Are Rabi oscillations a pure quantum process?

Question

Rabi oscillations are commonly known as the oscillations in time of the occupation probability of a quantum two-level system under the action of a coupling interaction between the two-levels.

Nevertheless, I think that Rabi oscillations do not really probe quantum light-matter effects until discrete Rabi frequencies are observed, as was done e.g. in

M. Brune, F. Schmidt-Kaler, A. Maali, J. Dreyer, E. Hagley, J.-M. Raimond & S. Haroche. Quantum Rabi Oscillation: A Direct Test of Field Quantization in a Cavity. Physical Review Letters 76 1800–1803 (1996). (free to read article)

So my question follows: Are Rabi oscillations a probe of the quantum-ness or not? (by quantum-ness I here mean a kind of particle-wave duality) In particular: are similar effects observable between two oscillating modes? To understand a bit more this last question, it is clear that the discreteness of the Rabi frequencies are a probe of the particle-wave duality. So the question can be recast as: What if I forget the two-levels system? For instance, what happens if I replace the two-levels system with a quantum harmonic oscillator, and then take the classical limit for this oscillator?

Answer 1

Classical oscillators can display Rabi oscillations. For example, if you take two identical pendulums and (weakly) couple them, then the energy is transferred back and forth. These are Rabi-oscillations.

If the oscillators have different frequencies, $f_1$, $f_2$, and the coupling force is modulated at the difference frequency $f_1 - f_2$, you also get Rabi-oscillations. If you accidentally modulate at the sum frequency, $f_1+f_2$, then both amplitudes blow up exponentially (which makes me wonder: Is there a quantum-mechanical analogy for this blow-up?).

These are well-known properties of classical oscillators. They get re-discovered every few years. To me, Rabi-oscillations and their cousin, the adiabatic rapid passage, are purely classical phenomenona. In quantum physics, we model each energy level as a perfectly harmonic oscillator with a frequency given by the energy, and an amplitude/phase given by the quantum amplitude of that level. If we use a suitable coupling force, quantum systems will therefore exhibit Rabi oscillations. The coupling force can realized by, for example, a modulated electromagnetic field, such as light with the right frequency.

Answer 2

Rabi oscillations can probe the "quantumness" of the electromagnetic field. Quantized fields interacting with two-level systems can lead to collapses and revivals in Rabi oscillations. This is a pure quantum effect. Any textbook on quantum optics will explain this phenomenon. This is how they look like [from Quantum Optics, by M. Scully and M. Zubairy]