Page 354 - Electrical Properties of Materials

336 Lasers

What do we need to produce an ordinary laser? We need to confine the
photons by a resonator and ensure that they all have the same energy. In a
matter wave laser the atoms need to be confined to a finite space, and all of
them must be in the same state. If many atoms are to be collected in the same
state, they must be bosons, as we mentioned briefly in Chapter 6.
How can we confine the atoms? If they have a magnetic moment, they can
be trapped by magnetic fields. The simplest example of a trap is a magnetic
field produced by two parallel coils carrying opposite current, which yield zero
magnetic field in the centre. An atom moving away from the centre will be
turned back.
How can we have a sufficient number of atoms in the ground state? By
cooling the assembly of atoms, we can make more of them remain in the
ground state. The lower the temperature, the larger the number of particles
in the ground state. When the density is sufficiently large and the temperat-
ure is sufficiently low, we have a so-called Bose–Einstein condensation, which
means that most of the atoms are in their ground state.
How do we know if we have achieved a Bose–Einstein condensation? In the
same manner as we know whether we have coherent electromagnetic radiation,
we derive the two beams from a laser and make them interfere with each other.
Coherence is indicated by the appearance of an interference pattern. Can we
do the same thing with an atom laser? We can.
In a particular experiment, sodium atoms were trapped in a double well:
there were two separate condensates, each one containing about five million
atoms. The trap was then suddenly removed, and the atom clouds were allowed
to fall for 40 ms. They were then illuminated by a probe beam from an ordinary
laser. The absorption of the light as a function of space showed an interference
pattern in which the fringes were about 15 μm apart.
This subject, you have to realize, is still in its infancy. Will it be useful when
it reaches adulthood? Nobody can tell. Remember that nobody knew what to
do with ordinary lasers when they first appeared on the scene.

Exercises
12.1. Calculate (a) the ratio of the Einstein coefficients A/B these points appear to change their brightness as the eye is
and (b) the ratio of spontaneous transitions to stimulated moved?
transitions for 12.3. An atomic hydrogen flame is at an average temperat-
ure of 3500 K. Assuming that all the gas within the flame
(i) λ = 693 nm, T = 300 K is in thermal equilibrium, determine the relative number of
(ii) λ = 1.5 cm, T =4 K electrons excited into the state n =2.
If the flame contains 10 21 atoms with a mean lifetime of
Take the index of refraction to be equal to 1. –8
10 s, what is the total radiated power from transitions to the
At what frequency will the rate of spontaneous trans-
ground state? Is the radiation in the visible range?
itions be equal with the rate of stimulated transitions at room –1
temperature? 12.4. The gain constant γ is found to be equal to 0.04 cm for
a ruby crystal lasing at λ = 693 nm. How large is the inverted
11
–2
12.2. What causes the laser beam on a screen to appear as if population if the linewidth is 2 × 10 Hz, t spont =3 × 10 s,
it consisted of a large number of bright points, and why do and n = 1.77.