# Photons and Bose Einstein statistics

by DanP
Tags: bose, einstein, photons, statistics
 P: 617 Can a photon gas undergo a Bose Einstein condensation ?
 P: 4,513 First: does the question make sense in some way? What's a Bose-Einstein condensate? Second: if it does, it's a question of human or natural capability to make it happen. For the first, isn't a resonate cavity of monochromatic radiation already a condensate?
 P: 480 Bose-Einstein condensate is a well-defined term, and it's clear what the OP is asking, so your "First" argument isn't necessary at all. I am not sure what you mean by resonate cavity of monochromatic radiation though. You mean "light" in a cavity resonator?
P: 480

## Photons and Bose Einstein statistics

To the OP:

Lasers could be thought of Bose-Einstein condensates of photons.
P: 4,513
 Quote by sokrates Bose-Einstein condensate is a well-defined term
oh. How do you define it?

Look, I could go to wiki and read in paragraph one about how condensate bosons are weakly interacting. But photons are not weakly interacting. I can then go to paragraph two and read about photons as the inspiration for condensate.

It's good to define, in common, what we are talking about.
P: 480
 Quote by Phrak How do you define it?
Do you actually want me to do the definition myself, or do you want me to refer you to one of the thousands of webpages and books that define it?
 PF Patron P: 413 For someone with a name like sokrates.... :)
 P: 480 Here is one from Eric Cornell> http://www.fortunecity.com/emachines/e11/86/bose.html "This Bose-Einstein condensate (BEC), the first observed in a gas, can be thought of as the matter counterpart of the laser-except that in the condensate it is atoms, rather than photons, that dance in perfect unison."
 Sci Advisor P: 1,405 There are well defined differences between lasers and BECs. For example the BEC is supposed to be a macroscopic population of the ground state in thermal equilibrium, while lasers need population inversion and are therefore completely out of equilibrium. In my opinion the closest thing to a BEC of photons is the topic of nonequilibrium polariton condensation, which is an "in-topic" since 2006 (see for example Nature 443, 409-414 (2006) by Kasprzak et al. http://www.nature.com/nature/journal...ture05131.html). Here you have a microcavity resonant with some quantum well exciton transition. If you are in the strong coupling regime you get a dressed quasiparticle with mixed excitonic and photonic content. The photonic and excitonic content can be tuned by changing the detuning between cavity and bare exciton. Therefore you can get quasiparticles with a photonic content (and extremely light mass) of 50% to condense. However, this also means extremely short lifetimes of this quasiparticle so that you do not get equilibrium with the lattice, but only an equilibrium of the quasiparticles. As it is basically a 2D-system this is not a "complete" BEC, but rather a Kosterlitz- Thouless phase transition. Nevertheless it shows some of the essential features of the BEC like macroscopic population of the ground state, spontaneous build-up of coherence and linear polarization, a linear Bogoljubov (Goldstone) mode, quantized vortices and half-vortices and a second order intensity correlation function differing from the value expected for a laser. However, whether this should be called BEC is still a debate in the scientific community. However, at the moment those in favour of BEC write the "heavier" papers.
P: 617
 Quote by Phrak First: does the question make sense in some way? What's a Bose-Einstein condensate?

