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arXiv · 2202.03545

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

A. U. Leonau·N. Q. San·A. P. Ulyanenkov·O. D. Skoromnik·I. D. Feranchuk
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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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A. U. Leonau, N. Q. San, A. P. Ulyanenkov, O. D. Skoromnik, I. D. Feranchuk. 2022-02-07. Eigenstates of two-level systems in a single-mode quantum field: from quantum Rabi model to $N$-atom Dicke model. https://doi.org/10.1088/1751-8121%2Faca571

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