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I'm interested in Electromagnetically Induced Transparency (EIT), Lasing Without Interference (LWI) and/or Stimulated Raman adiabatic passage (STIRAP) and have some basic questions.
First, I think the concepts involved, at this basic level, are similar for these three. Yes?
I don't understand some of the explanations given in sources. Here are two quotes to illustrate:
"One approach is to extend the density matrix treatment used to derive Rabi oscillation of a two-state, single field system. In this picture the probability amplitude for the system to transfer between states can interfere destructively, preventing absorption."
"Another approach is the 'dressed state' picture, wherein the system + coupling field Hamiltonian is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination of Autler-Townes splitting and Fano interference between the dressed states."
- For the time being, I'm giving up on Rabi oscillation and Autler-Townes splitting, etc, and want to get an intuitive picture using basic ideas.
Key question: is this simple approach (that I'm about to show) close enough to be, at least, intuitively useful? Or is it hopeless, and the new (to me) concepts are necessary for any understanding at all?
Now consider the "ladder" configuration, with 3 states at ascending energy levels. For example 3 adjacent orbitals for an electron in an atom.
Let's call the 3 states a, b, and c instead of (what seems to be usual) |1>, |2> and |3>, to simplify notation. Should be good enough for this discussion. a is the ground state.
Transitions a=>b and b=>c must be allowed by selection rules. But a=>c is not; normally you must go through b to get from a to c. The key idea here is to make that a=>c transition possible without stopping at b. Or, for EIT (not so much STIRAP), the key idea is to disallow a=>b. Is there much of a difference between these two "key ideas"?
We have two lasers tuned to the two allowed transitions: "probe" for a=>b, "coupling" for b=>c. I.e., the photons have the energy needed to transition between those states. For instance if W is the energy gap between a and b, then the probe photons' frequency is W/h.
First we shine the coupling laser on the atom(s). That "couples" b and c. Thus, if the electron were in b state, it would absorb a photon and "jump" to c.
Note that it's required for state c to be robust and metastable.
Question: Since c is metastable the electron won't readily fall to b (which is not very stable). But in the presence of the coupling laser, it would fall easily, due to stimulated emission - right?
Second, we now shine the probe laser, at a lower intensity. Normally that would cause the electron in a (the ground state) to absorb a probe photon and jump (i.e. transition) to b. Then the coupling photon would be absorbed, the electron would jump to c; it would then transit back to b, by stimulated emission (or, just drop naturally), then maybe it would drop to a. In general it would hop around in the presence of these 2 lasers.
This is where the "trick", sometimes called "dark state", comes in. There are two paths the electron can take from a to b:
a=>b
a=>b=>c=>b
So we cleverly "tune" or "adjust" the whole set-up so that the amplitudes of the wave function for these two paths are out of phase. So, they interfere and cancel, making it impossible for the electron to occupy state b.
Obviously this adjusting is difficult. Probably that's the "hard part" of the whole technique. But at the moment I'm not interested in those details, just want to get the picture.
Given it can't live in state b, but it's being stimulated to leave state a, there's only one place it can go, state c. Mission accomplished.
Question: why doesn't it just stay in, or return to, state a? Or, it can stay in a, and that's alright - the point is just to keep it out of b?
For EIT the point is not so much to keep it out of b, rather to stop it from absorbing the probe photon, by using it to transit from a=>b. That absorption would destroy the transparency. But then, is it important for it to actually go to c?
That's as far as I've gotten; getting confused at the end. It may be that my picture is more appropriate for STIRAP, which is what I was first looking at. What I'm hoping to hear is that I've got the right idea, BUT ... followed by an intuitive answer, phrased in my language. (Perhaps I shouldn't try to put together these 3 different techniques?) But if instead, I have to learn Fano interference, etc, to get anywhere, then a link for same would be appreciated. If you wish to give your take on it using those more correct concepts, fine, but don't waste too much of your time. If that's the way it is I'll study any links you might provide and come back later.
