of the iteration scheme of the operator method in respect of calculating the eigenstates of the quantum Rabi model with different values of the free parameter which plays an important role when treating the problem beyond the rotating wave approximation. The two ways of selecting equations for the aforementioned parameter are analyzed: 1) the one which is based on putting to zero the nearest diagonal non-trivial matrix element of the Hamiltonian of the model; 2) the one when the value of the free parameter coincides with the value of the coupling constant between the two-level system and external quantum field that was used in our previous papers. It is shown that the first way of selection leads to the maximal (and uniform in respect of the coupling constant) rate of convergence that has almost no dependence on the coupling constant of the model, whereas the second way allows one to obtain both better qualitative and quantitative behavior of its zeroth order approximation however reducing the rate of convergence of the method that is of oscillatory character in case of small coupling constants. The obtained results could be useful for description of the double-photon and asymmetric Rabi models as well as for investigation of atomic systems in the strong external fields.
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