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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?

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    $\begingroup$ IMO, this is very interesting question but I find your last paragraph very confusion (despite knowing a thing or two about atom-light interaction). What is your criterion of "quantum-ness"? Also, define Rabi oscillations (for Brune & Co there is back-and-force oscillation an atom and a field; more conventionally it is between two discrete states within the same atom). $\endgroup$
    – Slaviks
    Commented Sep 4, 2013 at 12:48
  • $\begingroup$ Your question is not quite clear to me. Why exactly do you think that Rabi oscillations do not probe 'quantumness', and in what regime? Do you mean the quantum nature of light or of the driven system? On your last paragraph, what are you thinking your 'two oscillating modes' would be? Do you propose to completely eliminate the TLS? or replace it with something else? $\endgroup$ Commented Sep 4, 2013 at 15:56
  • $\begingroup$ @Slaviks Thanks for pointing out I was unclear. I've tried to be more explicit. Please let me know if it's still unclear. $\endgroup$
    – FraSchelle
    Commented Sep 6, 2013 at 11:28
  • $\begingroup$ @EmilioPisanty Thanks for your comment. I was indeed unclear. I would like to know (for instance) what would be the effect of a laser shining on a quantum harmonic oscillator for instance. I think I should obtain Rabi-like oscillations (in the sense: they will be oscillations of the occupation probability, but they could be much more complex than a simple sinus), and I wonder if it probes the discrete levels of the quantum oscillator, and/or the quantum nature of the light field. In the Haroche, Brune, Raimond & co. experiment, they probe only the quantum nature of light. $\endgroup$
    – FraSchelle
    Commented Sep 6, 2013 at 11:35
  • $\begingroup$ ... But I'm always confused with this. For me, neither the atom nor the light has a quantum behaviour, only the interaction behaves quantum-mechanically. Say differently, I don't think photon is an electromagnetic excitation particle, rather a photon is the energy-exchange between matter and light. But this is a rather semantic issue, not of much interest I guess. Please let me know if I'm still unclear. $\endgroup$
    – FraSchelle
    Commented Sep 6, 2013 at 11:41

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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] Collapse and revivals of Rabi oscillations

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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.

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