Can electrons transition collectively, emitting 1 photon?

Click For Summary

Discussion Overview

The discussion centers around the possibility of loosely-bound electrons transitioning collectively to a lower energy state, potentially emitting a single high-frequency photon instead of multiple photons. Participants explore the theoretical implications of such transitions, particularly in the context of quantum mechanics and collective electron behavior.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether loosely-bound electrons can evolve collectively to a low-energy state, emitting a single photon, and seeks deeper theoretical reasoning for this possibility.
  • Another participant suggests that the concept of collective electron behavior may relate to phenomena like free electron lasers or Bose-Einstein condensates, but expresses skepticism about the coherence of static electricity.
  • Some participants note that collective movement of thermal electrons is problematic due to random phases, and that the frequency of emitted photons is fundamentally linked to energy differences rather than the number of electrons transitioning.
  • There is a discussion about the photoelectric effect, with references to the necessity of multiple photons for electron ejection and the inverse scenario of multiple electrons absorbing a high-energy photon.
  • One participant mentions selection rules and the conditions under which collective transitions might occur, emphasizing the need for symmetry and angular momentum considerations.
  • Another participant acknowledges that while collective transitions are theoretically possible, they are of very low probability compared to other processes.
  • There is a mention of the indistinguishability of electrons and the collective behavior of the electron field as a whole, which complicates the notion of individual electron transitions.
  • A later reply introduces the concept of experimental quantum mechanics involving large ensembles of spins, suggesting that collective behavior can be studied in specific contexts.

Areas of Agreement / Disagreement

Participants express a range of views on the feasibility of collective electron transitions, with some supporting the idea theoretically while others highlight significant challenges and low probabilities. The discussion remains unresolved, with no consensus on the possibility or implications of such transitions.

Contextual Notes

Participants note limitations related to the coherence of static electricity, the dependence on selection rules, and the complexities introduced by indistinguishable electrons. The discussion also touches on the need for quantum field theory to fully understand the interactions involved.

TubbaBlubba
Basically, I'm asking about loosely-bound electrons, e.g. everyday static electricity. Can their combined wavefunction evolve to a low-energy state "at once", so that they emit a single high-frequency photon, rather than multiple photons of energies suggested by the potential difference?

If not, what is the deeper theoretical reason for it? How does it differ from the collective excitation of a nucleus?

As a 3rd (final) year undergrad this question hasn't occurred to me. I've taken introductory courses in QM, Subatomic, Statistical and Atomic-Molecular physics (exam on Monday actually). I have not taken courses in Solid State Physics (that's next term) nor in Lagrangian/Hamiltonian mechanics (that's my next course).

Thanks.
 
Physics news on Phys.org
Free electron laser perhaps?

How do moles worth of electrons all combine coherently as you seem to suggest. Only thing close I can think of are Bose Einstein condensates and phonons...not electrons.

By definition static electricity is incoherent.
 
houlahound said:
Free electron laser perhaps?

How do moles worth of electrons all combine coherently as you seem to suggest. Only thing close I can think of are Bose Einstein condensates and phonons...not electrons.

By definition static electricity is incoherent.
I'm not sure. I was thinking of collective movement across a potential from one bound state to another resulting in a greater photon frequency than the potential difference suggests.
 
The collective movement seems a problem with thermal electrons with random phases.

Secondly as basic QM showed the frequency is only dependent on the energy difference and independent of how many objects making the transition.
 
houlahound said:
The collective movement seems a problem with thermal electrons with random phases.
I'm imagining it as a rare but theoretically possible fluctuation.

Secondly as basic QM showed the frequency is only dependent on the energy difference and independent of how many objects making the transition.
Sure, but I have only studied many-electron systems and combined wavefunction shallowly. Pretty far removed from "particle in a box".
 
Think photoelectric effect, more photons below the threshold frequency will not eject an electron no matter how intense the beam.
 
houlahound said:
Think photoelectric effect, more photons below the threshold frequency will not eject an electron no matter how intense the beam.
I thought of that as an inverse analogy, yeah, but that would involve multiple photons and a single electron. The symmetrical inverse would be multiple electrons simultaneoysly absorbing a high-energy photon without being ejected. Presumably one could attempt to painstakingly observe it using a single-photon source.
 
As long as the selection rules are obeyed, it should be possible. The initial and final electron states should have angular momentum that differs by 1 unit, and if the initial and final states are symmetric, they can't have the same parity.
 
  • #10
bhobba said:
Yes - but with very very low probability. Other processes are of much much higher probability.

Its tied up with the fact the electron is coupled to the quantum EM field that permeates the universe. Its one of the first indications we need QFT:
http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Thanks
Bill
Thank you!
 
  • #11
Since all electrons are indistinguishable, and there is no precise notion of ''outer electron'' (except in the Hartree-Fock approximation), any transition must be regarded as being a collective behavior of the electron field as a whole.
 
  • Like
Likes   Reactions: TubbaBlubba
  • #12
A. Neumaier said:
Since all electrons are indistinguishable, and there is no precise notion of ''outer electron'' (except in the Hartree-Fock approximation), any transition must be regarded as being a collective behavior of the electron field as a whole.
Excellent point. Thank you.
 
  • #13
The answer is indeed yes.
There is a whole sub-field of experimental QM where people study large ensembles of spin interacting with for a example a microwave cavity, i.e. it is basically the generalization of "standard" cavity-QED (single spin 1/2 in a cavity) to a situation with many spin 1/2 systems. See Tavis-Cummings Hamiltonian.

There are papers out there showing store and retrieval of single photons using relatively large (10^10 or so) spin systems.
 
  • Like
Likes   Reactions: TubbaBlubba and bhobba
  • #14
And how is there frequency different to the single spin emission frequency?
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 47 ·
2
Replies
47
Views
5K
  • · Replies 4 ·
Replies
4
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 1 ·
Replies
1
Views
1K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 52 ·
2
Replies
52
Views
6K
  • · Replies 15 ·
Replies
15
Views
4K
  • · Replies 2 ·
Replies
2
Views
3K