# A Dispersive Regime in Jaynes-Cummings Model

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1. Mar 8, 2016

### Raptor112

From the reading I have done:

In the presence of a drive, which is described by an addition term in the Jaynes-Cummings Hamiltonian, the Hamiltonian cannot be solved analytically. The dynamics of the system become non-trivial, with the behaviour depending on the specic parameter regime. So, the bad cavity limit is where the cavity relaxation $\kappa$ is much greater than the dephasing rates of the qubit $\gamma$. A system that obeys both the dispersive regime and bad cavity limit allows for a hierarchical scale to be established:

$\gamma << \kappa <<\frac{g^2}{\Delta}<< \Delta << \omega_c$

where $\Delta$ is the difference in the cavity and field frequency and g is the coupling between the qubit and cavity.

So finally my question: What do $\kappa$ and $\gamma$ actually represent? Are the rate at which caivty/qubit emit photons?

2. Mar 8, 2016

### f95toli

They are the decay rates of the qubit and the cavity. For the qubit this would be 1/T1 and for the cavity omega_r/Q, where omega_r is the centre frequency.
So, yes it would be the rate of spontaneous photon emission if you were working with Fock states.
Note, however, that the decay rate of the cavity is just another way of specifying its quality. Hence, you can use it even for purely "classical" states as well in which case it is just the rate of energy loss.

3. Mar 8, 2016

### Raptor112

So is this why the dispersive regime and bad cavity limit results in a high qubit fidelity read out?