# Rabi Oscillations

Author: the photonics expert Dr. Rüdiger Paschotta

Definition: oscillations of level populations (or quantum mechanical probability amplitudes) under the influence of an incident light field

If light interacts with a two-level system (e.g. an atom or ion with a ground state and an excited state), according to quantum optics this can lead to a periodic exchange of energy between the light field and the two-level system. Such oscillations, which are called *Rabi oscillations* (with reference to the Nobel Prize winner Isidor Isaac Rabi), are associated with oscillations of the quantum mechanical amplitudes and with expectation values of level populations and photon numbers. They can be modeled using the Bloch vector formalism. A competing process, which can prevent these oscillations, is spontaneous emission.

Note that Rabi oscillations involve continuous changes of quantum-mechanical amplitudes, rather than discrete processes of absorption and stimulated emission of photons. The oscillating amplitudes in the end indicate the probability of finding the atom in a certain state when applying a measurement – but such a measurement is not part of the situation leading to the Rabi oscillations.

A *Rabi cycle* corresponds to one period of a Rabi oscillation.

The angular frequency of the Rabi oscillations (<$2\pi$> times the number of Rabi cycles per second) is called the *Rabi frequency*. It is <$2\pi$> times the product of the transition dipole moment of the optical transition and the electric field amplitude divided by Planck's constant. A generalized Rabi frequency can be defined for a light field which is detuned against the transition; it is larger than the ordinary Rabi frequency.

When a solid-state gain medium is optically pumped, Rabi oscillations usually cannot be observed, since the upper and lower states actually consist of Stark level manifolds (containing multiple sub-levels) and coherence is quickly destroyed by phonons. Further, inhomogeneous broadening may occur, and the optical intensities are usually not spatially uniform.

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2023-05-22

Just checking if I understood correctly: Rabi oscillations are

an effect of stimulated emission? Is there any way to explain physically why this decrease in probability to find the system in the excited state happens?notAnother question is about the exponential decay of the probability due to spontaneous emission: Surely at some point the probability starts to increase again, right? After which time is this the case?

The author's answer:

No, it is not that absorption and stimulated emission processes would have nothing to do with Rabi oscillations. Only, in the context of Rabi oscillations we consider the temporal evolution of quantum-mechanical amplitudes

withoutany measurement taking place, which would lead to a collapse of the quantum superposition states.If there is no driving field, we have only spontaneous emission, and the quantum amplitude of the excited state drops exponentially – it will not rise again later on.