Photon/lightwave velocity in different mediums

[echoSwe]

The question is, how exactly it is that light can travel slower when not in vaccum, and how for example Bose-Einstein condensates can be used to slow light a lot, or even stopping it? http://www.osa-opn.org/abstract.cfm?URI=OPN-16-5-30

I've read:
http://en.wikipedia.org/wiki/Photon#Photons_in_matter
http://en.wikipedia.org/wiki/Dispersion_(optics)
http://en.wikipedia.org/wiki/Phonon
http://en.wikipedia.org/wiki/Exciton
http://en.wikipedia.org/wiki/Polariton
http://en.wikipedia.org/wiki/Quantum_superposition

What I don't understand from the discription given by wikipedia is when it says, syllogistically:

1. In a material, photons couple to the excitations of the medium.
2. "Coupling" means here that photons can transform into these excitations (that is, the photon gets absorbed and medium excited, involving the creation of a quasi-particle) and vice versa (the quasi-particle transforms back into a photon, or the medium relaxes by re-emitting the energy as a photon). However, as these transformations are only possibilities, they are not bound to happen and what actually propagates through the medium is a polariton; That is the quantum-mechanical superposition of the energy-quantum, i.e. the q-m superposition of the photon; being a photon and of it being a quasi-particle matter excitations. That is; the linear combination of the two eingenstate of the photon and the electron.
3. Thus, a polariton is the result of the mixing of a photon with an excitation of a material. The most discussed types of polaritons are [...]; exciton-polaritons, resulting from coupling of visible light with an exciton;
4. The linear combination of two or more eigenstates results in quantum superposition of two or more values of the quantity.
5. An exciton is a bound state of an electron [its eingenstate?] and an imaginary particle called an electron hole in an insulator or semiconductor, and such is a Coulomb correlated electron-hole pair. It is an elementary excitation, or a quasiparticle of a solid.

So what does it say? There IS a photon coupling (1), which is photons transforming into polaritons (3) by the superpositioning (4) of the electron- (5) and quantum/photon-eigenstates (2), into the quasi-particle: "exciton-polaritons" (3).

What bothers me is that it also states that the photon absorptions/transformations doesn't necessaryly happen (2). The quasi-particle is the polariton (probably named from the electron-polarity from its spin?)

Have I understood it correctly?

It begs the question - what is it that makes photons/exciton-polaritons speed slower because of the superpositioning?

Matter excitations have a non-linear dispersion relation; that is, their momentum is not proportional to their energy. Hence, these particles propagate slower than the vacuum speed of light. (The propagation speed is the derivative of the dispersion relation with respect to momentum.) This is the formal reason why light is slower in media (such as glass) than in vacuum. (The reason for diffraction can be deduced from this by Huygens' principle.) Another way of phrasing it is to say that the photon, by being blended with the matter excitation to form a polariton, acquires an effective mass, which means that it cannot travel at c, the speed of light in a vacuum.

Can you say that the photon enters the medium, interferes with the electron(s) to create a matter excitation/an exciton, whereafter the same photon's eigenstate becomes quantum mechanically superpositioned with the eigenstate of the quasi-particle-exciton, forming the exciton-polariton, which cannot go above c, because it has rest-mass?

Has it got something to do with: "The propagation speed is the derivative of the dispersion relation with respect to momentum."? Has it got rest-mass at all, or is it just to be taken metaphorically?

Post scripum:
I'd love maths, to explain it, as long as I can follow it upwards, from the level of an IB Mathemathics Higher Level education.

 

[ZapperZ]

Have you read our FAQ in the General Physics forum?

Zz.

 

[echoSwe]

Well, now I have, but it still doesn't answer my question; just makes me more confused. It stated that the lattice of ions and electrons form some sort of phonon absorption spectrum which is similar to the eigenfrequency of objects - so that photons outside the possible absorption range will NOT be absorbed but rather just "absorbed" and then reemitted, following the logic that something cannot be emitted unless firstly absorbed.

On the other hand, if a photon has an energy beyond the phonon spectrum, then while it can still cause a disturbance of the lattice ions, the solid cannot sustain this vibration, because the phonon mode isn't available. [...] So the lattice does not absorb this photon and it is re-emitted but with a very slight delay.

...which I find confusing.

Also, your FAQ page doesn't falsify, nor justify what I have written in the first post. It only feels like that FAQ is trying to "dummify" me since my first post is way above the level of that FAQ.

