Why is the limit to observe quantum phenomena $k_B T < \hbar \omega_0$ in cavity QED?

Question

In cavity QED you have to cool down the appartus so that quantum effects may be observed in a way that $k_B T << \hbar \omega_0$. I suppose that $\omega_0$ here means the frequency which the cavity doesn't suppress and the frequency equvivalent to the energy difference between the two energy eignstates of the two sate atoms usually used in these experiments. What does this limit describe? What is the physics behind it? Thank you in advance.

Answer 1

If $kT \gt \hbar \omega$, the thermal energy of the system is able to populate noticeably the states of the system you are trying to study. The quantum dynamical effects will be masked by thermal noise as mentioned by DanielSank in the comments. The surrounding degrees of freedom he mentions can be in the system itself, just not the degrees of freedom being studied. It is the beauty of statistical mechanics that as long as the system is not completely isolated, you don't have to worry about what, exactly, is behind the coupling.