Thermal effects on the stability of excited atoms in cavities

An atom, coupled linearly to an environment, is considered in a harmonic approximation in thermal equilibrium inside a cavity. The environment is modeled by an infinite set of harmonic oscillators. We employ the notion of dressed states to investigate the time evolution of the atom initially in the first excited level. In a very large cavity (free space) for a long elapsed time, the atom decays and the value of its occupation number is the physically expected one at a given temperature. For a small cavity the excited atom never completely decays and the stability rate depends on temperature.

Figure 1

Solutions of Eq. (36), with $y=\cot (x)$ and $x=\pi \Omega \delta /g$, for cavities satisfying the condition given in Eq. (37). The asymptotes of the cotangent curve correspond to the frequencies of the field modes ${\omega }_k$.

Figure 2

Time evolution of the thermal-dependent occupation number $n_0^{\prime }(\tau ,\beta )$ for a temperature $T=300$ K. The scale for the vertical axis is $N_0=(n_0^{\prime }-1)\times {10}^{12}$; time is in seconds ($\tau =t\times {10}^{-14}$).

Figure 3

Time evolution of the thermal-dependent occupation number $n_0^{\prime }(\tau ,\beta )$ for a temperature $T={10}^5$ K Time is in seconds ($\tau =t\times {10}^{-13}$).

Figure 4

Temperature behavior of the lower bound for the minimum of $n_0^{\prime }(\tau ,\beta )$, $Y=n_0^{\prime }(\beta )\times {10}^{31}$, given by Eq. (51). Temperature is given in 10 K.