 

[ZapperZ]

Well, now I have, but it still doesn't answer my question; just makes me more confused. It stated that the lattice of ions and electrons form some sort of phonon absorption spectrum which is similar to the eigenfrequency of objects - so that photons outside the possible absorption range will NOT be absorbed but rather just "absorbed" and then reemitted, following the logic that something cannot be emitted unless firstly absorbed.

...which I find confusing.

All it means is that the lattice ions react to the oscillating E-field of the photon (i.e. gain energy from it), and then retransmit since they can't sustain such modes. If you look at the optical band structure of the material, this is equivalent to having an optical band gap that is larger than the photon energy.

On the other hand, if the phonon modes exists, these oscillations can be sustained and dissipated as lattice vibrations. In the band structure picture, this means that the photon energy is now larger than the optical band gap and can cause an absorption. Upon such absorption, depending on the material, it can either retransmit the photon, or the photon's energy is lost via other means.

Also, your FAQ page doesn't falsify, nor justify what I have written in the first post.

I wasn't trying to falsify or justify anything, since you are trying to tackle too many things in your post. Keep in mind that optical conductivity can occur via differnt mechanisms in different systems. That's why the FAQ was written specifically for one such system. It cannot explain the optical absorption and transmission in BE gasses.

Zz.

 

[echoSwe]

"The lattice ions react to the oscillating electromagnetic field of the photon and e.g. gain energy from it, then retransmit"
So how would the lattice of ions together with the electrons react? By modes of vibrations? As heat - that is? But that goes, as the FAQ said, not to reemission then.

Through excitation of electrons? Quantinizations of the emitted light? No...

What is the optical band gap?

Perhaps you cannot explain it by yourself. But the forum is large, and it's fully possible to post links and to write what you have time for. I don't expect people not having to time answer, obviously. I'm merely asking for explanations of something I find interesting, and I tried to do the dirty work myself - but I still have questions.

 

[ZapperZ]

What is the optical band gap?

Do you know what an electronic band structure is? Y'know, the one that can show you a band gap for semiconductors, etc.? If you do, then this is the optical equivalent.

Zz.

 

[echoSwe]

Yes, http://en.wikipedia.org/wiki/Electronic_band
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html
- so kind of a description of the first energy of ionisation, or the "work function" as in the photoelectric effect?

So you're saying that the photon energy has to be large enough to overcome the optical band gap. Then the photon can be absorbed.

So how does the re-emission of a photon whose energy is less then the optical band gap, work together with the discussion about quasi-particles and the eigenstates? What about the stuff about the rest-mass/the nonlinear energy-momentum relationship for polaritons?

 

[ZapperZ]

Yes, http://en.wikipedia.org/wiki/Electronic_band
http://hyperphysics.phy-astr.gsu.edu/hbase/solids/band.html
- so kind of a description of the first energy of ionisation, or the "work function" as in the photoelectric effect?

Oh no. There are considerable difference between this and the photoelectric effect. That's a different issue.

So you're saying that the photon energy has to be large enough to overcome the optical band gap. Then the photon can be absorbed.

So how does the re-emission of a photon whose energy is less then the optical band gap, work together with the discussion about quasi-particles and the eigenstates? What about the stuff about the rest-mass/the nonlinear energy-momentum relationship for polaritons?

If you simply look at this using the optical band picture, then the photon isn't absorbed, and that's that. It will continue to be transmitted since there's nothing to swallow it up.

The problem here is that you are juggling way too many stuff that's going in all different directions. Is there a particular reason why you are looking this up in such details? It would help if you describe a particular system you are trying to understand, because if you want to just learn about optical conductivity in ALL systems, then that is the subject of whole books in condensed matter. I have no ability to provide such instructions on here.

Zz.

 

[echoSwe]

No reason. I'm just interested in how things work (isn't that the whole reason you study physics in the first place?). Take glass for an example. The question I posed in msg.1 will do, I won't be demanding much more than that...

Also, as opposed to what you state in your FAQ about quantum mechanics and the hardships non-university people experience when trying to learn it, is not from the nature of the subject of study as such, but rather from the simplified and metaphorical explanations one get when trying to learn it. Because as you state yourself - QM doesn't necessarily follow the "feeling" that you have about how nature works, and therefore the simplifications can be rather bad from a learning perspective. It's hard to get answers, simply put; for numerous reasons.

My physics teacher either says: "Let's take it after the lesson" (like 5 minutes before the next lessons, that is), or "Well, we got to save some for the university teachers, don't we...". lol...

 

[ZapperZ]

No reason. I'm just interested in how things work (isn't that the whole reason you study physics in the first place?). Take glass for an example. The question I posed in msg.1 will do, I won't be demanding much more than that...