Thanks for reading, if in fact you did!
First, I think the concepts involved, at this basic level, are similar for these three. Yes?
I don't understand some of the explanations given in sources. Here are two quotes to illustrate:
"One approach is to extend the density matrix treatment used to derive Rabi oscillation of a two-state, single field system. In this picture the probability amplitude for the system to transfer between states can interfere destructively, preventing absorption."
"Another approach is the 'dressed state' picture, wherein the system + coupling field Hamiltonian is diagonalized and the effect on the probe is calculated in the new basis. In this picture EIT resembles a combination of Autler-Townes splitting and Fano interference between the dressed states."
- For the time being, I'm giving up on Rabi oscillation and Autler-Townes splitting, etc, and want to get an intuitive picture using basic ideas.
Key question: is this simple approach (that I'm about to show) close enough to be, at least, intuitively useful? Or is it hopeless, and the new (to me) concepts are necessary for any understanding at all?
Now consider the "ladder" configuration, with 3 states at ascending energy levels. For example 3 adjacent orbitals for an electron in an atom.
Let's call the 3 states a, b, and c instead of (what seems to be usual) |1>, |2> and |3>, to simplify notation. Should be good enough for this discussion. a is the ground state.
Transitions a=>b and b=>c must be allowed by selection rules. But a=>c is not; normally you must go through b to get from a to c. The key idea here is to make that a=>c transition possible without stopping at b. Or, for EIT (not so much STIRAP), the key idea is to disallow a=>b. Is there much of a difference between these two "key ideas"?
We have two lasers tuned to the two allowed transitions: "probe" for a=>b, "coupling" for b=>c. I.e., the photons have the energy needed to transition between those states. For instance if W is the energy gap between a and b, then the probe photons' frequency is W/h.
First we shine the coupling laser on the atom(s). That "couples" b and c. Thus, if the electron were in b state, it would absorb a photon and "jump" to c.
Note that it's required for state c to be robust and metastable.
Question: Since c is metastable the electron won't readily fall to b (which is not very stable). But in the presence of the coupling laser, it would fall easily, due to stimulated emission - right?
Second, we now shine the probe laser, at a lower intensity. Normally that would cause the electron in a (the ground state) to absorb a probe photon and jump (i.e. transition) to b. Then the coupling photon would be absorbed, the electron would jump to c; it would then transit back to b, by stimulated emission (or, just drop naturally), then maybe it would drop to a. In general it would hop around in the presence of these 2 lasers.
This is where the "trick", sometimes called "dark state", comes in. There are two paths the electron can take from a to b:
a=>b
a=>b=>c=>b
So we cleverly "tune" or "adjust" the whole set-up so that the amplitudes of the wave function for these two paths are out of phase. So, they interfere and cancel, making it impossible for the electron to occupy state b.
Obviously this adjusting is difficult. Probably that's the "hard part" of the whole technique. But at the moment I'm not interested in those details, just want to get the picture.
Given it can't live in state b, but it's being stimulated to leave state a, there's only one place it can go, state c. Mission accomplished.
Question: why doesn't it just stay in, or return to, state a? Or, it can stay in a, and that's alright - the point is just to keep it out of b?
For EIT the point is not so much to keep it out of b, rather to stop it from absorbing the probe photon, by using it to transit from a=>b. That absorption would destroy the transparency. But then, is it important for it to actually go to c?
That's as far as I've gotten; getting confused at the end. It may be that my picture is more appropriate for STIRAP, which is what I was first looking at. What I'm hoping to hear is that I've got the right idea, BUT ... followed by an intuitive answer, phrased in my language. (Perhaps I shouldn't try to put together these 3 different techniques?) But if instead, I have to learn Fano interference, etc, to get anywhere, then a link for same would be appreciated. If you wish to give your take on it using those more correct concepts, fine, but don't waste too much of your time. If that's the way it is I'll study any links you might provide and come back later.
Thanks for reading, if in fact you did!