Thermodynamics, Statistical Physics, and Quantum Mechanics

THERMODYNAMICS AND STATISTICAL PHYSICS 39

4.80 Einstein Coefficients (Stony Brook)

You have two-state atoms in a thermal radiation field at temperature T.

The following three processes take place:

1) Atoms can be promoted from state 1 to state 2 by absorption of a

photonaccording to

2) Atoms can decay from state 2 to state 1 by spontaneous emission

according to

3) Atoms can decay from state 2 to state 1 by stimulated emission ac-

cording to

The populations and are in thermal equilibrium, and the radiation

density is

a)

b)

c)

What is the ratio

Calculate the ratios of coefficients and

From theratio ofstimulated to spontaneous emission, how does the

pump power scale with wavelength when you try to make short-

wavelength lasers?

4.81 Atomic Paramagnetism (Rutgers, Boston)

Consider a collection of N identical noninteracting atoms, each of which
has total angular momentumJ. The system is in thermal equilibrium at
temperature and is in the presence of an applied magnetic field
The magnetic dipole moment associated with each atom is given by
where is the gyromagnetic ratio and is the Bohrmagneton.
Assume the system is sufficiently dilute so that the local magneticfield at
each atom may be taken as the applied magneticfield.

a) For a typical atom in this system,list thepossible values of the

magnetic moment along the magnetic field, and the corresponding

magneticenergyassociatedwith each state.