Yes, but I'd rather do it "right" than picking up a hodge podge of stuff that I read off the web. It is my main criticism against web-based sources, such as Wikipedia.

Learning isn't just reading about disconnected facts. It is the presentation of a series of ideas in a coherent and systematic fashion. What this means is that a textbook, for instance, must try to think of the most logical and pedogogical way of presenting something. This is what is missing in websties such as Wikipedia (ignoring for the moment the accuracy of the information you get) where you do not get such a thing due to the many "cook" involved in making the soup. So you end up with a disjointed set of information in which, as you can see for yourself, appears to be going in all directions.

Also, as opposed to what you state in your FAQ about quantum mechanics and the hardships non-university people experience when trying to learn it, is not from the nature of the subject of study as such, but rather from the simplified and metaphorical explanations one get when trying to learn it. Because as you state yourself - QM doesn't necessarily follow the "feeling" that you have about how nature works, and therefore the simplifications can be rather bad from a learning perspective. It's hard to get answers, simply put; for numerous reasons.

But you on your part must also be reasonable in seeking answers to such questions, considering the "vocabulary" with which you are equiped with. There's no point in my giving you the full-blown technical answer if these things simply zip past your head. It is why we did our FAQ in the first place. While one can easily open various books to find answers to such questions, the FAQ was meant to answer this in the most naive form without invoking the technical details that most people without a physics background can understand. It isn't meant to be the definitive answer. It was meant to be a stop-gap measure to stop a number of misconception that many people hold.

There are no shortcuts to learning physics. People on here have heard me say that many times. One cannot learn it in bits and pieces. Just because you want to know about optical conductivity in a medium does not mean you don't have to learn about classical mechanics, even when it isn't apparent what the connection is between the two.

Zz.

 

[echoSwe]

Well, I have some physics background. I just graduated the ib course physics higher level.

So what's your point? That I'm wrong in asking? That I should rather borrow a book instead of bothering the forum? That I'm naive, trying to learn it without a teacher or a book? The least you could do, would be to give me a tip for a book for deals with what basics you feel I need to know plus an explanation of my question, instead of telling me off for asking the question... Which you in fact are to some extent.

Sincerely
Henrik

 

[ZapperZ]

Well, I have some physics background. I just graduated the ib course physics higher level.

So what's your point? That I'm wrong in asking? That I should rather borrow a book instead of bothering the forum? That I'm naive, trying to learn it without a teacher or a book? The least you could do, would be to give me a tip for a book for deals with what basics you feel I need to know plus an explanation of my question, instead of telling me off for asking the question... Which you in fact are to some extent.

Sincerely
Henrik

Maybe you have forgotten, but I was responding to this:

Also, as opposed to what you state in your FAQ about quantum mechanics and the hardships non-university people experience when trying to learn it, is not from the nature of the subject of study as such, but rather from the simplified and metaphorical explanations one get when trying to learn it. Because as you state yourself - QM doesn't necessarily follow the "feeling" that you have about how nature works, and therefore the simplifications can be rather bad from a learning perspective. It's hard to get answers, simply put; for numerous reasons.

I never said one shouldn't ask. But when one demands complete answers to something, one has to be aware that maybe one isn't equiped to handle the answer. Physics isn't just some handwaving description. Every concept, principles, and ideas have underlying mathematical description. So if I were to describe to you something in words, these are nothing more than a superficial description, and thus, subjected to some degree of ambiguity and vagueness. The ONLY way to get the full picture is to study it in its formalism. That is why these things are "methophorical". There's no other way to do this other than the formalism.

You want text? I'll give you text:

G.D. Mahan "Many-Particle Physics"
Ashcroft and Mermin "Solid State Physics".

Zz.

 

[Dense]

You know, I see this happening all the time on this forum. Someone asks a question, and gets the reply that the physics forum isn't the place to get answers, and instead they should go study.

I disagree that using words rather than equations will present a merely superficial description. I firmly believe that, if one understands what they're talking about, one can explain it in plain language.

I also disagree that the only way to comprehend a concept is to study it formally. It is common to feel that, hey, I had to bust my hump studying to get the concept, so why shouldn't you. But that is not a good reason to withhold an explanation.

I also disagree that it is appropriate to withhold an explanation merely because one perceives that the audience is not sophisticated enough to understand it.

All that is required is a straightforward explanation in plain language of a given concept. If the questioner still doesn't get it, then a polite (emphasis on "polite") direction to sources that might help would be appropriate. Or better yet, a re-thought-out explanation that is even clearer.

But politeness should be the rule here, as opposed to huffy bickering over the appropriateness of asking questions.

