1. H’(t)=E-M field
D  = - fi
Transition dipole moment

2. Probability of being in state f increases at long times
Probability of being in state f depends on detuning (amount off-resonance)
f(t,Dw) height increases as t2
Width scales as 1/t
Therefore the area is proportional to t and the probability of being in state f increases linearly with time.

3. In the limit of long time this function is approximately a delta function
(- sign absorption)
Fermi’s Golden Rule

4. To this point have not included the intensity of the light field as a function of frequency.
Assume the source is not monochromatic but rather has a frequency distribution that varies slowly compared to f(t,Dn).
And thus:

5. For discussion next week
For discussion next week. Put some numbers to this equation for the specific case of transitions from the ground state to the first rotational level, first vibrational level and first electronic state of CO.

6. Stimulated Emission
dE removes

8. See section 4.5 for QM derivation

9. Properties
Stimulated emission appears in the same cavity mode as the incident light that produced it and is emitted in phase.
Spontaneous emission is independent of incident beam and can be in any direction and phase.

10. For discussion next Friday (2/15).
Consider ISM: Other than H2, CO is the most abundant molecule. If CO is 1molecule/m3 how many km are required to have a detectable signal? Assume “detectable” is 3 times the background cosmic blackbody radiation (3K) or the blackbody of a LN2 cooled detector (77K)?

11. Spontaneous emission in Hydrogen:
Matrix element needed is <1s|m|2p>
Also need to average over random orientations of the atomic transition dipoles with respect to observing angle: 1/3
Plugging in the numbers gives: Wif=620x106 s-1
or a lifetime of 1.6 ns

12. Which is a more accurate way to go about measuring transition moments?
I/I0 t

13. -0.85 eV
-1.51eV
-3.4 eV
-13.6 eV
n3~.3
n3~4
n3~1000