Relation between blackbody radiation and spontaneous emission

[IcedCoffee]

TL;DR Summary

Is spontaneous emission the source of blackbody radiation?

I'm wondering what the relationship between blackbody radiation and spontaneous emission is.

As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER.

And it seems like light emission from an atom can be separated into two categories - spontaneous and stimulated emission.

LASER is driven by stimulated emission, initiated by spontaneous emission in right direction.

What about the other two?

Is it correct to say that spontaneous emission is the main source of blackbody radiation?

What about dipole radiation? Classically, it wouldn't require any electron transition... So is it just intrinsic phenomenon of electromagnetism?

 

[vanhees71]

Black-body radiation is an em. (quantum) field in thermal equilibrium and as such its phase-space distribution function results from "detailed balance", i.e., it's the state, where emission and absorption rates get the same. As Einstein derived already in 1917, to get the correct Planck radiation law you need spontaneous and induced emission and absorption. The spontaneous emission is, btw. the most simple argument for the necessity for "field quantization".

 

[WernerQH]

As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER.

This not a very useful categorization. All electromagnetic radiation is produced by accelerated charges (electrons, in most cases). Quantum mechanically this means that an electron jumps from one state to another one.

Is it correct to say that spontaneous emission is the main source of blackbody radiation?

No. Radiation from the sun is pretty thermal (though not exactly blackbody). It is not possible to determine if a particular photon was created through a process of spontaneous or stimulated emission, not to say meaningless. Stimulated emission enters only as a correction to the absorption coefficient, and the photon that escapes need not be the one that was created by spontaneous emission. It could have originated along the way by stimulated emission. As they say, photons are identical.

What about dipole radiation? Classically, it wouldn't require any electron transition... So is it just intrinsic phenomenon of electromagnetism?

Also classically a radiating electron makes transitions to lower energy states. In synchrotron radiation, for example, the energy of the radiated photons is just much smaller than that of the electrons. And radiation from atoms in the sun is mostly dipole radiation. You can think of a radiating atom as a dipole. Considering the idealized case of a harmonic oscillator, you find that it radiates photons of the exact same energy (corresponding to the frequency of the oscillator) until it reaches the ground state.

 

[vela]

As far as I know, there are three sources of EM radiation - thermal radiation, oscillating dipole (multipole?), and LASER.

Which category does a fluorescent light bulb fall into? :)

It would be better to categorize sources as either classical or quantum mechanical.

Classically, when charges are accelerated, disturbances in their electromagnetic field can propagate away. We call that disturbance an electromagnetic wave. This is how you would model how a dipole antenna works.

Quantum mechanically, light is produced when, say, an atom transitions from high energy state to a lower energy state, and the difference in energy is carried off by a photon. Whether the drop is induced by another photon (stimulated emission) or happens randomly (spontaneous emission) doesn't really matter.

Traditional lasers fall under the quantum description as they depend on stimulated emission.

Thermal radiation results from many atoms interacting with each other and exchanging energy so they can attain thermal equilibrium. As you may know, Planck's solution to theoretically predict the spectrum of a blackbody was one of the first indications of the quantum mechanical nature of the universe.

 

[WernerQH]

It would be better to categorize sources as either classical or quantum mechanical.

We are really talking about different descriptions of one and the same physics. Fundamentally there are only quantum processes, and classical physics is only an approximation valid as long as you can ignore the actual graininess of matter. It makes sense to ignore the individual electrons in a dipole antenna and consider only the combined effect of their synchronous motion (currents). But fundamentally it's the same effect of electrons interacting with photons.

Traditional lasers fall under the quantum description as they depend on stimulated emission.

Stimulated emission is considered a "quantum effect", because Einstein couldn't derive Planck's law without it. But already Einstein explained that stimulated emission has a classical analog. An electron oscillating in an electromagnetic field can not only absorb energy from the field, but also add energy, depending on the phase relation between the wave and the electron's oscillation. Plasma instabilities are usually described classically, but you could also talk about stimulated emission and "population inversion" instead of an "unstable distribution function". In thermal equilibrium stimulated emission is always smaller than "absorption" by the Boltzmann factor ${\rm exp}(-h\nu / kT)$, because the upper level is less likely to be populated than the lower level. The actual (observable) absorption coefficient is the miscroscopic "absorption" coefficient introduced by Einstein minus stimulated emission, and at low frequencies ($h\nu << kT$) is much smaller. But as you already know, it can even become negative if the equilibrium is disturbed.

 

[vanhees71]

I'd also say that stimulated emission is already present in classical electromagnetism: If you accelerate some currents due to an external em. wave, it's itself starting to irradiate em. waves as any accelerated charge does (almost always). Spontaneous emission, i.e., the deexcitation of some bound state to a lower bound state without stimulation due to an em. field, however, is explainable only by quantization of the em. field an the corresponding quantum fluctuations.

For black-body radiation Einstein's derivation in terms of kinetic theory goes as follows: Take for simplicity a cavity wall consisting two-level atoms with energy levels $E_1<E_2$ and $n_1$ and $n_2$ the number densities for the atoms in these states:

https://en.wikipedia.org/wiki/Einstein_coefficients

 

[vela]

We are really talking about different descriptions of one and the same physics. Fundamentally there are only quantum processes, and classical physics is only an approximation valid as long as you can ignore the actual graininess of matter. It makes sense to ignore the individual electrons in a dipole antenna and consider only the combined effect of their synchronous motion (currents). But fundamentally it's the same effect of electrons interacting with photons.

I agree. I could have said it better, but my point was which model of light is appropriate depends on the situation.