Open AccessAnalytical diagonalisation of the Hamiltonian of the quantum Rabi model in the Coulomb gauge
Author(s) -
A. U. Leonau,
И. Д. Феранчук
Publication year - 2022
Publication title -
žurnal belorusskogo gosudarstvennogo universiteta. fizika
Language(s) - English
Resource type - Journals
eISSN - 2617-3999
pISSN - 2520-2243
DOI - 10.33581/2520-2243-2022-1-44-51
Subject(s) - hamiltonian (control theory) , unitary transformation , physics , gauge theory , quantum mechanics , gauge fixing , hamiltonian lattice gauge theory , eigenvalues and eigenvectors , coulomb , quantum electrodynamics , quantum , mathematics , gauge boson , mathematical optimization , electron
In the present paper we investigate the approximate analytical diagonalisation of the Hamiltonian of the quantum Rabi model written in the Coulomb gauge and taking into account the gauge invariance of the system. It is shown that the Hamiltonian of the model can be diagonalised with high accuracy on the basis of a unitary operator of the gauge transformation utilising a simple basis set of state vectors. It is essential that the obtained approximate expressions do not depend on the variational parameters and are valid within the whole range of the parameter values. The zeroth-order approximation and uniformly available approximation are derived for the eigenstates of the system, and their comparison with the results of the numerical simulation is elaborated. The second-order correction to the zeroth-order approximation is deduced and its contribution to the energy of the system is estimated. The obtained results could be useful for description of the evolution of the quantum Rabi model as well as for investigation of systems of two-level atoms in the resonant quantum field.