Thus a large fraction of the radiation is emitted (and reabsorbed) without a large energy shift.
(Remember that the crystal may have 10^23 atoms in it and that is a large number.
The M ̈ossbauer effect has be used to measure the gravitational red shift on earth. The red shift
was compensated by moving a detector, made from the same material as the emitter, at a velocity
(should be equal to the free fall velocity). The blue shift was measured to be
∆ω
ω= (5. 13 ± 0 .51)× 10 −^15
when 4. 92 × 10 −^15 was expected based upon the general principle of equivalence.
29.12.2LASERs
Light Amplification through Stimulated Emission of Radiation is the phenomenon with the acronym
LASER. As the name would indicate, the LASER uses stimulated emission to genrate an intense
pulse of light. Our equations show that the decay rate of a state byemission of a photon is propor-
tional to the number (plus one) of photons in the field (with the samewave-number as the photon
to be emitted).
A~(~r,t) =[
2 π ̄hc^2
ωV]^12
ˆǫ(√
Nei(
~k·~r−ωt)
+√
N+ 1e−i(
~k·~r−ωt))Here “plus one” is not really important since the number of photons isvery large.
Lets assume the material we wish to use is in a cavity. Assume this material has an excited state
that can decay by the emission of a photon to the ground state. Innormal equilibrium, there will
be many more atoms in the ground state and transitions from one state to the other will be in
equilibrium and black body radiation will exist in the cavity. We need to circumvent equilibrium to
make the LASER work. To cause many more photons to be emitted than are reabsorbed a LASER
is designed to produce apoplation inversion. That is, we find a way to put many more atoms in
the excited state than would be the case in equilibrium.
If this population inversion is achieved, the emission from one atom willincrease the emission rate
from the other atoms and that emission will stimulate more. In a pulsed laser, the population of the
excited state will become depleted and the light pulse will end until theinversion can be achieved
again. If the population of the excited state can be continuously pumped up, then the LASER can
run continously.
This optical pumping to achieve a population inversion can be done in a number of ways. For
example, a Helium-Neon LASER has a mixture of the two gasses. If a high voltage is applied and an
electric current flows through the gasses, both atoms can be excited. It turns out that the first and
second excited states of Helium have almost the same excitation energy as the 4s and 5s excitations
of Neon. The Helium states can’t make an E1 transition so they are likely to excite a Neon atom
instead. An excited Helium atom can de-excite in a collision with a Neon atom, putting the Neon
in a highly excited state. Now there is a population inversion in the Neon. The Neon decays more
quickly so its de-excitation is dominated by photon emission.