Dono. Do you make sense in some way ? Its a physics forum, for god's sake. If you dont understand the terms, don't bother to answer.
P: 617
 Quote by Cthugha There are well defined differences between lasers and BECs. For example the BEC is supposed to be a macroscopic population of the ground state in thermal equilibrium, while lasers need population inversion and are therefore completely out of equilibrium. In my opinion the closest thing to a BEC of photons is the topic of nonequilibrium polariton condensation, which is an "in-topic" since 2006 (see for example Nature 443, 409-414 (2006) by Kasprzak et al. http://www.nature.com/nature/journal...ture05131.html). Here you have a microcavity resonant with some quantum well exciton transition. If you are in the strong coupling regime you get a dressed quasiparticle with mixed excitonic and photonic content. The photonic and excitonic content can be tuned by changing the detuning between cavity and bare exciton. Therefore you can get quasiparticles with a photonic content (and extremely light mass) of 50% to condense. However, this also means extremely short lifetimes of this quasiparticle so that you do not get equilibrium with the lattice, but only an equilibrium of the quasiparticles. As it is basically a 2D-system this is not a "complete" BEC, but rather a Kosterlitz- Thouless phase transition. Nevertheless it shows some of the essential features of the BEC like macroscopic population of the ground state, spontaneous build-up of coherence and linear polarization, a linear Bogoljubov (Goldstone) mode, quantized vortices and half-vortices and a second order intensity correlation function differing from the value expected for a laser. However, whether this should be called BEC is still a debate in the scientific community. However, at the moment those in favour of BEC write the "heavier" papers.
Thanks a lot.
 P: 2,141 You can also think of the classical Maxwell equations to be analogous to the Gross-Pitaevski equation that describes a BEC. If you have a gas of a large number of N particles, then the gas can be described by a wavefunction of N position variables (if the gas is completely isolated, otherwise one needs to describe it using a density matrix). If all the N particles are in the same state, then the gas can be described by a wavefunction that depends on a single position variable. The Schrödinger equation for the N-particle wavefunction is a linear differential equation, but if you want to rewrite this in terms of the single particle wavefunction, you get a non-linear differential equation, because the original linear equation contains interaction terms between particles that have to be accounted for by an effective self interaction term. This then becomes the Gross-Pitaevski equation, a.k.a. "nonlinear Schrödinger equation". You can interpret this as a classical field equation, similar to the Maxwell equation.
P: 480
 Quote by Cthugha There are well defined differences between lasers and BECs. For example the BEC is supposed to be a macroscopic population of the ground state in thermal equilibrium, while lasers need population inversion and are therefore completely out of equilibrium. In my opinion the closest thing to a BEC of photons is the topic of nonequilibrium polariton condensation, which is an "in-topic" since 2006 (see for example Nature 443, 409-414 (2006) by Kasprzak et al. http://www.nature.com/nature/journal...ture05131.html). Here you have a microcavity resonant with some quantum well exciton transition. If you are in the strong coupling regime you get a dressed quasiparticle with mixed excitonic and photonic content. The photonic and excitonic content can be tuned by changing the detuning between cavity and bare exciton. Therefore you can get quasiparticles with a photonic content (and extremely light mass) of 50% to condense. However, this also means extremely short lifetimes of this quasiparticle so that you do not get equilibrium with the lattice, but only an equilibrium of the quasiparticles. As it is basically a 2D-system this is not a "complete" BEC, but rather a Kosterlitz- Thouless phase transition. Nevertheless it shows some of the essential features of the BEC like macroscopic population of the ground state, spontaneous build-up of coherence and linear polarization, a linear Bogoljubov (Goldstone) mode, quantized vortices and half-vortices and a second order intensity correlation function differing from the value expected for a laser. However, whether this should be called BEC is still a debate in the scientific community. However, at the moment those in favour of BEC write the "heavier" papers.
Great post!
P: 4,513
 Quote by DanP Dono. Do you make sense in some way ? Its a physics forum, for god's sake. If you dont understand the terms, don't bother to answer.
How does one ignore a member?
P: 617
 Quote by Phrak How does one ignore a member?
You focus on a point somewhere between Mars and Jupiter and concentrate. Repeat to yourself "I'm ignoring him" between 414 and 481 times.
 Mentor P: 37,655 We're watching, folks.
P: 4,513
 Quote by DanP You focus on a point somewhere between Mars and Jupiter and concentrate. Repeat to yourself "I'm ignoring him" between 414 and 481 times.
berkeman is telling us that we are both in danger of having our wrists slapped for insulting each other n stuff.

I would like to start over.

I'm sorry to have insulted your intelligence. Really, I mean it. I was attempting to ask "does this question make sense?" Scrolling down through unanswered threads, I thought--and still think, that your question deserved a bump. It's a good one. In fact, it was Einstein who asked himself, can massive bosons behave like coherent light (also bosons) in indistinguishable energy states?
P: 617
 Quote by Phrak I'm sorry to have insulted your intelligence. Really, I mean it. I was attempting to ask "does this question make sense?" Scrolling down through unanswered threads, I thought--and still think, that your question deserved a bump. It's a good one. In fact, it was Einstein who asked himself, can massive bosons behave like coherent light (also bosons) in indistinguishable energy states?
No harm done,man. I didn't perceived your lines as a insult on my intelligence. Late last night I went through some of your posts and certainly you do know what you are talking about. Id like to make amends, and I present you my apologies.

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