An illustrative argument easily comprehensible by non-experts would be most helpful
Dear Sergey,
It is very difficult to help you just knowing what you are telling about this question. You need to say what kind of materials are you thinking about and what is the magnetic response that you hope to find, for instance, are you thinking in coherent magnetic response?
Dear Daniel,
Thanks for the response,
Yes, coherent magnetic response is a good counter-example that indeed can be observed in optics (for example in atomic systems with prohibited electric dipole transitions). But can we identify a large class of optical systems/devices exhibiting and exploiting such properties, or would we say that such phenomena are a bit more exotic and not so ubiquitous?
If we can agree that the latter is the case, why is it so?
Dear Sergey,
If we restrict to this effect we can say that it is really exotic. The explanation is that the electric dipole transitions since they are stronger by about five orders of magnitude, and therefore it is much easier to have electronic transition from the ground level to an excited level due to the electric field and no to the magnetic one. Thus you must look for a material which has the electric dipole transition forbidden which is not so common. One material is an europium doped crystal using 7F0 → 5D1 magnetic-dipole transition within the 4f shell and an external electromagnetic field providing such frequency (in microwaves).
Thanks Daniel,
We normally explain that the electric dipole transitions are more probable as they come as a first term in the expansion of a time-dependent perturbation of the Hamiltonian. This explanation, however, is a bit heavy on math for non-specialists, and it is difficult to see an intuitive physics behind. I wonder if there can be a more intuitive explanation, or it is unlikely to "apply intuition" here as in some other cases in quantum mechanics?
On the other hand, at lower frequencies (e.g. microwaves) where the corresponding transitions happen not between different levels, but between different sublevels of the same level, it is more common to find a magnetic response. I also wonder if this can be explained without math.
Dear Sergey.
If you try to explain that behaviour as a consequence of a perturbative method you have problems. These always "mathematical" reasonings. What I have tried to tell you is a physical reason, the elecric coupling is almost 5 orders of magnitude higher than the magnetic one. Thus the Hamiltonian has to take into account this physical condition and that can be done for many different forms, for instance using the Golden Fermi rule for calculating transitions, etc...
Thanks Daniel,
My question was why the magnetic response is weak, e.g. why the electric coupling is almost 5 orders of magnitude higher than the magnetic one. While the perturbative method answers the "why" question, I wonder what would be a good physical reasoning.
Maybe if you regard the magnetic effect as a relativistic effect of moving charges? It might be an approach to linking general relativity to quantum scale effects? I'm not a physicist so I don't know the answer to that!
You can find the answer in chapter 5 in optical metamaterials book for Vladimir Shalaev.
The answer is:
the magnetic coupling to atom = alpha*q*ao/2, where alpha is structural parameter= 1/137.
the electric coupling= q*ao, thus for the EM wave , the magnetic field will be weaker than the electric field by 1/137 times.
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