Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model

• URL: http://arxiv.org/abs/2202.03545v1
• Date: Mon, 7 Feb 2022 22:14:13 GMT
• Title: Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model
• Authors: A. U. Leonau and N. Q. San and A. P. Ulyanenkov and O. D. Skoromnik and I. D. Feranchuk
• Abstract summary: We show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In the present paper we show that the Hamiltonian describing the resonant interaction of $N$ two-level systems with a single-mode electromagnetic quantum field in the Coulomb gauge can be diagonalized with a high degree of accuracy using a simple basis set of states. This allows one to find an analytical approximation for the eigenvectors and eigenvalues of the system, which interpolates the numerical solution in a broad range of the coupling constant values. In addition, the introduced basis states provide a regular way of calculating the corrections and estimating the convergence to the exact numerical solution. The obtained results are valid for both quantum Rabi model ($N = 1$) and the Dicke model for $N \geq 2$ atoms.

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