# Dephasiing in cavity QED

1. Oct 13, 2012

### Niles

Hi

In cQED and the Jaynes-Cummings model, three parameters are usually introduced which describe the atom-cavity system: The radiative lifetime γ, the cavity linewidth κ and the pure dephasing rate 1/T2. However I am not that familiar with the latter parameter.

Basically I guess it describes how fast the off-diagonal elements of the density matrix decay. But how do the coherences physically enter in the interaction between an atom and light? What is it that they do?

Best,
Niles.

2. Oct 14, 2012

### f95toli

Before I try to answer your question. Do you understand what the "normal" T1 and T2=1/2T1 do?

The "pure" dephasing is just an extra term that takes into account dephasing that does not come about due to the energy relaxation (T1).

3. Oct 14, 2012

### Niles

Hi

Thanks for replying. My current understanding is that T1 is the radiative lifetime of the excited state and that T2 is the "lifetime" of the coherences when they decay only due to the radiative lifetime, i.e. there are no collisions for example. Is this more or less correct?

4. Oct 16, 2012

### f95toli

Yes, more or less.

T1 is essentially connected to how long the system will oscilllate once initialized in an excited state; i.e. Rabi oscillations.
T2 is tells you how long it takes for the phase to become "randomized" (making he off-diaganal elements go to zero) and is measured using Ramsey spectroscopy.
Pure dephasing is just a term that descibes any interaction that causes dephasing that is NOT connected to energy loss (T1), usually some sort of inhomogeneity or fluctuating background (this is not the strict mathematical definition, pure dephasing is something along the line of dephasing due to fluctuations parallell to the bath, but in reality this corresponds to what I just described).

When it comes to what the coherences "do" that is a bit difficult to answer. Remember that you can't separate the atom and the light; if you describe it using a J-C hamiltonian it all becomes one system with the energy continously being transfered between the atom and one (in he simplest case) photon. This process goes on forever if T1 and T2 are infinitly long.
You can then add Lindblad operators to your J-C Hamiltonian to include the effects of relaxation and dephasing.

Now, the fact that this is one system means we can describe in on a Bloch sphere and there it is a bit easier to see the effects. T1 just corresponds to the arrow becoming "shorter" whereas dephasing effects are parallell deviations to the free precession; the latter effect means that the phase eventually loses all "memory" and the oscillations will stop.

Note that in real system dephasing is a bit more complicated. Some of the effects can be mitigated using refocusing techniques (standard in NMR/MRI) and you can also have effects such as revivals.

.

5. Oct 16, 2012

### Niles

Thanks for your detailed answer. I'll have to read more about this, specifically how the Bloch-vector is affected. But you gave me a good push forward, thanks for that. BTW, isn't it correct that your profile picture are the modes of a coupled atom-cavity system? So if I scan from the lower right corner to the upper left I just get the normal modes, distanced by twice the vacuum Rabi splitting?

Best,
Niles.

6. Oct 17, 2012

### f95toli

Sort of.
It is the frequency response of a resonator coupled to a 2-level system that can be tuned using a magnetic field. It is from a paper I published a few years ago where I was doing some numerical simulations. It is nothing sophisticated, I just solved the J-C Hamiltonian with added Lindblad operators to account for relaxation and dephasing.

Btw. I don't work in atomic physics, so I am not an expert in cavity-QED; my field is (mainly) superconducing devices.