- #1
SomeonenoemoS
- 4
- 0
So, this is something I've never understood in detail.
If an excited system decays and emits a photon, the lifetime of the decay will broaden the spectrum of the photon right?
Basically just a Fourier transform of the "shape" of the emission in time to get the frequency components of the emitted light.
As this emitted photon is a superposition of a continuous range of frequencies, if it passes trough a spectrometer, I can detect it as having one of those frequencies with respective probability right?
But if I detect a photon with 'more' energy than I thought was present in the excited system, where does that energy come from? Was this uncertainty in energy already present in the system?What's wrong with the following thought experiment?
1) I generate a photon in a very good optical cavity. With this single photon, I can associate a very well defined frequency and energy.
2) I now pass an atom (or 2 level system with same energy difference) in ground state trough this optical cavity. It stays inside the optical cavity for half a Rabi cycle and absorbs the photon with 100% certainty.
3) The atom is now out of the cavity and is excited with 100% certainty.
4) The excited atom now starts decaying and emits a photon. But due to the decay the spectrum is "broad".
5) I can now detect the photon with a slightly different energy? At what step did extra energy get in or get out?I'm missing something. I've asked it to people before, but I never got a good answer. (or I didn't get it).
Thanks!
If an excited system decays and emits a photon, the lifetime of the decay will broaden the spectrum of the photon right?
Basically just a Fourier transform of the "shape" of the emission in time to get the frequency components of the emitted light.
As this emitted photon is a superposition of a continuous range of frequencies, if it passes trough a spectrometer, I can detect it as having one of those frequencies with respective probability right?
But if I detect a photon with 'more' energy than I thought was present in the excited system, where does that energy come from? Was this uncertainty in energy already present in the system?What's wrong with the following thought experiment?
1) I generate a photon in a very good optical cavity. With this single photon, I can associate a very well defined frequency and energy.
2) I now pass an atom (or 2 level system with same energy difference) in ground state trough this optical cavity. It stays inside the optical cavity for half a Rabi cycle and absorbs the photon with 100% certainty.
3) The atom is now out of the cavity and is excited with 100% certainty.
4) The excited atom now starts decaying and emits a photon. But due to the decay the spectrum is "broad".
5) I can now detect the photon with a slightly different energy? At what step did extra energy get in or get out?I'm missing something. I've asked it to people before, but I never got a good answer. (or I didn't get it).
Thanks!