Is there a similar law of atomic de-excitation like radioactive disintegration?

If one starts with $N_0$ nuclei at $t=0$, then after time $t$, the number of nuclei left un-disintegrated are given by $$N(t)=N(0)\exp(-\lambda t)\tag{1}.$$

Is there a similar statistical decay law for an assembly of atoms in a two-level system with energies $E_1$ and $E_2(>E_1)$? If at $t=0$, $N_0$ atoms are made to populate the excited state $E_2$, do we expect at a later time the population of the level $E_2$ to exponentially deplete like (1)?

If not, what type of depletion law in time do we expect?

I'm not interested in what a single atom does in presence of interaction. I know that in presence of time-dependent interactions, a single atom in a simple two-level system makes back and forth transition between the levels. My question is about the overall statistical behavior of an assembly of atoms in a two-level system prepared in the excited state at $t=0$.

• Assuming the transitions are a Poisson process then yes. – lemon Jun 24 '17 at 14:10
• Are they Poisson Processes? – Tausif Hossain Jun 24 '17 at 15:57
• @TausifHossain Sorry. I'm not aware of what a Poisson process is though I'm aware of Poisson distribution. – SRS Jun 24 '17 at 17:15
• I think that depends on how the atoms in your assembly can interact. For example, if they're clustered within a laser cavity with an appropriate mode, they are more likely to de-excite in a sudden cascade than if they're just sitting in a vacuum. – Henning Makholm Jul 10 '17 at 17:26
• taken from Wikipedia: "where $A _{21}$ is the Einstein coefficient for spontaneous emission, which is fixed by the intrinsic properties of the relevant atom for the two relevant energy levels." – jim Jul 10 '17 at 18:35