Open both JCApp and QEDApp. Set the field in JCApp to be a Fock state with **n=0**. Minimize QEDApp. Run JCApp and observe how the lower state changes. Initially the atom was in the upper state, but then the system begins to Rabi oscillate as it would in BlochApp if no damping were present. At first, this result may seem quite mundane---it is not. The field that was initialized is the vacuum state which corresponds to an electromagnetic field which has no probability of any photons existing in the field. The atom is somehow coerced by the vacuum field to emit a quantum of radiation. This effect is spontaneous emission for a single field mode. In order to model spontaneous emission in BlochApp a phenomological constant had to be added to the derived density matrix. In the Jaynes--Cummings model, this effect is merely a result of the quantum mechanics. These oscillations are often called vacuum fluctuations.

Spontaneous emission is an effect caused by the coupling of the atom to the vacuum state. Analogously, stimulated emission is caused by the coupling of the atom to the other states of the field. These effects are quantum mechanically equivalent. Yet, the semiclassical theory treats them like apples and oranges. This result is similar to the Gibbs paradox in statistical mechanics. If the Sakur--Tetrode equation for an ideal gas is derived without quantum mechanics, then an extra must be utilized at one point in the derivation. This term accounts for the fact that the particles in an ideal gas are identical. When a quantum mechanical treatment of the same problem is used, the Sakur--Tetrode equation follows directly from the theory.

Wed May 17 14:34:24 EDT 1995