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Casimir-Polder forces from density matrix formalism

T. N. C. Mendes·C. Farina
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Abstract

We use the density matrix formalism in order to calculate the energy level shifts, in second order on interaction, of an atom in the presence of a perfectly conducting wall in the dipole approximation. The thermal corrections are also examined when $\hbar ω_0/k_B T = k_0 λ_T \gg 1$, where ${$ω_0=k_0 c$}$ is the dominant transition frequency of the atom and $λ_T$ is the thermal length. When the distance $z$ between the atom and the wall is larger than $λ_T$ we find the well known result obtained from Lifshitz's formula, whose leading term is proportional to temperature and is independent of $c$, $\hbar$ and $k_0$. In the short distance limit, when $z\llλ_T$, only very small corrections to the leading vacuum term occur. We also show, for all distance regimes, that the main thermal corrections are independent of $k_0$ (dispersion is not important) and dependent of $c$, which means that there is not a non-retarded regime for the thermal contributions.

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T. N. C. Mendes, C. Farina. 2006-04-05. Casimir-Polder forces from density matrix formalism. https://doi.org/10.1088/0305-4470/39/21/s51

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