Rabi problem

The Rabi problem concerns the response of an atom to an applied harmonic electric field, with an applied frequency very close to the atom's natural frequency. It provides a simple and generally solvable example of light-atom interactions.

In the classical approach, the Rabi problem can be represented by the solution to the driven, damped harmonic oscillator with the electric part of the Lorentz force as the driving term:

where it has been assumed that the atom can be treated as a charged particle (of charge e) oscillating about its equilibrium position around a neutral atom. Here, x_a is its instantaneous magnitude of oscillation, ${\displaystyle \omega _{a}}$ its natural oscillation frequency, and ${\displaystyle \tau _{0}}$ its natural lifetime:

which has been calculated based on the dipole oscillator's energy loss from electromagnetic radiation.

To apply this to the Rabi problem, one assumes that the electric field E is oscillatory in time and constant in space:

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