  Using the underlying su(2) algebra of the Jaynes-Cummings Model (JCM), we
construct a time dependent interaction term that allows analytical solution for
even off-resonance conditions. Exact solutions for the time evolution of any
state has been found. The effect of detuning on the Rabi oscillations and the
collapse and revival of inversion is indicated. It is also shown that at
resonance, the time dependent JCM is analytically solvable for an arbitrary
interaction term.

Quantum Physics