Title: PG lectures 2004-05 Spontaneous emission
1PG lectures 2004-05 Spontaneous emission
2Outline
Lectures 1-2 Introduction What is it?
Why does it happen? Deriving the A
coefficient. Full quantum description 3-4
Modifying the environment. Two atoms
superradiance A mirror Cavity QED.
3Oscillating charge
2p(m1) to 1s
2p(m1) to 1s
2p(m0) to 1s
4Dipolar radiation
2p(m0) to 1s
2p(m1) to 1s
5Spontaneous emission what do the greats have to
say?
I understand that light is emitted when an atom
decays from an excited state to a lower energy
state. Thats right And light consists of
particles called photons Yes So the photon
particle must be inside the atom when it is in
the excited state. Well no. Well how do you
explain that the photon comes out of the atom
when it was not there in the first place. Im
sorry. I dont know I cant explain it to you.
Dad Feynman Dad Feynman Dad Feynman Dad Pau
se Feynman
(Feynman, Physics Teacher 1969)
The light quanta has the peculiarity that it
apparently ceases to exist when it is in one of
its stationary states, namely the zero
state.When a light quanta is absorbed it is said
to jump into this zero state and when one is
emitted it can be considered to jump from the
zero state to one in which it is physically in
evidence, so that it appears to have been
created. Since there is no limit to the number of
light quanta that may be created in this way we
must suppose that there are an infinite number of
light quanta in the zero state. (Dirac 1927)
6What is this zero state? Vacuum energy.
Second quantisation of the electromagnetic
field see Loudon The quantum theory of light pp.
130-143
The idea of a photon is most easily expressed for
an EM field inside a perfectly reflecting
cavity. Loudon p. 1
creation
One mode of EM field
k
destruction
l1,2 polarisation
a
a
n photons
Vacuum state
7Quantum theory of spontaneous emission
University of Durham
8Statement of the problem
- Interpret spontaneous emission as
- transition induced by the vacuum field.
- (a) only accounts for half the spontaneous
decay rate - (b) vacuum fluctuations alone also lead to the
- wrong sign of the electron spin anomaly g-2
- Solution vacuum fluctuations self-reaction
- (the interaction of an electron with its own
field) - both contribute to observable processes.
- However, their respective contributions cannot
- be uniquely defined.
- 4. A matter of interpretation!
9Outline
- Semi-classical Fermis golden rule
- vacuum only accounts for half the decay rate.
- QED Radiative reaction or self reaction
- (electromagentic mass)
- Decay rate and level shifts (Lamb shift)
- due to radiative reaction
- Vacuum fluctuations radiative reaction
- excited states decay at a rate G
- lowest energy state does not decay
P. W. Milonni, The quantum vacuum, (Acad. Press,
1994). P. W. Milonni, Why spontaneous emission?
Am. J. Phys. 52, 340 (1984).
102-level time dependent perturbation theory
where
electric dipole approximation