Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Probability of one-photon loss from a cavity

  1. Oct 8, 2016 #1
    Why is the probability of one-photon loss from a cavity in the time interval ##[t, t+\delta t]## is:
    ##\kappa \delta t\langle \psi(t)| \hat{a}^{\dagger}\hat{a} |\psi(t)\rangle##
    where ##\kappa## is the decay rate. It looks like the Fermi Golden rule but it's not exactly it.
  2. jcsd
  3. Oct 9, 2016 #2


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    Do you have a source for this equation? I guess, it's indeed an application of Fermi's golden rule, but from which model Lagrangian/Hamiltonian?
  4. Oct 10, 2016 #3
    For example here: https://books.google.co.uk/books?id=UnTNBQAAQBAJ&pg=PA37&lpg=PA37&dq=cavity+probability+of+emitting+a+photon&source=bl&ots=ivGtnIlmCz&sig=6qJjKian0MrATDeRY9nt4pDA1xQ&hl=el&sa=X&ved=0ahUKEwiPlq7C9LvPAhVIdR4KHejJD3EQ6AEIODAE#v=onepage&q=cavity probability of emitting a photon&f=false

    page 37, equaiton (2.41).

    They assume that this probability is proportional to the expectation value of the number of photon in the cavity. Based on what is this assumption?
    Also, is ##\kappa## defined as the average number of photons that leak out of cavity per unit of time or as the probability of loosing a photon per unit of time?
  5. Oct 10, 2016 #4


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    It's the number of photons. It's a reasonable assumption that it is the more probable to loose a photon the more photons are there. It's like the radioactive-decay law: The rate at which a nucleus decays is proportional to the number of nuclei present. This leads to the usual exponential decay. Quantum-theoretically that's a bit more tricky. Strictly speaking the exponential decay law cannot be exactly right (due to unitarity of time evolution). See, e.g., the textbook by Sakurai, Modern Quantum Mechanics, 2nd ed., Addison-Wesley.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Probability of one-photon loss from a cavity
  1. Photon in cavity (Replies: 4)