I am trying to understand rotating wave approximation in terms of quantum optics used in Rabi Oscillations. What is the physical meaning of this approximation? And more importantly why do we need it? Energy conservation?
In simple words, it's an approximation to find an approximate analytic solution for time dependent schrodinger eqn. of a two level system coupled to a weak electric field in resonant with the transition. To understand more please read this notes. It's very simple and elementary.
http://arxiv.org/pdf/1301.3585v3.pdf
or read
http://books.google.fr/books?id=PJxAzgU4PqgC&pg=PA147&dq=rotating+wave+approximation&hl=en&sa=X&ei=KhN7VPOQCYKyabSDgpAP&ved=0CDAQ6AEwAg#v=onepage&q=rotating%20wave%20approximation&f=false
For a two level atomic system which interacts with oscillating electric field , whose frequency is near resonance with the atomic transition frequency, when we solve the time dependent Schrodinger equation, we get the time dependent coefficient of eigen function to be dependent on the sum (w + w0 ) and difference (w - w0 ) of frequencies. Since w ≈ w0 , detuning is very small, so we neglect the term which oscillates rapidly , as on an appreciable time scale these oscillations will quickly average to zero.
@Raiju...thnx. Ignore my earlier post, I had not read the pdf at arxiv.
Good answer from Raiju Puthumpally Joseph. You may read Bruce Shore book's where the RWA is really well explained.
You want to know a physical sense of RWA. This is a mathematical model, which is used for description of the dynamics of population transfer in a two level quantum system. It does not have any clear physical sense. The situation here is similar to those in a quantum physics as a whole. The main difference is that in the case of quantum mechanics we discuss it’s different physical interpretations, but in the case of RWA we do not have any physical interpretation at all.
For example, such interesting and important physical phenomenon, as adiabatic population transfer in a two level quantum system due to sweeping of resonance conditions, does not have any physical explanation till now.
I believe that this physical phenomenon is not a proof, but is one of a numerous manifestations of the fundamental property of quantum physics – inequality of it’s forward and reversed processes (see arXiv:0706.2488v6).
Adding some more notes to the explanation of Raiju Puthumpally Joseph, just to mention that RWA also works when the system is coupled to strong fields (not only weak), however, in this aspect, the frequency of the external field should be slower than the Rabi frequency!
All the answers that I read refer to the mathematical aspects of this approximation while the question is mainly about the physics behind this approximation (What is the physical meaning of this approximation?). Despite the fact that there are some conditions that should exist in order to be allowed to apply this approximation, physically it corresponds to neglecting all terms which do not conserve the number of excitations. In other words whenever we want to describe a quantum light-matter interaction by a model in which the number of excitations is conserved (and we have some other conditions like weak coupling) then we can use this approximation and go from the quantum Rabi model to Jaynes Cummings model. In fact, in the quantum Rabi model, these terms remain, and as a consequence, the number of excitations can change.
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