 

[Dense]

Anyway, my ultra-super-glib (yet accurate) answer to your question is:

1) The speed of light is always c. It does not slow down in any media.

2) The apparent reduction in speed is because photons get absorbed by the matter in the media, which then re-emits photons. It takes time for that to happen. This absorbtion and re-emission is what "slows light down" and also what refracts it.

 

[inha]

2) The apparent reduction in speed is because photons get absorbed by the matter in the media, which then re-emits photons. It takes time for that to happen. This absorbtion and re-emission is what "slows light down" and also what refracts it.

This is not correct except for the x-ray energy scale in which the photons can trigger atomic transitions. Otherwise (and even with x-rays) you must consider photon-phonon, photon-band electron etc. interactions.

 

[Super Nade]

So what does it say? There IS a photon coupling (1), which is photons transforming into polaritons (3) by the superpositioning (4) of the electron- (5) and quantum/photon-eigenstates (2), into the quasi-particle: "exciton-polaritons" (3).

What bothers me is that it also states that the photon absorptions/transformations doesn't necessaryly happen (2). The quasi-particle is the polariton (probably named from the electron-polarity from its spin?)

Have I understood it correctly?

It begs the question - what is it that makes photons/exciton-polaritons speed slower because of the superpositioning?

You have to view this as a quantum mechanical phenomena. When you do the math, it looks something like this:

H0 = Hamiltonian of the bare atom
HL= Hamiltonian of the photon
HI= Interaction Hamiltonian between matter and light (usually under the rotating wave approximation)

H= Net hamiltonian, which is the sum of the above three.

Now, if you work in the Interaction picture i.e solve Schrodinger's equation in the interaction picture, with HI, you obtain the time evolution of the system.

The point of this was to lay utmost emphasis on the word system. You can no longer treat light and matter seperately. For example, imagine we have one photon and one 2 level atom in a cavity. The state of the system is given as:-

(no photon, atom in the excited state)c1+(one photons, atom in the ground state)c2.

c1 and c2 are probability amplitudes and the stuff in brackets are the composite states I was referring to. Again, the emphasis is on the quantum system as a whole. This emphasis comes about because of the interaction hamiltonian term, which specifies how light couples with the atom.

In case of slow light experiments, we are looking at a three level lambda type system interacting with a weak probe and a strong coupling beam. Now, if you write the interaction Hamiltonian and solve for its eigen-values and eigen-vectors, you see something peculiar. In the new base states of the interaction hamiltonian, absoption of the probe completely vanishes. The original energy levels of the atom are "dressed" by the photon fields, i.e there is a shift. If you take the expectation value of the atom being in the excited state (lambda system so there is one excited state) of the bare atom basis, it turns out to be 0.

Thus, the probe passes unabsorbed.

In case of a collective excitation of atoms, the refractive index becomes very very large (if you calculate the susceptibility for the atomic medium, you will see). Thus light is "slowed or stopped".

Now, this collective atom-photon entanglement (going back to the system emphasis) is called a polariton.

Why is it called a polariton? This is because this is essentially an effect due to the atomic dipoles interacting with light.

This whole body of work comes under coherent preperation of an atomic medium by light. The key here is the word coherence, which, mathematically speaking are the off diagonal terms in the interaction hamiltonian. There are several sources of decoherence in real world experiments, most notably, atomic collisions. The article you were referring to (I didn't read it) would have referred to experiments of Lene V. Hau and M.O Scully, S.E Harris and M.Fleischhauer. Hau's experiment was with BEC and Harris et al used "hot" (70-80 C) rubidium atoms. So, it was shown that under proper conditions, doppler broadning was not a big deal.

I forgot to mention that this is called Electromagnetically Induced transparency. It is characterized by a very narrow window, within which the probe beam can pass unattenuated. Within this window (plot the complex part of the susceptibility), the refractive index increases by several orders of magnitude.

This should be useful:-
http://www.unl.edu/amop/pdf_files/RMP_EIT_Fleischhauer.pdf

What you have proposed below is incorrect. I love the math as well, but it sucks to type out equations :p

In case

Can you say that the photon enters the medium, interferes with the electron(s) to create a matter excitation/an exciton, whereafter the same photon's eigenstate becomes quantum mechanically superpositioned with the eigenstate of the quasi-particle-exciton, forming the exciton-polariton, which cannot go above c, because it has rest-mass?

Has it got something to do with: "The propagation speed is the derivative of the dispersion relation with respect to momentum."? Has it got rest-mass at all, or is it just to be taken metaphorically?

Post scripum:
I'd love maths, to explain it, as long as I can follow it upwards, from the level of an IB Mathemathics Higher Level education.