This is why I always say that I learn from you more than you think!and this "operation in the zone" will happen to everyone at some point in their life. I was just fortunate that it came at a critical time when I needed it. But, I think there is a lesson here. If you prepare to the fullest extent of your ability and KNOW you deserve to do well, there is a sense of calm you will have when you enter the "arena". This confidence can do nothing but improve your chances of success.
I'm using this text.Second, consider the physics. Thermal excitation occurs when the thermal energy KT is comparable to or greater than the energy difference E2-E1. If kT is small, there is not enough energy to cause the excitation and N2<<N1. If KT is large, then there is plenty of energy to cause excitation. This might lead you to believe that this leads to N2>N1, but if that happened, you would need an energy input to the system to maintain the population inversion. However, an energy source causing excitation is not a case of thermal equilibrium. In other words if N2 could be greater than N1, you would be able to make a laser without an input energy source and you would have free energy. So energy conservation requires N2< N1 in thermal equilibrium.
Yes, that's exactly what I said. And, this is for thermal equilibrium only.I would say that in case of two-level energy state system even when the temperature T is infinite, the number of atoms in the excited state, N2, cannot exceed the number of atoms in the ground state, N1.
A two or three level system can support population inversion. But neither will happen in thermal equilibrium. What is needed is an external source of energy other than thermal energy. When I mentioned energy input, I was implying energy other than thermal energy. For example, light or electricity would qualify as an energy source.It simply means that a material with two-level energy states cannot support population inversion, i.e. N2 > N1, even when a lot of energy is input into the system. On the other hand, three-level energy system can support population inversion due to its metastable states assuming it is supplied with constant source of energy.
In a sense, the two levels are competing with each other. When the lower level absorbs a phonon (phonons are the quantum particles associated with heat and act similarly to photons in that they can be emitted and absorbed in a material) and gets excited to the higher level, that higher level can then emit the same type of phonon, either spontaneously or in a stimulated way. This is why thermal equilibrium can not give you a net energy in usable form. The more excited states there are, the more phonons are emitted. This competition can never let N2=N1 unless the temperature becomes infinite, which is not possible by known physics.I'm also confused about one other point. It is seen, using Maxwell-Boltzmann distribution, that in case of two-level energy system we needed to raise the temperature to such high level just to get some fraction of the atoms into the excited state. Perhaps, we needed such a high temperature because a lot of energy from the raised temperature goes into other processes such as heating effect.
Thermal equilibrium does not provide a usable energy source. If it did, we could power all our devices from ambient temperature. But, we know that we can only get energy via temperature differences, which is not thermal equilibrium. When you provide power to a system (electric power, optical power, mechanical power etc) you no longer have thermal equilibrium.I understand that Maxwell-Boltzmann distribution is used for gases. But I was just thinking that perhaps using an electric current could be more efficient in the way that most of the energy goes only into exciting the atoms. In other words, raising temperature in order to excite the atoms is not an efficient way to do this..
Yes, the long metastable lifetime makes the threshold energy/power less, and makes it easier to achieve population inversion and lasing.
So, population inversion is also possible in two-level energy system but it required an source of energy other than thermal energy, right? I had thought that in two-level system the population inversion is impossible. Perhaps it would be more right to say that in two-level system population inversion is achievable but overall the process is very inefficient and a lot of energy, say electrical, needs to be pumped in to maintain the inversion.A two or three level system can support population inversion. But neither will happen in thermal equilibrium. What is needed is an external source of energy other than thermal energy. When I mentioned energy input, I was implying energy other than thermal energy. For example, light or electricity would qualify as an energy source.