# What is Rabi frequency?

1. Aug 16, 2009

### KFC

I am trying to find out the physical significance of Rabi frequency in wiki and some text, but it still hard for me to understand it. So what does Rabi "frequency" really refer to? From the point of physical view (not from dimension), why call it "frequency"?

2. Aug 17, 2009

### Cthugha

The term Rabi frequency occurs in several branches of physics, but its most common occurence is in the realm of two-level systems. So imagine some two-level system, which can be properly initialized (a two-level-atom, an electron state and a trion state inside a singly charged quantum dot or whatever).

Now you initialize the system in the upper state and drive the transition resonantly using a resonant laser pulse or something like that. Usually you will see just some random superposition of stimulated emission and some spontaneous emission. But if you are in the strong coupling regime - so the coupling strength is large compared to all mechanisms causing decoherence like spontaneous emission or nonradiative recombination- you will see some coherent energy transfer between the light field and the two-level system. If the two-level system is initially in the excited state, you will have stimulated emission, the system will go to the ground state, you will have stimulated absorption, the system will go to the excited state, you will have stimulated emission again and so on and so on. Therefore the occupation expectation values of the two levels will also oscillate periodically. The frequency of the periodic exchange of energy and of the oscillation of the occupation probabilities is the Rabi frequency.

3. Aug 17, 2009

### KFC

So what's the typical value for Rabi frequency?

4. Aug 17, 2009

### f95toli

It can be anything; the typical frequency depends on what type of system it is.

5. Aug 17, 2009

### Cthugha

This is diffivult to say. The exact value depends on the system, the dipole moment of the transition and (for optical transitions) the amplitude of your optical pulse. If you use a pump pulse with higher amplitude, the Rabi frequency will increase, too. This makes it very complicated to determine the frequency experimentally. So the common experimental way to show Rabi oscillations is to measure the time resolved differential transmission in a pump-probe-setup, where the fixed time delay between pump and probe pulse is longer than the pump pulse width, but shorter than the dephasing time.

If one now increases the pump pulse amplitude, the corresponding differential transmission shows oscillations depending on the pump pulse area. Here the pump puls area does not mean some spatial extent, but is measured in radians. So if there is no pump present, the system will not be in an excited state giving a pulse area of 0. Increasing the pump amplitude, at some point you will have a fully excited system at your chosen probe delay, indicating a pump pulse area of pi. Further increasing the pump amplitude will again deexcite the system at your chosen probe delay. So there will again be a minimum in the differential transmission at a pump pulse area of 2 pi. And so on and so on.

See for example Phys. Rev. Lett. 87, 133603 (2001) by Stievater et al. for a more detailed description of what pulse area is.