# Rabi cycle

In physics, the Rabi cycle is the cyclic behaviour of a two-state quantum system in the presence of an oscillatory driving field. A two-state system has two possible states, and if they are not degenerate energy levels the system can become "excited" when it absorbs a quantum of energy.

The effect is important in quantum optics, nuclear magnetic resonance and quantum computing. The term is named in honor of Isidor Isaac Rabi.

When an atom (or some other two-level system) is illuminated by a coherent beam of photons, it will cyclically absorb photons and re-emit them by stimulated emission. One such cycle is called a Rabi cycle and the inverse of its duration the Rabi frequency of the photon beam.

This mechanism is fundamental to quantum optics. It can be modeled using the Jaynes-Cummings model and the Bloch vector formalism.

For example, for a two-state atom (an atom in which an electron can either be in the excited or ground state) in an electromagnetic field with frequency tuned to the excitation energy, the probability of finding the atom in the excited state is found from the Bloch equations to be:

$|c_b(t)|^2 \propto \sin^2 (\omega t/2)$

where $\omega$ is the Rabi frequency.

More generally, one can consider a system where the two levels under consideration are not energy eigenstates. Therefore if the system is initialized in one of these levels, time evolution will make the population of each of the levels oscillate with some characteristic frequency, whose angular frequency[1] is also known as the Rabi frequency.