Stability of excited atoms in small cavities

Abstract

We consider a system consisting of an atom in the approximation of a harmonic oscillator of frequency $\overline{\ensuremath{\omega}},$ coupled to the scalar potential inside a spherical reflecting cavity of radius R. We use dressed states introduced in a previous publication [Andion, Malbouisson, and Mattos Neto, J. Phys. A 34, 3735 (2001)], which allow a nonperturbative unified description of the atom radiation process, in both cases, of a finite or an arbitrarily large cavity. We perform a study of the energy distribution in a small cavity, with the initial condition that the atom is in the first excited state and we conclude for the quasi-stability of the excited atom. For instance, for a frequency $\overline{\ensuremath{\omega}}$ of the order $\overline{\ensuremath{\omega}}\ensuremath{\sim}4.00\ifmmode\times\else\texttimes\fi{}{10}^{14}/\mathrm{s}$ (in the visible red), starting from the initial condition that the atom is in the first excited level, we find that for a cavity with diameter $2R\ensuremath{\sim}1.0\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6} \mathrm{m},$ the probability of the atom being at any time still in the first excited level, will be of the order of 97%. For a typical microwave frequency $\overline{\ensuremath{\omega}}\ensuremath{\sim}2.00\ifmmode\times\else\texttimes\fi{}{10}^{10}/\mathrm{s}$ we find stability in the first excited state also of the order of 97% for a cavity radius $R\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2} \mathrm{m}.$